How hadron collider experiments contributed to the development of QCD: from hard-scattering to the perfect liquid
M. J. Tannenbaum
hep-ex nucl-ex







 


Physics Department, Brookhaven National Laboratory Upton, NY 11973-5000 USA  

A revolution in elementary particle physics occurred during the period from the ICHEP1968 to the ICHEP1982 with the advent of the parton model from discoveries in Deeply Inelastic electron-proton Scattering at SLAC, neutrino experiments, hard-scattering observed in p+p collisions at the CERN ISR, the development of ,  the discovery of the J/Ψ at BNL and SLAC and the clear observation of high transverse momentum jets at the CERN SPS p̅+p collider. These and other discoveries in this period led to the acceptance of  as the theory of the strong interactions. The desire to understand nuclear physics at high density such as in neutron stars led to the application of  to this problem and to the prediction of a Quark-Gluon Plasma () in nuclei at high energy density and temperatures. This  eventually led to the construction of the Relativistic Heavy Ion Collider (RHIC) at BNL to observe superdense nuclear matter in the laboratory. This article discusses how experimental methods and results which confirmed  at the first hadron collider, the CERN ISR, played an important role in experiments at the first heavy ion collider, RHIC, leading to the discovery of the  as a perfect liquid as well as discoveries at RHIC and the LHC which continue to the present day.

How hadron collider experiments contributed to the development of :
from hard-scattering to the perfect liquid
    M. J. Tannenbaummjt@bnl.gov
    December 30, 2023
==============================================================================================================



§ INTRODUCTION


The beginning of the revolution in understanding the strong interactions of elementary particles took place in the period from the 14th International Conference on High Energy Physics in Vienna, Austria in 1968 (ICHEP1968) to the 16th ICHEP at Fermilab & Chicago in 1972. 


 §.§ ICHEP1968

Ironically it was a result from Deeply Inelastic Scattering (DIS) that started it. This was presented at the end of Pief Panofsky's rapporteur talk in the Electromagnetic Interactions - Experimental session at ICHEP1968 <cit.>. The preliminary results from the SLAC-MIT electron+proton scattering experiment showed two very striking features, the first in the structure function and the second in the ratio of the inelastic to elastic scattering cross sections.

The inelastic scattering cross section for the case when only the outgoing electron is detected is given by the formula <cit.>

    d^2 σ/dQ^2 dν=4πα^2/Q^4[ W_2(Q^2,ν)( 1-ν/E-Q^2/4E^2) + 2 W_1(Q^2,ν) Q^2/4E^2]

where W_2(Q^2,ν) and W_1(Q^2,ν) are structure functions which each depend on the 4-momentum transfer squared, Q^2, and the energy loss ν=E-E' of the incoming electron with energy E and outgoing energy E'.    
The amazing result was that although one might expect many plots of W_1 and W_2 as functions of various values of Q^2 and ν, they all collapse to one curve 
as suggested by Bjorken <cit.>  

    F_2(Q^2,ν)≡ν W_2(Q^2,ν)=F_2(Q^2/ν)

and thus known as Bjorken Scaling (Fig. <ref>a). 
The other important point made by Panofsky (Fig. <ref>b) <cit.> was that the inelastic  cross sections in the continuum “are very large and decrease much more slowly with Q^2 than the cross-sections for elastic-scattering and the specific resonant states.”


All this led Bjorken (inspired by Feynman) <cit.> to the concept of a proton composed of fundamental pointlike constituents (partons) from which the electrons scatter elastically, incoherently  as viewed in a frame in which the proton has infinite momentum. The free partons each have longitudinal momentum a fraction x of the proton longitudinal momentum 𝐏 where the probability of the parton to have the momentum x𝐏 is given by F_2(x) where x=Q^2/(2Mν) and M is the mass of the proton. As an experimentalist, I had done muon-proton elastic scattering in the more usual frame where the proton is at rest in a liquid hydrogen target. The proton recoils with kinetic energy ν from an elastic scattering by the μ (or e) with 4-momentum-transfer^2 Q^2 where ν=Q^2/(2M) so that it was easy for me to understand that DIS of an e from a proton is just quasi-elastic scattering from a parton at rest with a fracton x of the mass of the proton which would become a fraction of the momentum in any moving frame. 



 §.§ ICHEP1972

Frankly many physicists did not accept the idea that the proton was composed of a gigantic number of massless constituents (partons) <cit.>. In fact we used to call Manny Paschos, who worked at Brookhaven National Laboratory (BNL) in this period, “Manny Parton”. Everything changed for most people at the 16th ICHEP in 1972 at Fermilab and Chicago where three spectacular new results were presented.


  1. Don Perkins in his conclusions <cit.> from new measurements of neutrino scattering cross sections and nucleon structure functions from the CERN Gargamelle collaboration emphasized: i) that both ν and ν̅ cross sections in the range 2-10 GeV are linear with energy, in accord with Bjorken scaling; …iv) In terms of constituent models, the fractional charged (Gell-Mann/Zweig) quark model <cit.> is the only one that fits both the neutrino and electron data (∫ F_2^ν N(x)  dx/∫ F_2^e N(x)  dx=3.4± 0.7≈ 18/5); v) The fractional nucleon 4-momentum carried by gluons is 50% and vi) by antiquark constituents is only ∼ 10% of that carried by quarks and antiquarks together.

  2. The birth of  where Fritzsch and Gell-Mann <cit.> proposed that the three distinct colors assigned to the 3 s-quarks in the  <cit.> to allow them to be in the same state, avoiding simple Fermi statistics by obeying “para-Fermi statistics of rank 3” <cit.>, could also apply to gluons “which could form a color-octet of neutral vector fields obeying the Yang-Mills equations”. 

  3. The discovery of enhanced particle production at large transverse momentum p_T in p+p collisions at the CERN-ISR <cit.> with a power-law shape, which depended on the c.m. energy of the collision, √(s), quite distinct from the exponential e^-6p_T <cit.> spectrum at low p_T<1 GeV/c which depended minimally if at all on √(s) (Fig. <ref>a). This was proof that the partons of DIS interacted strongly with each other rather than simply scatter electromagnetically which must occur in a p+p collision since the partons are charged (Fig. <ref>b) <cit.>. 



This last result changed the focus of many experimenters from the small angle, low transverse momentum region where most particles were produced, typical of fixed-target experiments in beams of high energy particles from an accelerator, to the region of large transverse momentum production, which at the CERN-ISR, the first hadron collider, was perpendicular to the axis of the colliding beams, a perfect location for the study of “high p_T physics”. 

The first proposals of experiments to the ISR in early 1969 had been dominantly in the forward direction so that the ISR committee decided to divide up the angular regions for different experiments at several interaction points to three regions <cit.>: small angles (up to 150 mrad); medium angles (100-300 mrad) and large angles (300 mrad to π/2 rad). The ISR did make discoveries and obtain important results on low p_T “soft” physics <cit.> so one may ask why some of the experiments wanted to run at the largest angles, where few if any particles were expected. The answer is that they were looking for W^±-bosons, the proposed quanta of the weak interactions <cit.>.  





§ WEAK BOSONS FROM STRONG INTERACTIONS? 1960-1970

The completion of the two highest energy (∼ 30 GeV) proton accelerators, the PS at CERN (November 1959) and the AGS at BNL (August 1960) opened the possibility of studying weak interactions at high energy rather than only by radioactive decay. The idea of the left-handed parity violating W^± bosons as the quanta of the weak interactions <cit.> led to proposals for neutrino beams and experiments at the two laboratories <cit.> <cit.> to measure neutrino scattering and to discover the W which would prevent the otherwise point-like neutrino interaction cross sections from increasing monotonically with energy until they violated unitarity <cit.>. Although a Nobel Prize winning discovery, the muon neutrino <cit.>, was made with the first accelerator neutrino experiment, the W was not observed in the early neutrino experiments. Relatively low limits were set for the mass of the W^± (>2 GeV) <cit.><cit.> because of the low energy neutrino beams with small neutrino cross sections and it was realized that p+p collisions might be more favorable for producing the W, e.g p+p→ d+W^+ <cit.> <cit.> <cit.>. This last reference is interesting for three reasons:


  1. There is a comment from A. (Antonino) Zichichi <cit.> on studies at CERN to observe the W^± in p+p collisions, which is so clear that it deserves a verbatim quote:“We would observe the μ's from W-decays. By measuring the angular and momentum distribution at large angles of K and π's, we can predict the corresponding μ-spectrum. We then see if the μ's found at large angles agree with or exceed the expected numbers.” The W^± would be visible above the background as a Jacobian peak at lepton transverse momentum p_T^μ=M_W/2. 

  2. The proposed experiment was never done because the original calculation did not include the p or d form factors and thus the original cross section calculation needed be reduced by a factor of ≈ 3000 <cit.>.  

  3. This is exactly the way that the W was discovered at the CERN Sp̅pS collider 19 years later <cit.> as best shown in Ref. <cit.>.




 §.§ First p+p experiments searching for the W 1965–1970

Experiments overcame the low cross section for large angle muons from the reaction p+p→ W+anything by interacting the entire extracted proton beam in a well-shielded dense target where only muons could penetrate the shielding (beam dump experiments); but no signal was observed <cit.> <cit.>. This brought up the question of how to know how many W bosons should have been produced. Chilton, Saperstein and Shrauner <cit.>  
emphasized the need to know the time-like form factor of the proton to calculate the cross section for producing W's and used the Conserved Vector Current (CVC) theory to estimate the W production cross section by relating it to di-muon production in the reaction p+p→μ^+ + μ^-+anything. Yamaguchi <cit.> then proposed that the time-like form factor could be found by measuring the number of e^+ + e^- or μ^+ + μ^- “massive virtual photons” of the same invariant mass as the W in the p+p reaction but warned that the individual leptons from these electromagnetically produced pairs or from real photons from the decay π^0→γ+γ from the huge number of π^0 produced  might mask the leptons from the W^±. 

These developments led Leon Lederman to propose in August 1967 a more elegant beam dump di-muon experiment at the BNL-AGS (AGS 420) with a thick Uranium target and muon momentum measurement by range in a series of iron and concrete absorbers to search for W bosons, measure the time-like form factor and possibly look for `massive' vector meson production. I had proposed a di-muon experiment in May 1967 (AGS 412) modifying an existing Harvard photoproduction experiment (AGS 310)  so as to search for μ^+ μ^- pairs produced in a Pb target by an incident muon beam—muon tridents. With three muons in the final state, two of them identical, we could test whether muons obeyed Fermi statistics or para-statistics and whether there was a force between muons other than electromagnetic. 

Leon and I had been in contact about μ^+ μ^- pairs via mail over the summer but I decided to stick with my trident experiment which did in fact measure that the muon was a 
Fermion <cit.>. My story then loops around to Panofsky's talk at the ICHEP1968 <cit.>; but the outcome of Leon's di-muon experiment turned out to be one of the pillars of the parton model and just missed a truly revolutionary discovery at the BNL-AGS in 1974, the J/Ψ <cit.>, that cemented the parton model and belief in real quarks, which will be discussed in its chronological order below. 


 §.§ Drell-Yan leads to better W searches and other discoveries
 
Having seen Lederman's preliminary results at an American Physical Society meeting, Sid Drell and Tung-Mow Yan at SLAC <cit.> used the parton model and Bjorken scaling in m^2/s to calculate large mass  timelike virtual-photon i.e. lepton pair production in hadron-hadron `inelastic collisions' by parton-antiparton annihilation, or in today's terminology q̅+q→μ^+ + μ^-. There was also another calculation described in Ref. <cit.> which “employs light-cone commutators and Regge theory, yielding a relative cross section in good agreement with the shape of the experimental distribution.” <cit.> (Fig. <ref>a). 



Lederman was very excited about this agreement with the measured dσ/dm_μμ distribution <cit.>. This was because with the use of the CVC theory <cit.> and Bjorken scaling he could calculate the W cross section at any √(s) and thus predict the sensitivity of his di-muon proposal (E70,  which I initially joined <cit.>) at the newly opening Fermilab (Fig. <ref>b), as well as the di-electron proposal at the CERN ISR <cit.> which became the experiment that discovered the unexpectedly large high p_T π^0 spectrum announced at ICHEP1972 <cit.>. 
	
The high p_T discovery represented totally new physics, strongly interacting partons, which excited me very much. I resigned from all my Fermilab proposals, and being on the faculty of the Rockefeller University since 1971 I was able to move to Geneva to be with the Rockefeller group there and continue the work of the CERN-Columbia-Rockefeller (CCR) series of experiments which helped lead to the confirmation of   as the theory of the strong interactions. 

Before returning to the aftermath of the high p_T discovery, a comment from the di-muon measurement paper <cit.> is worth noting. Resonances were one of the original purposes of the experiment stated in the AGS 420 proposal, and were mentioned in the di-muon publication <cit.>: “As seen in both the mass spectrum and the resultant cross section dσ/dm, there is no forcing evidence of any resonant structure” although “Indeed in the mass region near 3.5 GeV/c^2, the observed spectrum may be reproduced by a composite of a resonance and a steeper continuum.” A proposal was actually made in September 1970 (AGS 549) by some younger members of the Lederman group to follow up the resonance possibility; but it never really got off the ground for various reasons.[See Ref. <cit.> for further information about this issue and other issues raised but not discussed in full detail in this article.] As noted above the situation was finally cleared up in November 1974; but there were also many exciting developments in high p_T physics and  from 1971 to 1974.



§ 1971-1973 , ASYMPTOTIC FREEDOM, 𝐱_𝐓 SCALING AND MORE.

Theoretical physicsists were very busy in this period inventing the theory of asymptotic freedom and   
“from a Yang-Mills gauge model based on colored quarks and color octet gluons” <cit.>,<cit.>, <cit.>,  <cit.> A quick summary of asymptotic freedom in   is that the coupling constant obeys the equation <cit.>:

    α_s(Q^2)=12π/(11N_c-2n_f)ln(Q^2/Λ^2)=12π/25ln(Q^2/Λ^2)
 
for N_c=3 colors and, as will turn out, n_f=4 flavors of quarks. The asymptotic freedom is the decrease  
of α_s(Q^2) as Q^2 increases. 
However, at this point in time asymptotic freedom had minimal if any impact on experimentalists at hadron colliders who were much more interested in the scaling rules and models directly related to the high p_T measurements.  



 §.§ First scaling law 1971

In addition to calculating the cross sections for Coulomb scattering of partons in p+p collisions, BBK <cit.> presented a scaling law for the Coulomb scattering which must exist for charged partons: 

    E d^3σ/dp^3=4πα^2/p_T^4 F
    (-û/ŝ,-t̂/ŝ)

where α=e^2/ħ c is the fine structure constant.  
The two factors are a 1/p_T^4 term, 
characteristic of single photon exchange, and a form factor F that scales, i.e. is only a function of the ratios of the Mandelstam variables, ŝ, t̂ and 
û, the constituent-scattering invariants for scattering of a parton with 4-momentum p_1, on another parton with 4-momentum p_2 to give an outgoing parton pair with p_3 and p_4, i.e. 
p_1+p_2→ p_3 +p_4. 




  §.§.§ Quick kinematics review

      Relativistic kinematics are important for understanding parton-parton scattering and eventually  so I give a brief description here with the Minkowski convention [1]. The  four-vector 
momentum p of a particle with 3-vector momentum P, energy E, in a 
particular rest frame, and invariant mass m, in units where the speed of light c is taken as unity, is denoted such that the 4-th (time) component ≡ i E :

    p=( P, i E)     p=(P_x,P_y,P_z,i E)     p^2=p· p= P· P - E^2=-m^2
       .

The squared modulus of the 4-vector, p^2, is invariant under a Lorentz transformation. 

The Lorentz Invariant quantities to describe two-two scattering kinematics are:      
    
    -ŝ   =   (p_1 + p_2)^2=(p_3 +p_4)^2 
        -t̂   =   (p_1 - p_3)^2=(p_4 - p_2)^2 
        -û   =   (p_1 - p_4)^2=(p_3 - p_2)^2 ŝ+t̂+û   =    m^2_1 + m^2_2 + m^2_3 + m^2_4     .

where ŝ is the parton-parton center of mass energy squared, Q^2=-t̂ is the 4-momentum-transfer-squared in the parton-parton elastic scattering. See appendix <ref> for a full 
discussion of parton-parton scattering kinematics.




 §.§ A better scaling rule, 𝐱_𝐓 scaling, 1972


Inspired by “The recent measurements at CERN ISR of single-particle inclusive scattering at 90^∘ and large transverse momentum” which “revealed several dramatic features of pion inclusive reactions”, Blankenbecler, Brodsky and Gunion (BBG) proposed a new general scaling formula, x_T scaling  <cit.>: 

    E d^3σ/dp^3=1/p_T^n_ eff F(x_T)          x_T≡2 p_T/√(s)   .
 
The power n_ eff is determined by the force-law 
between constituents, the quantum-exchange governing the reaction. Thus, n_ eff=4 for QED or “Vector Gluon Exchange”. However, BBG also included a new model of their own, the “constituent interchange model (CIM)” which predicted that the “proton beam at the ISR behaved like a meson beam of much lower energy” so that high p_T pions were produced by “quark-meson scattering by the exchange of a quark” which gave n_ eff=8 in their model “which does give an excellent account of the data” <cit.>. 


 §.§ The 3 ISR experiments publish, 1973

Three ISR experiments published observation of enhanced high p_T production at 90^∘ in the c.m. system in 1973. The first publication, from the British-Scandinavian ISR Collaboration <cit.> measured non-identified charged hadrons with 1.5≤ p_T≤ 4.5 GeV/c at √(s)=44 and 53 GeV, with the comment “no strong energy dependence is observed for these transverse momenta”. The second publication by the Saclay-Strasbourg group <cit.> used a Cerenkov counter to identify π^± with 3.5≤ p_T≤ 5 GeV/c and noted an e^-2.4 p_T dependence for the invariant cross section in this range “in sharp contrast with the” e^-6 p_T shape of the spectrum below 1 GeV/c. More importantly, they also measured π^0 by conversion of the π^0→γ+γ decay photons in the ISR vacuum pipe but found no single e^± with p_T >3 GeV/c so set a limit for single electron production.   

 

The best and most influential measurement was the final publication of the preliminary data (Fig. <ref>a) shown at ICHEP1972 by the CERN Columbia Rockefeller (CCR) group (Fig. <ref>a) <cit.>. The π^0 were detected in two identical Pb Glass electromagnetic calorimeters  preceded by tracking chambers located at 90^∘ on both sides of the colliding proton beams. The π^0 spectrum was measured in the range 2.4≤ p_T≤ 9 GeV/c at 5 c.m. energies √(s)=23.5,30.6,44.8, 52.7 and 62.4 GeV.  A  very large √(s) dependence was observed for the cross sections, which were all “orders of magnitude” higher than an extrapolation of the “well known exponential”, e^-6 p_⊥. 
The break in the cross-section due to parton-parton electromagnetic scattering anticipated by BBK (Fig. <ref>b) <cit.> was observed but did not agree with magnitude or the form of their Coulomb prediction, E d^3σ/dp^3∝ p_⊥^-4 F(x_T). However, as noted above, the data for all √(s) could be well fit by the BBG x_T scaling form (Eq. <ref>) with the value n_ eff=8.24± 0.05(stat)± 0.70(sys) with F(x_T)=A exp (-bx_T), in agreement with the CIM prediction <cit.>, as illustrated by a plot of the data in the form p_⊥^8.24× E d^3σ/dp^3 (Fig. <ref>b).


§ 1974-1976 A CHARMING PERIOD.
 


 §.§ The discovery of charm particles by direct 𝐞^+/- production at the CERN ISR
 
   
This discovery <cit.> is not generally credited to the ISR, nor even mentioned in many articles about charm physics <cit.> or the ISR <cit.> because charm quarks (c) were only a theoretical idea <cit.>,<cit.> at that time. 
The discovery came about because two of the experiments, CCR <cit.> and Saclay-Strasbourg <cit.>, whose searches for W bosons by detecting single electrons at large p_T were overwhelmed by the high p_T pion discovery, decided to combine. 
 
The combined experiment, the CERN, Columbia, Rockefeller, Saclay (CCRS) collaboration <cit.>, had  two spectrometer arms located around 90^∘ on opposite sides of ISR intersection region I1 with vastly improved e^±, e^+ + e^-, π^± and and π^0 detection as well as outstanding  features to eliminate the background in this difficult measurement:
 


  1. ≥ 10^5 charged hadron rejection from electron identification in gas Cerenkov counters combined with matching the momentum and energy of an electron candidate in the magnetic spectrometer and the PbGlass Electromagnetic Calorimeter; 

  2. precision measurement of π^0→γ +γ and η→γ+γ decays, the predominant background source;[This was better in `arm2' with the CCR PbGlass than in `arm1' with the Saclay 3X_o shower counters.] 

  3. a minimum of material in the aperture to avoid external conversions of photons;

  4. zero magnetic field on the axis to avoid de-correlating conversion pairs; 

  5. rejection of conversions in the vacuum pipe (and small opening angle internal conversions) by requiring single-particle ionization in a hodoscope (H) of scintillation counters close to the vacuum pipe, preceded by a thin track chamber to avoid conversions in the hodoscope; 

  6. precision background determination in the direct-single-e^± signal channel by adding external converter—to distinguish direct single-e^± from e^± from photon conversion.


Preliminary results on “the observation of leptons at large p_T” from 6 experiments were presented at the ICHEP in London in July 1974: one for e^± by CCRS <cit.>, <cit.>; one for both e^± and μ^± channels by Lederman's E70 <cit.> at Fermilab; and four for μ^±: one by Cronin and collaborators, E100 at Fermilab <cit.>; one from Serpukhov <cit.> that had previously claimed that the observed ratio μ/π=2.5× 10^-5 at √(s)=12 GeV was from “electromagnetic production of muon pairs” (later improved <cit.>); and two others that were upper limits on W^±→μ^± +X production. CCRS and the Fermilab experiments all found that the ratio e,μ/π≈ 10^-4. There were no clear ideas about the source of these direct leptons at this time, as well summarized by Lederman at ICHEP1974 <cit.>.
   
Following these results, many experiments that were not originally designed for these measurements, which are extremely difficult, also attempted to look for direct single leptons. This only added confusion to the situation because they mostly found results that were incorrect. A beautiful summary of all these experiments and their difficulty was again presented by Leon Lederman at the 1975 Lepton Photon Symposium <cit.> <cit.> paraphrased succintly as:


  μ^±: Muon detection requires an understanding of the trivial but devastating background of pion and kaon decay.

  e^±: Electron detection suffers from problems of conversions of photons (principally from π^0 decay)in any residual material, from Dalitz pairs, from electron decay of long-lived sources (K, Λ, Σ, ...)

Here I point out that Leon left out η→γ +μ^+ +μ^- (Dalitz) decay as a background for muons. In fact, in 1977 at the Lepton Photon Symposium, Jim Cronin <cit.> made a strong claim in his talk from which I quote the abstract: “A review of direct production of leptons and photons in hadron-hadron collisions is presented. Production of lepton pairs with large mass is well accounted for by the Drell-Yan process. The origin of direct single leptons is principally due to the production of lepton pairs. A dominant source of lepton pairs is at low effective mass, m<600 MeV.” 
I strenuously disagreed with him for the CCRS result in a comment <cit.>. Here is why.


 §.§ The CCRS measurement
 
We made an extraordinary effort to measure all the possible backgrounds, the primary one being external conversions of decay photons or internal conversions (Dalitz pairs) from the decay π^0→γ +e^+ +e^- and η→γ+e^+ +e^-. We did this by adding material of a few percent of a radiation length X_o in addition to the 0.016 X_o thickness of the stainless steel corrugated vacuum pipe (Fig. <ref>a) <cit.>. Measurements were made for the accepted single e^± events and also for selected conversions by requiring double (or more) ionization in the H hodoscope. The data are normalized to the normal running conditions with only the ISR vacuum pipe of 0.016 X_o. 
 



  §.§.§ Dalitz pairs–Internal conversion

 
  The converter method to determine the external and internal conversions, γ→ e^+ + e^- from π^0→γ +γ and η→γ+γ decay is straightforward to understand with a few equations.
  The total Dalitz (internal conversion) probability is <cit.>: 

    δ=Γ_eeγ/Γ_γγ=2α/3π(lnM^2/m_e^2-7/2)=[ 1.19%π^0;   1.62%η ]     ,
 
where M is the mass of the π^0 or η. With additional external converter present
the probability of internal and external conversion per γ is 

    e^-|_γγ = e^+|_γγ 
    =δ_2 2 + t 9 7 X_0≡δ_eff
  
where: t/X_o, is the total external converter thickness in radiation lengths;  δ_2 /2 is the Dalitz (internal conversion) branching ratio per photon 
= 0.6% for π^0→γγ, 0.8% for η→γγ; and the factor 9/7 
comes from the ratio of conversion length to radiation length. 
For π^0 and η decays, the yield extrapolates to zero at the “Dalitz 
point”  -9 14δ_2 ∼ -1%—actually -0.8% for π^0 and 
-1.0% for η—so the method has the added advantage that it depends 
very little on the η/π^0 ratio. In Fig. <ref>a, the extrapolation 
for the e^± from selected conversions (∘) extrapolates nicely to zero at the Dalitz point, indicating a photonic source, while the accepted prompt e^± events (∙)
show only a small decrease from the normal thickness used 
for data-collecting (t/X_o=1.6%) to the Dalitz point: the value at the Dalitz point is the normalized yield of the prompt single e^± with the photonic background subtracted. 

The same method doesn't work at all for the single μ^± which have the `devastating background' from meson decay. Furthermore the  η→γ+μ^+ +μ^- decay which would fit Cronin's description of the source of his single muons is not given correctly by Eq. <ref> when m_μ is substituted for m_e because it is valid only to leading order in m^2/M^2 <cit.>. The correct answer is δ_ημμγ=(0.08±0.01)% <cit.> <cit.>. Furthermore, the converter method can not be used because a radiation length for muons is (m_μ/m_e)^2=42727 times as large as X_o, the radiation length for e^± and γ. In fact, what I used to say in the 1970's is still valid today "all those who try to measure direct leptons become the world's experts on η Dalitz decay” <cit.>.


  §.§.§ A final obstacle, then publication.

The last possible background source was the decay of the vector meson ϕ→ e^+ e^- with the cross section σ_ϕ=1.1σ_π^0. Such copious ϕ production should be easy to detect via the principal decay mode K^+ K^-, so we removed the Cerenkov counter from the trigger in `arm2' and made a short run looking for charged hadron h^+ +h^- pairs with p_T>1.6 GeV/c. We didn't find any and set a limit σ_ϕ=≤ 0.4σ_π^0 to 90% confidence which implied that the possible ϕ contribution was less than 0.25 to 0.5 the observed single e^± signal. The result was that the direct single e^± cross section in the range 1.6<p_T<4.7 GeV/c at √(s)=52.7 GeV is (1.2± 0.2)× 10^-4 that of the π^± cross section (Fig. <ref>b) <cit.>. 
We submitted the publication on 28 October 1974 but of course we had spent the time since the ICHEP in July 1974 trying to find the e^± that was balancing the p_T of the observed e^± spectrum in the opposite spectrometer `arm1', but didn't find any thing. However, we did find out the answer two weeks later with the `November revolution' in particle physics caused by the discovery of a new “heavy particle J with  mass m=3.1 GeV/c^2 and width approximately zero” <cit.> in p+Be collisions at the BNL-AGS (Fig. <ref>a) simultaneously with the same particle except called Ψ in e^+ +e^- → hadrons in the storage ring (SPEAR) at SLAC <cit.>. 


 §.§ Charmonia—the November Revolution that made everybody believe in partons



  §.§.§ First: new proposals, new results
 

CERN went into a frenzy over the J/Ψ discovery <cit.> as did the individual experiments. Within another 2 weeks, just in time for a “second narrow resonance” the Ψ' with m=3.7 GeV/c^2 to be discovered at SLAC <cit.>, two proposals for new e^+ e^- measurements from members of CCRS were submitted to the ISRC. Also in this interval CCRS found the reason why we didn't find anything balancing our single e^± in the opposite spectrometer: a computer bug in `arm1' that rejected  tracks in the entire H hodoscope rather than just near the spaces between counters. In fact in the CCOR proposal <cit.> there were 7 e^+ e^- events shown of which 4 clustered near m_ee=3 GeV/c^2. The issue of why there were two proposals from CCRS members is also interesting. 

In May 1973, the CCR part of CCRS had made a proposal <cit.>[Joined by Oxford in January 1974 (CERN/ISRC/73-13 Add. 2).] for a totally new detector with much larger solid angle than either the original CCR or CCRS experiments, which was approved in March 1974. It consisted of a solenoid magnet with a thin aluminum-stabilized superconducting coil, only 1.0 X_o thick, outside of which were two PbGlass EMcalorimeters, opposite in azimuth, each covering a polar angle θ=± 30^∘ around 90^∘ and azimuthal angle ϕ=± 20^∘ around the median plane. Tracking and momentum measurement of charged particles was accomplished by a set of cylindrical drift chambers inside the solenoid which covered the full azimuth in a polar angle range θ=± 37^∘ around 90^∘.  Ironically, the day that the J/Ψ discovery was announced, November 11, 1974, was the same day that removal of the CCRS experiment from the ISR intersection region I1 began in order to start building the CCOR detector. 

Immediately after the J/Ψ announcement, the CCRS group together with Pierre Darriulat's group started discussing a “mini” experiment to look for the single e^± and e^+ e^- pairs; but quickly couldn't agree. Thus, CCOR <cit.> and the new Darriulat+Saclay group <cit.> quickly submitted new proposals to the ISRC. The CCOR proposal <cit.> was basically the CCR experiment with Cherenkov counters added for e^± identification and triggering, so was orthogonal to the approved CCOR experiment <cit.> and was wisely rejected by the ISRC. The CERN-Saclay proposal, which was basically CCRS with larger acceptance and PbGlass EMcalorimeters in both arms, was approved on December 11 and eventually became the CERN-Saclay-Zurich (CSZ) experiment with a small muon spectrometer added perpendicular to the e^± spectrometers. 



  §.§.§ Then more work, discussions and publications
   
Work continued on looking for more e^+ e^- events in CCRS eventually ending in 11 total events. Meanwhile the rest of the CERN physicists were not idle and a series of Discussion Meetings was held in the CERN auditorium, the most memorable for me being the one on February 21, 1975: “The new particles: what are CERN experimentalists doing?” We in CCRS had the only J/Ψ data and I had collected the events we had found up to that time and submitted a plot to the ISR coordinator, Ugo Amaldi, who gave the ISR presentation. I was sitting in the front row. Carlo Rubbia (my boss when I was a CERN post-doc in 1965-66) was seated in the second row, one seat to my left. When Ugo showed the plot (Fig. <ref>b), Carlo got very excited and pointed at the event at 3.7 GeV/c^2 and asked loudly repeatedly “What is that event at 3.7, what is that event at 3.7?” We couldn't really claim that it was the Ψ', so I turned to Carlo and said, “Oh Carlo, you are the expert in one-event experiments.” It was amazing: laughter filled the auditorium, moving up the rows in a wave until everybody in the audience (except Carlo) was laughing—very memorable! The CCRS result was submitted for publication on 22 April 1975 <cit.> (Fig. <ref>c). 


  §.§.§ OK so we found the J/Ψ (a bit late): was it the source of the single e^±?

    In addition to the observation of the `new particle' there was an important issue to address: was the J/Ψ the source of the single e^±? The answer was NO as shown in the final CCRS paper on “Electrons at the ISR” (Fig. <ref>b) <cit.> and also shown for charged hadron decays in Lederman's talk <cit.> (Fig. <ref>a).
     

    Another important issue addressed by CCRS <cit.> was the measurement of the cross section for the reaction:

    p+p→ J(3.1) + X → e^+ + e^- +X
 
with result

    B_ee×dσ/dy (p+p→ J+ X)=(7.5± 2.5)× 10^-33 cm^2
 
averaged over the rapidity acceptance |y|≤ 0.30. This result at √(s)≈ 50 GeV is two-orders of magnitude larger than the value for the BNL discovery <cit.> at √(s)≈ 7.5 GeV. The reason that CCRS <cit.> was able to measure the cross section was that thanks to Cerenkov counters together with the EMcalorimeter that allowed a trigger on e^± in the range 1.0≤ p_T≤ 4.7 GeV/c, the cross section could be measured for J/ψ→ e^+ e^- for all p_T_ee>0. This was the first of three such measurements at the CERN ISR <cit.> with similar e^± triggers and not repeated at a hadron collider until RHIC <cit.> and eventually CDF at the Fermilab Tevatron <cit.>. The best measurement of the J/Ψ at the ISR <cit.> is shown in Fig. <ref>c. 

  


  §.§.§ What are the J/Ψ and Ψ'?
 
In less than a month, the J/Ψ was understood to be a narrow bound state of the `heavy' cc̅ charm quarks <cit.> and was given the name charmonium <cit.>. The quarks were proposed to be bound with a simple potential (the Cornell potential <cit.>) that incorporated both the Coulomb and confining forces:

    V(r)=-4/3α_s/r + σ r

where α_s is the  coupling constant (Eq. <ref>) and σ represents the string-tension in a string-like confining potential. Also predictions were made for heavier quarks Q with stronger binding of QQ̅ leading to `a rich assortment of rather narrow resonances' <cit.>.


  §.§.§ The Upsilon; and the ISR recognition problem

It is worth noting that in early 1976 a measurement of p+ Be → e^+ +e^- + anything using a 400 GeV proton beam at Fermilab <cit.> claimed that a “statistically significant clustering near 6 GeV suggests the existence of a narrow resonance”. This was made by the Lederman group  who suggested that “the name Υ (Upsilon) be given either to the resonance at 6 GeV if confirmed or to the onset of high-mass dilepton physics.” This later became known as the oopsLeon when, in a measurement of high mass μ^+ +μ^- pairs which allowed a higher data taking rate made possible by the filtering of most hadrons, the same group <cit.> observed that “the dimuon mass spectrum provides no evidence for fine structure above 5 GeV”. 

     

The situation was again reversed following a major redesign of the dimuon experiment, when the real Υ→μ^+ +μ^-, a narrow resonance at 9.5 GeV, was discovered <cit.> (Fig. <ref>a). This was a narrow bound state of heavier quarks as predicted <cit.> and turned out to be the discovery of the bottom quark b, a member of a third family of quarks much heavier than the first two families. 

This discovery cemented a negative view of the ISR by many CERN physicists <cit.> for missing the discoveries of the c quark (actually quarkonia) and now the b quark in dilepton production by lower energy but much larger luminosity conventional fixed target accelerators. They were drawn instead to the new 400 GeV Super proton Synchrotron (SpS) which started physics operation at the end of 1976 and which ironically made its greatest contributions by being turned into a proton-antiproton collider in mid 1981.   Unfortunately this negative pervasive attitude totally missed the most important physics contributions of the ISR which were in hadron physics and which made major contributions to the development of . 

Measurements of the Upsilons were also made at the ISR <cit.>,<cit.>, <cit.> but the best measurement (Fig. <ref>b) <cit.> was more concerned about Drell-Yan production.[Drell-Yan production, or q̅+q→μ^+ + μ^- +X is predominantly an electromagnetic process which measures the q̅ composition of a proton. It is mainly a parton model reaction.  enters only in the next to leading order.]  However, the Upsilon measurement <cit.> did correct an anomalously large value of the cross section claimed in their previous publication <cit.>. 


 §.§ The direct single 𝐞^± are from the semi-leptonic decay of charm particles.
 
With the J/Ψ issue out of the way, the comprehensive CCRS single e^± measurements <cit.> remained a very interesting challenge (Fig. <ref>).
The direct-single e^± spectra in the range 1.3<p_T<3.2 GeV/c were roughly constant at a level of 10^-4 of charged pion production at all 5 c.m. energies measured.  However, in detail, the ratio of e/π increased systematically by a factor of ∼ 1.8 from √(s)= 30 to 60 GeV<cit.> (Fig. <ref>).    




  §.§.§ The theorists rise to the occasion.

Although discovered in 1974, it was not until 1976 that the direct single e^± were shown to be from  the semi-leptonic decay of charm particles. Of course without the intervening J/Ψ charmonium discovery, it is unlikely that charm particles would have been considered. In fact, the first attempt of explaining the CCRS measurements was by Farrar and Frautschi <cit.> who proposed that the direct-single-e^± were due to the internal conversion of direct photons with a ratio γ/π^0∼10-20%. However CCRS was able to cleanly detect (and reject) both external and internal conversions, since there was zero magnetic field on the axis, so was able to set limits excluding this explanation to less than 6.6% of the observed signal <cit.>.  


 	The first correct explanation of the CCRS direct-single-e^± (prompt leptons) was given by Hinchliffe and Llewellyn-Smith <cit.> as due to semi-leptonic decay of charm particles. The predictions from charm decay <cit.> are in excellent agreement with the CCRS data <cit.>  submitted to the SLAC conference as shown in Fig. <ref>a.
   
A similar explanation was published by Maurice Bourquin and Jean-Marc Gaillard <cit.>, two experimentalists, who compared the measured e/π ratios to a cocktail of all known leptonic decays including “Possible contributions from the conjectured charm meson...” (Fig. <ref>b). It is interesting to note the usage of “conjectured” because it seems that this was the notation for D^+ and D^0 charm mesons from the first SLAC paper which failed to find open charm <cit.> a year before it was actually discovered at SLAC in August 1976 <cit.>.

Something important to note about the charm calculations <cit.>, <cit.> and clearly shown in Fig. <ref>b is that neither calculation could fit the data points 
for p_T<1 GeV/c at 30^∘ from the CHORMN experiment <cit.> at the ISR. 
The important issue from a historical perspective is that many experiments not designed for the purpose wanted to get into the prompt-lepton act, which resulted in questionable (i.e. incorrect) results, and this is only one example. See Ref. <cit.> for more details. This led to the unfortunate  situation that later papers about charm ignored the many disagreeing ISR measurements of the direct-single-e^± from charm, which were essentially ridiculed, or in the case of the original CCRS discovery <cit.>  downplayed in review articles <cit.>; or ignored <cit.> because it was published before either charm or the J/Ψ were discovered so there is no reference to the word “charm” in the publication. 

Later experiments at the CERN-ISR using the upgraded Split Field Magnet were designed for a program of heavy flavor searches. The CCRS direct e^± measurement at √(s)=62.4 GeV was confirmed by a well designed single e^± experiment performed by the Zichichi group <cit.>. Also the first direct evidence of charm hadron production in hadron interactions was the observation at the CERN-ISR of the charm D^+ meason via its D^+→ K^+ π^+ π^- decay by the CCHK experiment <cit.>.


  §.§.§ Why do I dwell on charm at the CERN-ISR?

One reason is the lack of recognition in the charm literature as noted. However the main reason is that the measurement of charm by direct single e^± in p+p and Au+Au collisions <cit.> 30 years later at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) was one of the principal observations that led to the discovery of the Quark Gluon Plasma and the conclusion that it was a perfect liquid with a viscosity to entropy density ratio “intriguingly close to the conjectured quantum lower bound” 1/4π <cit.>. 



§  MEETS HIGH 𝐩_𝐓 1977-1979


It wasn't until 1977 that   was applied to hard-scattering with the first theoretical calculations of the basic equations for the elementary  subprocesses at leading order <cit.> <cit.> <cit.>. However the first application of “asymptotic freedom (AF)” to “wide-angle hadronic collisions” was in 1975 in a publication <cit.> with an incorrect conclusion;  but with an improved x_T scaling formula, that experimenters liked, which included the evolution effects of “AF” and is still in use at present. 


 §.§ Improved x_T scaling.

The incorrect conclusion of Ref. <cit.> was that “single vector gluon exchange contributes insignificantly to wide angle hadronic collisions”; but, in my humble opinion, they may have been overly influenced by at least one author of the original (BBG) x_T scaling <cit.>. This is based on an acknowledgement in Ref. <cit.>:“Two of us (J. K. and L. S.) also thank S. Brodsky for emphasizing to us repeatedly that the present data on wide-angle hadron scattering show no evidence for vector exchange”.

Nevertheless the new x_T scaling formula, which introduced the “effective index” n_ eff(x_T, √(s)) to account for `scale breaking' (i.e.  evolution):

    E d^3σ/dp^3=1 p_T^n_ eff(x_T,√(s)) 
    F(x_T)=1√(s)^ n_ eff(x_T,√(s))  G(x_T)    where   x_T≡2p_T/√(s)

 was very useful in understanding the next round of high p_T measurements. 


 §.§ Second generation high 𝐩_𝐓 measurements

The second generation of high p_T experiments at the CERN-ISR straightened out the n=8 issue of the first round of experiments (recall Fig. <ref>) and made good use of Eq. <ref>.
The CCOR experiment presented their first results (Fig. <ref>) <cit.> together with data and a fit from a previous CCRS measurement <cit.> that had an order of magnitude more data than the original CCR and Saclay-Strasbourg measurements. Thanks to further increased integrated luminosity and acceptance, the CCOR data <cit.> extended another 4 orders of magnitude in cross section to p_T≈ 14 GeV/c. The CCRS fit, A e^-bx_T/p_T^n, to their data at all three √(s) with n=8.6 and b=12.5 (shown as dashed lines on Fig. <ref>) works in the CCRS p_T range but fails badly for p_T>7 GeV/c and remains well below the CCOR data out to p_T≈ 14 GeV/c. 





  §.§.§ 𝐱_𝐓 scaling with 𝐧_ 𝐞𝐟𝐟(𝐱_𝐓, √(𝐬))

x_T scaling fits to the CCOR data in Fig. <ref> for √(s)=53.1 and 62.4 GeV <cit.> confirmed the validity of the idea that n_ eff is a function of x_T and √(s) with results n_ eff=8.0±0.4 for the p_T interval 3.7<p_T< 7.0 GeV/c and n_ eff=5.13±0.14 for 7.5<p_T<14.0 GeV/c. The variation of n_ eff with x_T and √(s) is easier to observe with 
a log-log plot of the invariant cross section σ^ inv=Ed^3σ/dp^3 vs x_T (Fig. <ref>a) where n_ eff can be read off by inspection:

    n_ eff(x_T, √(s_1),√(s_2) )=ln[σ^ inv(x_T,√(s_1))
    /σ^ inv(x_T,√(s_2))]/ln[√(s_2)/√(s_1)]   .

The fact that the data for √(s)=53.1 and 62.4 GeV are essentially parallel for x_T≥ 0.3 in Fig. <ref>a indicates that n_ eff≈ 5 is roughly constant in this range as shown in Fig. <ref>b, where all the point by point calculated n_ eff(x_T, √(s_1),√(s_2) ) are plotted. Also the increase in the spacing in Fig. <ref>a for x_T≤ 0.2 compared to x_T≥ 0.3 indicates the region where n_ eff(x_T, 53.1, 62.4)≈ 8. An interesting observation about the fact that n_ eff≈ 5 for x_T≥ 0.3 is that this value is now close to the value n_ eff=4, originally expected by BBG <cit.> for QED or vector gluon exchange (Section <ref>), but modified by the scale breaking from  evolution as suggested by Ref. <cit.>.

Another nice feature of x_T scaling for experimentalists is that in the calculation of n_ eff(x_T, √(s_1),√(s_2)) from Eq. <ref> the systematic uncertainty in the absolute value of the p_T scale cancels, which eliminates the dominant source of experimental systematic uncertainty. This is nicely illustrated by the π^0 measurements from another `second generation' ISR experiment <cit.> based on liquid-argon–Pb plate calorimeters of high spatial resolution and large solid angle acceptance (Fig. <ref>c). Notably, the π^0 cross-sections from `this experiment' and `Ref.4' (CCOR) <cit.> disagree by a large factor ≈ 3 for p_T≥ 7 GeV/c but the values of n_ eff(x_T, 53.1, 62.4) (Fig. <ref>d) are in excellent agreement with the CCOR values (Fig. <ref>b). 



 §.§ First theoretical calculations of pion p_T spectra using : 1978
  
The first calculations of inclusive high p_T  pion cross sections using   were performed by Owens, Reya and Glück <cit.> (Fig. <ref>a) and Feynman, Field and Fox (FFF) <cit.> (Fig. <ref>b). 
 
Figure <ref>a shows all the  subprocesses that go into the calculation; but the total, which fits the data well for p_T>5 GeV/c,  falls below the data for p_T<5 GeV/c. Note that the data are preliminary results of CCOR <cit.> which agree with the final publication <cit.> shown in Fig. <ref>. The FFF calculations in Fig. <ref>b follow the BS <cit.> (π^+ +π^-)/2 and CCRS π^0 <cit.>  measurements at √(s)=53 GeV/c, as well as √(s)=19.4 GeV/c measurements from Fermilab, from p_T ≈ 7 GeV/c down to p_T≈ 2 GeV/c because the effect of k_T smearing was included. k_T, the transverse momentum of a parton in a nucleon, had been introduced by FFF the previous year <cit.> to explain ISR measurements of two-particle correlations which will be discussed in detail in a later section. A second calculation by Owens <cit.> which included the k_T effect also fit   the CCRS <cit.> data down to p_T=3 GeV/c.


 
These calculations all assume that high p_T particles are produced from states with two roughly back-to-back jets which are the result of scattering of a parton from each nucleon. The calculations require the purely theoretical elementary   subprocesses plus other quantities which must come from measurements.
It is also important to understand the kinematics of parton-parton scattering and the definition of the various kinematic quantites. These are given in the Appendix (section <ref>). 



§ ELEMENTS OF  FOR EXPERIMENTALISTS
 
 calculations at the parton level are relatively straightforward. For example consider the scattering:

    a+b→ c+d

where a and b are incident partons with c.m. energy √(ŝ) that scatter elastically through angle θ^*, with 4-momentum-transfer-square: 

    Q^2=-t̂=ŝ(1-cosθ^*)/2    .

The  cross section for this subprocess is simply: 

    .dσ/dt̂|_ŝ=πα_s^2(Q^2)/ŝ^2Σ^ab(cosθ^*)       ;
 
where the elementary  subprocesses involving quarks (q) and gluons (g) in hadron-hadron collisions and their characteristic angular distributions <cit.> <cit.> 
 Σ^ab(cosθ^*) are enumerated in Fig. <ref>a-h. 



 §.§ The Elementary  Subprocesses


At the elementary level, the lowest order  Born diagrams, shown in Fig. <ref>-(right), 
are analogous to the QED processes of Møller, Bhabha and Compton scattering indicated; and tests of their validity would be quite analogous to the studies of the validity of Quantum Electrodynamics (QED) which occupied the 1950's and 1960's <cit.>. The t̂ and û channels and  ŝ and t̂ channels are indicated for the qq and q̅q diagrams respectively. It is important to note that the diagrams in the dashed box are unique to QCD since the gluons carry color charge and interact with each other while the photons in QED do not carry electric charge and so do not self-interact. 

Although the different combinations of ŝ, t̂ and û for the cross sections in Fig. <ref>a-h may at first seem to be formidable, it can be seen by substituting t̂=-ŝ(1-cosθ^*)/2, û=-ŝ(1+cosθ^*)/2, that indeed the Σ^ab(cosθ^*) are nothing other than angular distributions. For example, for qq'→ qq' Fig. <ref>a:

    Σ^qq'(cosθ^*)=4/9 ŝ^2 +û^2/t̂^2= 4/9[ (2/1-cosθ^*)^2
    + (1-cosθ^*/1+cosθ^*)^2 ]


However, bringing Eqs. <ref> and <ref> to the p+p collision level leads to  complications.



 §.§ p+p hard-scattering in  

	The overall hard-scattering cross section A+B→ C + X (Fig. <ref>)

in “leading logarithm” p    is the sum over parton reactions a+b→ c +d 
(e.g. g+q→ g+q) at parton-parton center-of-mass (c.m.) energy √(ŝ) as given in Eq. <ref> <cit.>  
 

    d^3σ/dx_1 dx_2 dcosθ^*=
    s d^3σ/dŝ dŷ dcosθ^*=
    1/s∑_ab f^A_a(x_1) f^B_b(x_2) 
    πα_s^2(Q^2)/2x_1 x_2Σ^ab(cosθ^*)
 
where f^A_a(x_1), f^B_b(x_2), are parton distribution functions (PDF), 
the differential probabilities for partons
a and b to carry momentum fractions x_1 and x_2 of their respective 
protons (e.g. u(x_2)), and where θ^* is the scattering angle in the parton-parton c.m. system. 
The parton-parton c.m. energy squared is ŝ=x_1 x_2 s,
where √(s) is the c.m. energy of the p+p  collision. The parton-parton 
c.m. system moves with rapidity ŷ=(1/2) ln (x_1/x_2) in the p+p  c.m. system. The quantities f_a(x_1) and f_b(x_2), the “number” 
distributions of the constituents, are related 
(for the electrically charged quarks) to the structure functions measured in e+A lepton-hadron 
Deeply Inelastic Scattering (DIS), where A is p or n, e.g. 

    F^A_1(x,Q^2)=1 2∑_a e_a^2  f^A_a(x,Q^2)       
    F^A_2(x,Q^2)=x∑_a e_a^2  f^A_a(x,Q^2)

where e_a is the electric charge of the quark a. 

The transverse momentum of a scattered constituent is:

    p_T = p_T^* = √(ŝ) 2  sinθ^*   ,

and the scattered constituents c and d in the outgoing parton-pair have equal and opposite momenta in the parton-parton (constituent) c.m. system. 
A naive experimentalist would think of Q^2 = -t̂ for a scattering 
subprocess and Q^2 = ŝ for a Compton or annihilation subprocess.  


Equation <ref> gives the p_T spectrum of outgoing parton c, which then
fragments into a jet of hadrons, including e.g. π^0.  To go to the particle level the fragmentation function D^π^0_c(z) which is the probability for a π^0 to carry a fraction
z=p^π^0/p^c of the momentum of outgoing parton c must be multiplied in along with its differential dz. Equation <ref>
must be summed over all subprocesses leading to a π^0 in the final state weighted by their respective fragmentation functions. In this formulation, f^A_a(x_1), f^B_b(x_2) and D^π^0_c (z) 
represent the “long-distance phenomena" to be determined by experiment;
while the characteristic subprocess angular distributions,
Σ^ab(cosθ^*) (Fig. <ref>) 
and the coupling constant,
α_s(Q^2)=12π/25 ln(Q^2/Λ^2),
are fundamental predictions of  <cit.> <cit.>
for the short-distance, large-Q^2, phenomena. 
When higher order effects are taken into account, it is necessary to specify  factorization scales μ for the distribution and fragmentation functions in addition to renormalization scale Λ which governs the running of 
α_s(Q^2). 
As noted above, the momentum scale Q^2≈ p_T^2 for the scattering
subprocess, while Q^2≈ŝ for a Compton or annihilation subprocess,
but the exact meanings of Q^2 and μ^2 tend  to be treated as parameters  rather than as dynamical
quantities. 


§ DIRECT SINGLE PHOTON PRODUCTION, THE MOST ELEGANT  REACTION

Direct single photon (γ) production with a ratio γ/π^0∼ 10-20% <cit.> was one of the first proposed explanations of the direct single e^± discovery at the ISR but was excluded with  95% confidence level to γ/π^0< 5% for p_T>1.3 GeV/c  <cit.> [1]. 



 §.§ Direct-γ  elementary subprocesses: 1977

The first  calculation of direct-γ production, “the inverse  Compton Effect”, via the constituent reaction g+q→γ+q was presented by Fritzsch and Minkowski in 1977 <cit.>.  This reaction has many beautiful aspects as a hadronic probe. 


  1. The γ-ray participates directly in the hard-scattering and then emerges freely and unbiased from the reaction, isolated, with no accompanying particles. 

  2. The energy of this outgoing parton (the γ-ray) can be measured precisely. 

  3. No fragmentation function is required for Eq. <ref>.

  4. Since there are many fewer q̅ in a nucleon than quarks or gluons, the g+q reaction dominates so that the parton opposite the γ-ray is most likely a quark. 

  5. The scattered quark has equal and opposite transverse momentum to the direct-γ, so the transverse momentum of the jet from the outgoing quark is also precisely known (modulo k_T).  

The cross-section for the elementary  subprocess, g+q→γ+q is simply:

    .dσ/dt̂|_ŝ=πα_s α  e^2_q/3 ŝ^2(ŝ+t̂/ŝ+ŝ/ŝ+t̂ )     ,

Using the same argument as item 4 above, the  cross-section for the reaction A+B→γ +q with the direct-γ produced at rapidity y_c with p_T, and the quark-jet at y_d with p_T is analytical: 

    d^3σ/dp_T^2  dy_c  dy_d   =   
     x_1 G_A(x_1)  F_ 2B(x_2) 
    παα_s(Q^2)/3ŝ^2(1+cosθ^*/2+2/1+cosθ^* ) 
       +    F_ 2A(x_1)  x_2 G_B(x_2) 
    παα_s(Q^2)/3ŝ^2(1-cosθ^*/2+2/1-cosθ^* )

where 

    cosθ^*=tanh(y_c -y_d)/2     x_1,2=x_Te^± y_c + e^± y_d/2  √(ŝ)=2 p_T cosh(y_c -y_d)/2 .
 
Here F_2(x,Q^2) is the sum of the PDF's over all the quarks and anti-quarks (predominantly u and d) in the nucleons or nuclei A and B and  G(x,Q^2) is the gluon PDF which is the principal theoretical problem in the calculation since it is the least well known. However, the main difficulty with the measurement of direct photon production is experimenatal: a huge background from the decays π^0→γ +γ and η→γ+γ. 


  §.§.§ R_γ, `the double ratio' for signal/background

For measurements at mid-rapidity, the π^0 cross section is typically a power law with dσ/p_T dp_T∝ p_T^-n. In this case the p_T spectrum of the background γ rays from  relative to the π^0 spectrum  is given by the simple expression <cit.>[1]:

    .γ/π^0|_π^0=2/n-1⟹.γ/π^0|_ bkg≈1.19×2/n-1

where (γ/π^0)_ bkg includes the η→γ+γ background (η/π^0 ≈ 0.5 for p_T>3 GeV/c with η→γ+γ branching ratio 0.38 <cit.>).

Generally, the background is calculated using Monte Carlo calculations including efficiency, acceptance, etc. However the signal/background ratio is best presented by the double ratio:

    R_γ=(γ/π^0)_ Measured/(γ/π^0)_ Background≈γ_ Measured/γ_ Background
 
because the calculated background in the form (γ/π^0)_ Background can be checked by comparison to Eq. <ref>. R_γ>1.0 indicates a direct-γ signal.


 §.§ Experimental results

As in many reactions studied for the first time, the experimental results at the ISR, where direct-γ were eventually discovered, started with an incorrect measurement <cit.> while  other early experiments set limits using low mass e^+ e^- pairs[1]. The first correct results from an experiment specifically designed to detect real single photons at the ISR <cit.>  set a 95% confidence upper limit of γ/π^0<4% for 2.3≤ p_T≤ 3.4 GeV/c. 

The first experiment to actually correctly claim the observation of a signal for direct-γ/π^0 ≈ 0.2 for p_T≥ 4.5 GeV/c and generally given credit for the discovery of direct-γ production was the measurement by the AABC experiment  <cit.> a modification of the ABCS experiment using the high resolution calorimeters which could resolve the two γ's from π^0 decay. The first measurement of the direct-γ cross section was by CCOR <cit.> who could not resolve the two γs in a cluster but instead measured the fraction of clusters of a given p_T that would pass through the 1.0 radiation length thin-wall of the superconducting solenoid without making a conversion(47% for a single γ and ≈20-24% for 2 or more γ rays in the cluster). This led to a large systematic uncertainty which was not too bad for 9≤ p_T≤ 13 GeV/c (Fig <ref>a). The cross-sections in this region were in surprisingly good agreement with the final AABC (R806) results (Fig <ref>b) <cit.> as discussed in detail by  <cit.>. The final ISR direct-γ measurement  <cit.> also includes a summary of the previous measurements, which are all in impressive agreement over the range 4≤ p_T≤ 13 GeV/c as shown in Fig <ref>c. 


 



  §.§.§ Theoretical predictions of direct-γ data show that  really works.

The theoretical predictions of direct-γ cross-sections lagged behind the experimental measurements because the gluon structure functions (PDF), G(x,Q^2), in deeply inelastic e+p or neutrino scattering are not measured directly as are the quark PDF's, F_2(x,Q^2), but are measured via the scaling violations, the Q^2 evolution of F_2(x,Q^2) <cit.>. In fact, the first attempted direct measurement of G(x,Q^2) was made at the ISR by the AFS experiment <cit.> with measurements of direct-γ+jet, both at mid-rapidity, solving Eq. <ref> for x G(x) (Fig. <ref>a). 


It is interesting and informative to skip ahead to the present, where next-to-leading-order   calculations using the latest PDF's as well as “joint resummation of both threshold and recoil effects due to soft multigluon emission” are in excellent agreement with all existing direct-γ measurements at the time of publication <cit.> (Fig. <ref>b.)


 

         

From the experimental point of view, a better illustration of  in action is given by the x_T scaling of all the existing direct-γ measurements (Fig. <ref>). For x_T scaling with n_ eff=4.0 (the parton model)  non-scaling is visible; but x_T scaling with n_ eff=4.5 accounts for the non-scaling evolution which is a key element of  . 



§ TWO-PARTICLE CORRELATIONS.

It was natural for the experiments that had searched for single leptons and lepton-pairs at mid-rapidity but were overwhelmed by pions at large p_T to look for what was balancing the p_T of the pions: an outgoing parton with opposite p_T, as described by Bjorken <cit.> <cit.>, that fragmented into a collimated group of particles, “a jet” with a configuration like ordinary particle production e.g. e^-6p'_T where p'_T is perpendicular to the outgoing parton. In this case, the jets should be coplanar with the beam direction and balance transverse momenta. Viewed down the beam axis, in azimuthal projection (Fig. <ref>), the events should show strong azimuthal correlation.

Another possibility was balance as required by kinematics <cit.>. 
 
 In Fig. <ref> the different distribution of fragments in the jet p̂_Tt, triggered by a particle with p_Tt, and the away jet is no accident. Bjorken made a very important point in his parton scattering prediction, that the single high p_T particle used as a trigger to search for the opposite jet, would carry “a major fraction (60-80%) of the total trigger parton (or jet) momentum. 
This is known as “trigger bias” <cit.> and is related to the  Bjorken parent-child relation <cit.>. 

The cross-section for a pion with p_Tt which is a fragment with momentum fraction z=p_Tt/p̂_T in a jet from a parton q with p̂_T where D^q_π (z) is the fragmentation function (e.g ∼ e^-bz) is:
   
    d^2σ_π (p̂_T,z) p̂_T dp̂_T dz =dσ_qp̂_̂T̂dp̂_T× D^q_π (z)=A p̂_T^n× D^q_π (z) 
          .

The change of variables, p̂_T=p_Tt/z, dp̂_T/dp_Tt|_z=1/z, 
then gives the joint probability of the pion with transverse momentum p_Tt and fragmentation fraction z: 

    d^2σ_π (p_Tt,z)p_Tt dp_Tt dz 
    =A p_Tt^n× z^n-2 D^q_π(z)      .

Thus, the effective fragmentation function, for a trigger particle with p_Tt is weighted upward in z by a factor z^n-2, where n is the simple power fall-off of the jet invariant cross section (Eq. <ref>). This is the `trigger bias' <cit.>. 

The pion p_Tt distribution is the integral of Eq. <ref> over all values of the parton p̂_T from p̂_T=p_Tt, z=1, to p̂_T=√(s)/2, z=x_Tt, which has the same power n as the parton p̂_T distribution: 

    dσ_π (p_Tt)p_Tt dp_Tt 
    =1 p_Tt^n∫^1_x_Tt A z^n-2 D^q_π(z) dz≈ constantp_Tt^n,

since typically x_Tt≪ 1, so the integral depends only weakly on p_Tt. Thus the invariant p_Tt spectrum of the π^0 fragment is a power law with the same power n as the original parton p̂_T spectrum, for p_Tt≪√(s)/2. This is the Bjorken parent-child relation.   


 §.§ Two particle correlation measurements 1975-1977.


Historically, at the ISR <cit.>, since the trigger bias implied that the p_Tt of the trigger particle was a reasonable approximation to the p̂_T of the triggered jet, and the away jet would be approximately equal and opposite to the trigger jet, the transverse momentum of the away particle p_Ta was decomposed into components (Fig. <ref>) of which two are commonly used: one perpendicular to the trigger plane p_ out=p_TasinΔϕ,  and one in the trigger plane:
 
    x_E=-p_x/p_Tt=-p_Tacos(Δϕ)/p_Tt≃p_Ta/p̂_Ta/p_Tt/p̂_Tt≈z/z_ trig    .

 

With the assumption that the trigger and away jets balance transverse momenta, p̂_Ta=-p̂_Tt, as assumed in the last step of Eq. <ref>, the variable x_E was thought to measure the fragmentation fraction z of the away jet from the highly biased trigger jet with z_ trig→ 1. It was generally assumed that the p_Ta distribution of away side hadron fragments from an away-side parton opposite a single particle trigger with p_Tt, would be the same as that from a jet-trigger and follow the same fragmentation function of partons as observed in e^+ e^-  or DIS <cit.>
(Fig. <ref>). Because of the relatively large trigger bias at ISR energies and small range of z_ trig, 0.8z_ trig 0.9, it was also assumed that x_E scaling <cit.> would hold, i.e. all x_E distributions measured at different p_Tt would be the same. 
    
 

These ideas were further clarified by Feynman, Field and Fox <cit.>, who showed that the away side correlations for a single-particle trigger with p_Tt would be roughly the same as the away-side correlations for a jet trigger with p̂_Tt=p_Tt/z_ trig due to the fact that “the `quark' from which the single hadron trigger came had a higher p̂_Tt than  
did the quark producing the jet trigger (by a factor of 1/z_ trig)”. (Fig <ref>).
The ideas of x_E scaling according to a fragmentation function were supported by later ISR measurements but first a contemporary experiment (CCHK) <cit.> did not find x_E scaling for values of p_Tt<4 GeV/c which led to an important discovery.

 



  §.§.§  k_T, the transverse momentum of a parton in a proton


The CCHK experiment at the CERN-ISR <cit.>  observed that x_E scaling <cit.> didn't work in the range 2.0≤ p_T_t≤ 3.2 GeV/c; i.e. different values of trigger p_T_t did not produce a universal x_E distribution (Fig. <ref>a). 
 
CCHK also looked at the p_ out variable and plotted p_ out versus x_E for triggers in the range 2.0≤ p_T_t≤ 3.2 GeV/c. They found that the p_ out  increased with increasing x_E up to a maximum value of p_ out∼ 0.65 GeV/c (Fig. <ref>b). 
The original parton model did not assign transverse motion to quarks in the proton, only longitudinal x,  but it had been  proposed by Levin and Ryskin <cit.> that quarks in the proton also carry   transverse momentum. This idea, coupled with the lack of x_E scaling for p_T_t < 3 GeV/c, was taken by CCHK <cit.> as evidence for the transverse momentum of quarks inside the proton. Calculations from their parton scattering model with k_T=0 and k_T=610 MeV/c are shown in Fig. <ref>b. This result led Feynman, Field and Fox (FFF) <cit.> to formally introduce k_T, the transverse momentum of a parton in a nucleon into their model of parton-parton scattering.  



 §.§ The second round of two-particle correlation measurements 1978-1979

The two experiments on two particle correlations at the CERN-ISR discussed above both used the Split Field Magnet Facility (SFM) <cit.> which could measure the momenta of charged particles in nearly the full polar angular range but was optimized for measurements at forward and backward angles. One experiment <cit.> moved their small E.M. calorimeter to mid-rapidity of the SFM  transverse to the beam axis while the CCHK measurement <cit.> used only the SFM in a self-triggering mode at polar angles of 20^∘ and 45^∘. 

The second round of two particle correlations with improved detectors started to present data in 1978. The BFS collaboration <cit.> had moved the British Scandinavian wide angle spectrometer to the SFM at an angle of  90^∘ at mid rapidity. They could trigger on identified charged particles with detection of the associated charged particles in the Split Field Magnet. The acceptance for associated charged particles, which was the same as CCHK, covered a rapidity range -4 ≤ y ≤ +4, with an azimuthal aperture of ± 40^∘ on the trigger side and ± 25^∘ on the away side. This experiment presented one of the most interesting results, a dramatic map of the two particle correlation function over nearly the full region in rapidity. Figure <ref> shows the ratio of the density of tracks with p_T>0.5 GeV/c, as a function of rapidity y and azimuthal angle ϕ, from a high p_T_t trigger with 3< p_T_t<4, GeV/c located at y=0 ϕ=180^∘, relative to minimum bias events (p_Tt≥ 0.5 GeV/c with elastic scattering events removed).  They called this ratio, which cancels the effects of acceptance variation, R+1. 
  
The main features of Fig. <ref> are an increase in the value of the correlation function in a small region in y and ϕ near the trigger particle and a much larger increase on the away side, mainly within |ϕ|<45^∘ (the limit of their acceptance), but extending in rapidity to |y|≃ 3. This illustrates the di-jet coplanar structure of high p_T_t triggered events. One can also see a smaller same side correlation extending out to |y|≃ 2. 


 The CCOR experiment, which was proposed in May 1973 <cit.> and approved in March 1974, was installed in the ISR as R108 (8th experiment at Intersection 1) at the end of 1976 along with a low β insertion for higher luminosity. It was debugged, tuned-up and started taking data in July 1977. This experiment <cit.> with its thin-coil superconducting solenoid and cylindrical drift chambers was the first at the CERN-ISR to provide charged particle measurement with full and uniform acceptance over the entire azimuth, with pseudorapidity coverage -0.7≤η≤ 0.7, so that the jet structure of high p_T scattering could be easily seen and measured. However, from August to October the liquid He refrigerator was broken, so the solenoid was turned off and only π^0 measurements in the EMcalorimeter could continue <cit.> (Section <ref>). The measurements of charged-particles associated to a π^0 trigger came a few months later (Fig. <ref>) <cit.>. 
 
  
In  Fig. <ref>a,b, the azimuthal distributions of associated charged particles 
relative to a π^0 trigger with transverse momentum p_Tt > 7 GeV/c are shown for five intervals of associated particle transverse momentum p_T. In all cases, strong correlation peaks on flat backgrounds are clearly visible, indicating the di-jet structure which is contained in an interval Δϕ=± 60^∘ about a direction towards and opposite the to trigger for all values of associated p_T  (>0.3 GeV/c) shown. The width of the peaks about the trigger direction (Fig. <ref>a), or opposite to the trigger (Fig. <ref>b) indicates out-of-plane activity from the individual fragments of jets. If the width of the away distributions (Fig. <ref>b) corresponding to the out of plane activity were due entirely to jet fragmentation, then  
⟨ |sin(Δϕ)|⟩=⟨ |j_T_ϕ|/p_T ⟩ would decrease in direct proportion to 1/p_T, since j_T_ϕ, the component of  the jet fragmentation transverse momentum, j_T, in the azimuthal plane, should be independent of p_T. These data were also further analyzed to measure j_T as well as k_T, the transverse momentum of a parton in a nucleon, as originally shown by the CCHK collaboration <cit.>, and elaborated by Feynman, Field and Fox (FFF) <cit.>.
 
The x_E distributions <cit.>, <cit.> from the data of Fig. <ref>b are shown in Fig. <ref>c.  The x_E scaling is evident for all values of p_T_t, with the expected fragmentation behavior, e^-6z∼ e^-6 x_E ⟨ z_ trig⟩. This figure also showed that there were no di-jets, each of a single particle, as claimed by another ISR experiment of that period <cit.>, and by Jacob and Landshoff <cit.>, since there is no peak at . There is a small anecdote concerning this measurement and Maurice Jacob's talk at the EPS1979 HEP Conference <cit.>. Maurice was originally only going to show a plot from the ABCS experiment <cit.> which appeared to show “a systematic wiggle departure from an exponential...The wiggle could bear witness to a specific process where the two jets would each only consist of one high p_T π^0” as he had predicted <cit.>. I insisted that Maurice also show Fig. <ref>c, a plot that I had made with three higher p_T points than the CCOR plot in Ref. <cit.>, “which challenged the one high p_T π^0 only jet idea” after I nearly broke the telephone in the ISR counting room when I heard that Maurice was only going to show the plot with the “wiggle” <cit.>. 

Even though this period ended with the strong belief <cit.> that jet fragmentation functions from ν+p and e^+ e^- reactions are the same as p+p x_E distributions, with the same dependence of the exponential slope b on p_T_t or √(s)/2 for e^+ e^- (Fig. <ref>b), it turned out that nature had the last laugh. This belief was one of the very few results from the “high p_T discovery period” that did not stand the test of time. It was discovered at RHIC <cit.>, a quarter of a century later, that the shape of the x_E distribution triggered by the fragment of a jet, such as a π^0 had nothing to do with fragmentation functions but instead measured the ratio of the away jet to the trigger jet (x̂_h≡p̂_Ta/p̂_Tt) and depended only on the power n of the invariant single particle high p_T cross section:
    
    .dP dx_E|_p_T_t  = N (n-1)1x̂_h1(1+ x_E x̂_h)^n      .

   


 §.§ Measurement of the jet fragmentation transverse momentum, j⃗_⃗T⃗, and k⃗_⃗T⃗, the transverse momentum of a parton in a nucleon
 
Following the idea of Levin and Ryskin <cit.> and CCHK <cit.>, Feynman, Field and Fox <cit.> established the formalism for k_T, the transverse momentum of a parton in a nucleon. 

In this formulation (Fig. <ref>), the net transverse momentum of an outgoing parton pair, where the two k_T add randomly, is √(2) k_T, which is composed of two orthogonal components, √(2) k_T_ϕ=k_T, out of the scattering plane, which makes the jets acoplanar, i.e. not back-to-back in azimuth, and √(2) k_T_x=k_T, along the axis of the trigger jet, which makes the jets unequal in energy. 

	FFF <cit.> gave the approximate formula to derive k_T from the measurement of p_ out as a function of x_E:

    ⟨ |p_ out|⟩^2=x_E^2 [2⟨ |k_T_ϕ|⟩^2 +  ⟨ |j_T_ϕ|⟩^2 ] + ⟨ |j_T_ϕ|⟩^2      .

This formula assumed that z_ trig=1 and that the jet energies are equal. 




CCOR <cit.> used a fit to this formula (Fig. <ref>a) to derive ⟨ |k_T_ϕ|⟩ and ⟨ |j_T_ϕ|⟩ as a function of p_Tt and √(s) (Fig. <ref>b) from the data of Fig. <ref>b.  This important result  showed that ⟨ |j_T_ϕ|⟩ is constant, independent of p_T_t and √(s), as expected for fragmentation, but that ⟨ |k_T_ϕ|⟩ varies with both p_T_t and √(s), suggestive of a radiative, rather than an intrinsic origin for k_T. Large values of √(k_T^2 )≈ 1 GeV/c were also reported in other CERN-ISR measurements <cit.>,<cit.>  but it took the e^+ e^- people several more years to get j_T correct <cit.> because they hadn't understood the “seagull effect” <cit.>: with increased momentum of fragments in a jet, their momentum transverse to the jet axis also increases until it reaches its true j_T. 



§ MULTIPARTICLE CORRELATIONS–THE SEARCH FOR JETS 1977–1980

The jet searches like many other new measurements, but perhaps the worst in this regard, started off with a major incorrect claim of the observation of the jets of hard scattering at Fermilab. Several fixed target experiments searched for jets using the energy detected in calorimeters with limited aperture (Δϕ=±45^∘, Δ y≈± 0.35 to 0.55) at mid-rapidity in the p+p c.m. system. The first claim for discovering the jets from the “quark-quark scattering model” was by Fermilab E260 <cit.>  who found that for √(s)=19.4 GeV the cross section for the jet, which was defined by summing all the energy in their calorimeter, was “similar in shape to the single particle cross section but two orders of magnitude larger.'"


As calorimeters in experiments got larger, the “jet” to single particle ratio kept getting larger until the jet fiasco ended dramatically when the NA5 fixed target experiment at CERN, with a hadron calorimeter which covered the full azimuth with a c.m. polar angular interval 54^∘<θ^*<135^∘ (Δ y≈± 0.9) in the p+p c.m. system at √(s)=23.8 GeV, presented their results <cit.>. The coup de grace was their conclusion:“The events selected by the full calorimeter trigger show no dominant jet structure. They appear to originate from processes other than two constituent scattering.” The actual publication of the NA5 result <cit.> was perhaps even clearer:“The large transverse energy observed in the calorimeter is the result of a large number of particles with a rather small transverse momentum”. 

The problem with the mistaken claim of `jets' was that the difference between single particle and multiparticle measurements was not understood. The principal multiparticle variables are the charge multiplicity distribution dN_ch/dη and the transverse energy (E_T) distribution <cit.> :

    E_T≡∑_i E_i sinθ_i    ,

where the sum is over all particles emitted on an event into a fixed but large solid angle. The NA5 result <cit.> was the first E_T measurement in the form that is still in use at present <cit.><cit.>.

The difference between single and multi-particle distributions is shown in Fig. <ref>. Single particle p_T distributions (left) follow the   

e^-6p_T <cit.> soft physics particle spectrum until p_T≈ 1-2 GeV/c where the hard-scattering power law begins to dominate, roughly 2–3 orders of magnitude down in cross section.  On the other hand, the spectrum of the neutral transverse energy E_T^0 at 
√(s)=62.4 GeV (right) falls exponentially for ≥ 6 orders of magnitude until the hard scattering component of the E_T^0 distribution becomes evident by the break from the exponential spectrum. In the exponential region there was a uniform azimuthal disribution of  E_T^0, with a dominant 2 jet structure for E_T^0>24 GeV <cit.>.

A much clearer separation between “soft" and “hard" physics in such  
spectra was determined at the ISR by the AFS collaboration <cit.> with a full azimuth EM and hadron calorimeter covering the rapidity range |y|<0.9. A study of the 
event shape as a function of E_T, was performed using a principal axis 
analysis. A quantity, “circularity", was defined which 
would be 1 for a totally uniform azimuthal distribution of the components of 
E_T and zero if all the E_T were in two narrow jets back to back in 
azimuth. The distributions (Fig.<ref>) show no evidence of jets for E_T< 25 GeV at 
any c.m. energy. However for E_T>25 GeV, there is an increase in 
low circularity events, leading up to a dominance of low-circularity events from a two-jet structure for 
E_T≥ 31 GeV at √(s)=63 GeV. 
 

 
 
     These beautiful measurements from the year 1983 made it clear that the jets of hard 
scattering could indeed be observed using E_T distributions; but that hard 
scattering effects have negligible influence on the shape of E_T spectra in 
proton-(anti)proton collisions for the first 4, or even 6, orders of magnitude 
of cross section, depending on the c.m. energy. However the first convincing evidence of jets and the validity of  as the mechanism for hard-scattering came at the ICHEP1982 conference in Paris.


§ THE FINAL PROOF OF JETS AND  BY MEASUREMENTS 1980–1982

The rejection of the Fermilab E260 <cit.> jet claim by the observation of no jets in a better measurement at CERN <cit.>, presented at the ICHEP1980, led to confusion in the High Energy Physics community in the U. S. during the period from the ICHEP1980 to the ICHEP1982. There was no clear understanding of why the jets of   were not observed in the full azimuth calorimeter which led to doubts by many of the utility and validity of   tests in hadron-hadron collisions. To get an idea of the thinking during this period, I had to give a seminar at my laboratory, BNL, in March 1982 with the title:“Why I believe in jets in spite of calorimeter experiments. For  tests try to minimize the effect of jets.”

In March 1980, I had moved from the Rockefeller University to BNL to help save ISABELLE, the √(s)=800 GeV superconducting p+p collider under construction. My assignment was to help sort out the problems they were having with the superconducting magnets that quenched at a much lower magnetic field than expected. I described my work in this period in a previous EPJH article <cit.>, so I'll skip to March 1982 when I transferred to the BNL Physics Department and resumed work on the CCOR experiment. One of the problems with the CCOR full azimuth superconducting solenoid detector was that it did not have any specific electron identification device like the Cherenkov counters in CCRS, so that in trying to measure e^+ e^- pairs we had to trigger on clusters with energy > 2.5 GeV in each arm of our EMcalorimeters (as described in Section <ref>). This left us with ≈ 750,000 π^0 pairs which 
we decided to analyze in the same way we would analyze e^+ e^- pairs in the detector, namely the invariant mass M_ππ of the pair, its net P_t and rapidity Y and cosθ^* in the c.m. system of the pair.  

There were enough events so that we could select π^0 pairs with net P_t<1 GeV/c (or P_t<2 GeV/c for M_ππ>11 GeV/c^2) and |Y|<0.35. Then we moved to the c.m. system of the pair, in which the two π^0 are back to back at an angle cosθ^*, by the simple rapidity shift y*=y-Y (Sec. <ref>) for each π^0. We knew from FFF <cit.> that the trigger π^0 had almost the same p_Tt as the parton p̂_Tt z_ trig≈ 1.0. Thanks to the full azimuth charged particle tracking we were able to measure z_ trig from our own data by summing over all charged particles within an azimuthal angle ± 60^∘ of the trigger in the rapidity range |y|<0.7, multiplying by 1.5 to account for the missing neutrals <cit.>.
We noted that the large measured values of z_ trig>0.9 for M_ππ>8 GeV/c^2 and measured value of |j_Ty|=0.44 GeV/c justify the assumption that the axis of the di-pion system in the pair c.m. system follows closely that of the original parton-parton scattering with √(ŝ)≈ M_ππ. These measured cosθ^* distributions are shown in Fig. <ref> and should be able to be compared directly to the cosθ^* distributions of the elementary  subprocesses in terms of dσ/dcosθ^* at fixed ŝ, Eq. <ref>, easily derived from Eq. <ref>:

    .dσ/dcosθ^*|_ŝ=πα_s^2(Q^2)/2ŝΣ^ab(cosθ^*)       .
 
The effect of |j_Ty| is negligible, well within the bins in cosθ^*.  



In fact the measured distributions for the various M_ππ≈ŝ all have the same shape which we compared directly to the  angular distributions from Eq. <ref> for the subprocesses, gg, qg, qq' and qq elastic scattering <cit.> also shown in Fig. <ref>. The measured distributions are steeper than all the  constituent scattering subprocess distributions with constant α_s(Q^2). However once the increase of the  coupling constant α_s(Q^2), with decreasing Q^2=-t̂ as cosθ^* increases, is taken into account as shown as the dashed curve for qq with α_s(Q^2), the measurement and   predictions agree very well. We had this data for two years until Dave Levinthal and Steve Pordes realized that we had to include the  α_s(Q^2) evolution.

I was lucky enough to present this result <cit.> at the ICHEP82 meeting in Paris after the session where UA2 <cit.> revealed their di-jet LEGO plot measured in a highly segmented total absorption calorimeter covering the azimuthal range Δϕ=300^∘ with |y|<1.0. This now famous plot (Fig. <ref>) clearly  indicated di-jets in collisions at √(s)=540 GeV, one of the first results at the CERN Sp̅pS p̅+p collider, which immediately convinced everybody that jets existed. 


These two measurements and Günter Wolf's outstanding rapporteur talk, in which he also verified the cosθ^* calculation with his own overlay plot (lowest right plot in Fig. <ref>), convinced all observers, and as the news spread, everybody else, that  and jets were the cornerstone  of the Standard Model. Quotes from Günter's proceedings <cit.> are worth repeating:“Amongst the most exciting results are the direct measurement of the parton-parton scattering angular distribution and the observation of very energetic jets at the SPS collider." “ provides a consistent description for the underlying constituent scattering processes." Since that time  and jets have become the standard tools of high energy particle physics. 



 §.§ A few more recent collider results on  and jets



When the CERN p̅+p collider experiments started to publish di-jet angular distribution measurements  compared to  constituent scattering subprocess distributions, e.g. UA1 <cit.> (Fig. <ref>a), I made a plot (Fig. <ref>b) of their data for √(s)=540 GeV and the CCOR measurement at 
 √(s)=62.4 GeV with my calculations of the  qq, gq and q̅q subprocess angular distributions . The p+p data aligned best with the qq calculation while the p̅+p data aligned beautifully with the q̅q calculation for |cosθ^*|≤ 0.5 which I thought was pretty neat in 1983 but I never published it.
 

The relatively recent jet cross section measurements (Fig. <ref>) as a function of p_T and rapidity at the Fermilab Tevatron in p̅+p collisions at √(s)=1.96 TeV and the CERN LHC p+p collider at √(s)=7 TeV agree incredibly well with Next to Leading Order (NLO)  . Note that at mid-rapidity the D0 data follow the typical hard-scattering power law but drop sharply at large p_T and y, due to conservation of energy. The drop is much weaker at large p_T and y for the CMS data because of the 3.5 times larger c.m. energy. 


Recent two-particle correlation measurements at RHIC (Fig. <ref>) nicely show that the x_E distribution of direct-γ-h correlations plotted as a function of ξ=-ln x_E really does measure the fragmention function as measured in e^+ e^- collisions at √(s)=14 and 44 GeV <cit.> and that the p_ out distribution has two components, a Gaussian likely to be from the intrinsic k_T of partons in the nucleon, and a power-law tail from NLO  gluon emission as suggested in <cit.>.  


§ HADRON COLLIDER DISCOVERIES, NOT EXACTLY  1983–2012




To keep the record straight, I think that it is important to note several major discoveries at hadron colliders that are not exactly  but nevertheless are key elements of the Standard Model.
The W and Z bosons of the Weak interactions were discovered at the CERN p̅+p collider in 1983 by experiments UA1 (W) <cit.>, (Z) <cit.>;  and UA2 (W) <cit.> (Z) <cit.>.   
Figure <ref>a shows a UA2 measurement of W^±→ e^± + X with a nice Zichichi signature and Fig. <ref>b the actual UA1 discovery plot of the Z^0→ e^+ + e^-.[The Z^0 plot reminds me of Fig. <ref>b; but for Fig. <ref>b it was Carlo Rubbia who had the last laugh, a well deserved Nobel Prize.] The top quark was discovered at the Fermilab Tevatron p̅p collider by D0 <cit.> and CDF<cit.> (Fig. <ref>c) and the Higgs Boson was discovered at the CERN-LHC by ATLAS <cit.> and CMS <cit.>(Fig. <ref>d).  


§  AT RELATIVISTIC HEAVY ION COLLIDERS 2000–2017 

    

 §.§ From Bjorken Scaling to  to the 
  
    
      Bjorken scaling not only led to the parton model and  as we have already discussed, but also led to the conclusion <cit.> that “superdense matter (found in neutron-star cores, exploding black holes, and the early big-bang universe) consists of quarks rather than of hadrons", because the hadrons overlap and their individuality is confused. This is different from earlier models which take hadrons as the basic entities <cit.>. Collins and Perry <cit.> called this state “quark soup" but used the equation of state of a gas of free massless quarks from which the interacting gluons acquire an effective mass which provides long-range screening. They also pointed  out that for the theory of strong interactions (), “high density matter is the second situation where one expects to be able to make reliable calculations—the first is Bjorken scaling". In the Bjorken scaling region, the theory is asymptotically free at large momentum transfers while in high-density nuclear matter long range interactions are screened by many-body effects, so they can be ignored and short distance behavior can be calculated with the asymptotically-free   and relativistic many-body theory. Shuryak <cit.> codified and elaborated on these ideas and provided the name “QCD (or quark-gluon) plasma"   for “this phase of matter", a plasma being an ionized gas.   
   
        It didn't take long for others to realize that relativistic heavy ion (RHI) collisions could provide the means of obtaining superdense nuclear matter in the laboratory <cit.> <cit.>. 
 The kinetic energy of the incident projectiles would be dissipated in the large 
volume of nuclear matter involved in the reaction.  The system is expected 
to come to equilibrium, thus heating and compressing the nuclear matter so that it undergoes a phase transition from a state of nucleons containing bound quarks and gluons to a state of deconfined quarks and gluons, the Quark Gluon Plasma (), in chemical and thermal equilibrium, covering the entire
volume of the colliding nuclei or a volume that corresponds to many units of the characteristic length scale. 

In the terminology of high energy physics, this is called a “soft” (low Q^2) process, related to the   confinement scale

    Λ^-1_ QCD≃ (0.2 GeV)^-1≃ 1       .

   With increasing temperature, T, in analogy to increasing Q^2, the strong coupling constant α_s(T) becomes smaller, reducing the binding energy,  and the string tension, σ(T), becomes smaller, increasing the confining radius, effectively screening the potential<cit.>: 
  
    V(r)=-4 3α_s r+σ r → 
    -4 3α_s r e^-μ_D r+σ (1-e^-μ_D r)μ_D
 
where μ_D=μ_D(T)=1/r_D is the Debye screening mass <cit.>. For r< 1/μ_D a quark feels the full color charge, but for r>1/μ_D, the quark is free of the potential and the string tension, effectively deconfined. The properties of the  can not be calculated in   perturbation theory but only in Lattice  Calculations <cit.>.



 §.§ From ISABELLE to CBA to RHIC 1983

Following the discovery of the W and Z bosons at CERN, the √(s)=800 GeV p+p collider at BNL, ISABELLE, which had been renamed Colliding Beam Accelerator (CBA), was cancelled by HEPAP (the U.S.  High Energy Physics Advisory Panel) on July 11, 1983, but was miraculously immediately resuscitated by NSAC (the U.S. Nuclear Science Advisory Committee) to eventually become the √(s_NN)=200 GeV A+A Relativistic Heavy Ion Collider (RHIC) <cit.> whose purpose was to discover the properties of nuclear matter under extreme conditions with possible discovery of new states of matter, e.g. the . In Ref. <cit.>, I discussed several lucky breaks that I had in being able to attend the  ICHEP82 and then to present the lecture with the results shown in Fig. <ref>. Well, it turned out that I had another important lucky break in August 1983 just after RHIC became a gleam in the eye of NSAC. The chair of the BNL physics department, Arthur Schwartzschild, a Nuclear Physicist,  offered me five BNL Nuclear Physicists to participate in the set-up and data taking of an α+α run which had been scheduled for 16–30 August 1983 at the CERN ISR,  as well as to help analyze the data. The purpose was to get collider experience for the RHIC proposal and to help understand an “exciting result” from the previous α+α run at the ISR. 


  §.§.§ “Exciting result”? How I became a nuclear physicist!

It started in 1979, when Martin Faessler <cit.> and collaborators proposed to measure p+α and α+α collisions in the CERN-ISR using the SFM. The proposal was approved which  led to runs with α+α at √(s_NN)=31 GeV and p+α at √(s_NN)=44 GeV in 1980, with a subsequent run in 1983 with α+α, p+α, d+d and p+p interactions all at the same √(s_NN)=31 GeV. The high energy physicists at the ISR had the option of turning off their detectors and resting for a few weeks or continuing to operate their detectors for the nuclear collisions, with the possibility of exciting new physics results. They all opted to continue. Exactly same option and, predictably, exactly the same outcome occurred at the LHC 30 years later.

Once again, the publications from measurements in a new field started out with an incorrect result from the 1980 run, this time  where I was a co-author <cit.>. Incredibly, it eventually turned out that this result was helpful. The 1980 α+α run was at the full ISR energy, √(s)=62.4 GeV for p+p collisions which was  only √(s_NN)=31.2 GeV for α+α where Z/A=1/2.  There was no comparison p+p data at √(s)=31.2 GeV in the 1980 run, only √(s)=62.4 GeV data. However, there was comparison p+p data at √(s)=31.2 GeV from the 1979 run which was not used because of uncertainty of a change in the absolute p_T scale for the EM calorimeter by ≈ 5%, a huge effect when trying to measure a cross section that drops like 1/p_T^n with n≈ 10. The √(s)=62.4 GeV p+p data were used for comparison, but extrapolated to √(s)=31.2 GeV by a method that I kept saying was wrong whenever I was able to communicate with my collaborators adequately (no internet!!!) because I was still making magnets at BNL ≈ 6000 km away. I told them to use x_T scaling but they ignored my advice. 

For high p_T hard-scattering, which is the result of scattering of pointlike partons, the ratio of the cross sections in p+A or B+A collisions to the p+p cross section should be simply equal to the product of the number of nucleons in the projectile and target, a factor A times larger for p+A and B× A for B+A collisions.  However an `anomalous nuclear enhancement' was found in p+A collisions by Jim Cronin and collaborators at Fermilab <cit.>. The pion cross section ratio increased as A^α(p_T) where α(p_T) peaked at ∼ 1.15 for p_T=4-5 GeV/c for 19.4≤√(s_NN)≤ 27.4 GeV. By contrast, the COR measurement in α+α collisions <cit.> for p_T≥ 5 GeV/c was equivalent to α(p_T)=1.3 a factor of ∼ 1.6 larger for the αα/pp cross section ratio than the extrapolation of Cronin's measurement. To quote a review by <cit.> of the results from the 1980 α+α run:“If this trend is confirmed, it could eventually signify that something very interesting is going on in nucleus nucleus collisions.” 

The interesting results from the α+α collisions spread to the CERN management and through the nuclear physics grapevine to the chairman of the BNL physics department, Arthur Schwartzschild, who offered me the five BNL Nuclear Physicists. My CERN collaborators were happy about this because they also wanted Nuclear Physicists to help them understand the “exciting result”.
  
Well, of course, we found out that the “exciting result” was wrong because our new result from the 1983 α+α and p+p runs at √(s_NN)=31 GeV <cit.> was α(p_T)=1.14± 0.01 which now agreed with Cronin's result. We also had a preliminary result which Sanki Tanaka <cit.> was able to complete in time to present at the Quark Matter 1983 conference, the last week in September 1983, which had been moved from Helsinki to BNL. This result showed that the ratio of the cross sections for αα/pp as a function of E_T varied by 2 to 6 orders of magnitude, so that the A^α(p_T) Cronin formalism was completely inadequate. We soon understood that this was because E_T was a multiparticle distribution <cit.> which turned out to be very useful in Relativistic Heavy Ion collisions. Based on these ISR α+α results, I joined with Chellis Chasman, Ole Hansen, Andy Sunyar of BNL, Lee Grodzins of MIT [Sunyar and Grodzins along with Maurice Goldhaber had made the famous measurement of the helicity of the neutrino at BNL <cit.>.], Shoji Nagamiya of Columbia and others in an experiment (E802) to explore all aspects of relativistic heavy ion collisions at the new heavy ion beam at the BNL-AGS built to prepare for RHIC.


 §.§ RHIC and its Experiments: Design and Construction-1991–2000
 
The initial proposal by BNL to the U.S. Department of Energy to build RHIC was in 1984; the first funds for construction of RHIC were in the U.S. budget for Fiscal Year 1991; construction was completed and the first Au+Au collisions at √(s_NN)=130 GeV were in 2000 and with the standard c.m. energy √(s_NN)=200 GeV in 2001 <cit.>. The first call for Letters of Intent for experiments was in April 1990 which were evaluated in November 1990 with updated LOI submitted in July 1991. The first Program Advisory Committee (PAC) to evaluate these updated LOI's approved the STAR proposal to join with a BNL TPC proposal to build a large Time Projection Chamber (TPC) concentrating on hadrons.  Three other proposals: di-muon, OASIS and TALES/SPARHC were rejected but told by the Associate Lab Director Mel Schwartz to merge into an experiment (most like TALES/SPARHC, my affiliation) to study electrons and photons emerging from the  , which became the PHENIX experiment. Two smaller experiments were also approved <cit.>. 

     The STAR experiment is similar to a conventional solenoid collider detector of the late 1980's except that its solenoid with 2.6m radius and magnetic field B=0.5 T is not superconducting. The TPC covers the full azimuth at mid-rapidity, |η|≤1.0. Particle identification is done with dE/dx in the TPC and Time of Flight counters. An EMcalorimter outside the solenoid has segmentation Δη×Δϕ=0.05× 0.05 with a shower-maximum pre-converter/detector 5 X_o deep for improved γ/π^0 separation. 
     
     The PHENIX experiment is a two-arm spectrometer with a fine grain EMcalorimeter Δη×Δϕ≈0.01×0.01 to separate single-γ and resolve π^0→γ+γ with p_T up to ≈ 20 GeV/c. Each arm has a Ring Imaging Cerenkov counter, time-of-flight (TOF) and drift-chamber tracking for e^±, γ and identified hadron measurements at mid-rapidity; with full azimuth muon spectrometers at forward and backward rapidity 1.1<|y|<2.2-2.4. Full azimuth Beam Beam Counters at 3.0≤|η|≤ 3.9 and Zero Degree hadron Calorimeters that measure forward going neutrons within a 2 mrad (|η|>6) cone are used for triggering and luminosity measurement.
     
     It was no accident that PHENIX had all the features of CCRS (Section:<ref>) plus precision TOF for particle identification: I was one of the principal proponents of TALES/SPARHC. This gave PHENIX the possibility of measuring single e^± for p_T>0.3 GeV/c which was crucial for J/Ψ and charm measurements. Measurements of identified hadrons (including charm), although not part of Mel Schwartz's directive, were obviously necessary for understanding the background from their decay. Also, it was always my intention to use single e^± to measure charm <cit.>, because there is no combinatoric background. This is a serious problem in A+A collisions where charged multiplicities rise to ≈ A times that in p+p for the most central collisions where the two nuclei fully overlap <cit.> (Fig. <ref>). 
 
    
        


 §.§ How to find the  1986–2000

At the time of the proposals for experiments at RHIC (also for the LHC <cit.>) in 1990-91, there were two proposed signatures of the : strangeness enhancement <cit.> and the “gold-plated”signature for  deconfinement in the , J/Ψ suppression <cit.>. 
Matsui and Satz predicted  that J/Ψ production in A+A
collisions will be suppressed by Debye screening of the quark
color charge in the . The J/Ψ is produced when two gluons
interact to produce a c c̅ pair which then resonates to form the
J/Ψ. In the , the c c̅ interaction is screened so that the 
c c̅ go their separate ways and eventually pick up other quarks at
the periphery to become open charm.  However, as pointed out a year later <cit.>, enhanced production of c and c̅ quarks in A+A collisions, so that many of the “other quarks” picked up are c or c̅, could lead to recombination of cc̅ into J/Ψ which might “hinder” J/Ψ suppression as evidence for the . Another problem was that the J/Ψ is suppressed in p+A collisions <cit.>. These issues were worked out in further detail by analysis of J/Ψ measurements at the CERN fixed-target heavy ion program <cit.> with the prediction of enhancement of J/Ψ at LHC energies. 



  §.§.§ A hard-scattering  signature based on  1997–1998

A new tool for probing the color response function of the  with a firm basis in   was developed shortly before RHIC turned on. I found out about this in 1998 at the  workshop in Paris <cit.>, when Rolf Baier asked me whether jets could be measured in Au+Au collisions because he had made studies in p <cit.> of the energy loss, by `coherent' (LPM) gluon bremsstrahlung, of hard-scattered partons “with their color charge fully exposed” traversing a medium, “with a large density of similarly exposed color charges”. This leads to a reduction of the p_T of both the outgoing partons and their fragments, hence a reduction in the number of partons or fragments at a given p_T, which is called jet quenching. The effect is absent in p+A or d+A collidons beause no medium is produced (Fig. <ref>a)
   

The energy loss of an outgoing parton, -dE/dx, per unit length (x) of a medium with total length L due to coherent gluon bremsstrahlung is proportional to the 4-momentum-square, q^2(L), transferred to the medium and takes the form:

    -dE  dx ≃α_s q^2(L)=α_s q̂  L      .

q̂, the transport coefficient of a gluon in the medium, is defined as the mean 4-momentum transfer-square, q^2, to the medium by a radiated gluon, per gluon mean free path, which can be calculated with  <cit.>. Figure <ref>b shows an early calculation of q̂ <cit.> . 

I told Rolf (and put in the proceedings) that because the expected energy in a typical jet cone R=√((Δη)^2+ (Δϕ)^2) in central Au+Au collisions at √(s_NN)=200 GeV would be π R^2×1/2π× dE_T/dη=R^2/2 × dE_T/dη ∼ 300 GeV for R=1, where the kinematic limit is 100 GeV, jets can not be reconstructed in Au+Au central collisions at RHIC. This is still correct at present (19 years later) where the solution is to make smaller jet cones, which may (or may not) be a problem. 

I also told Rolf the good news that the jet suppression could be measured by single particle inclusive and two-particle correlations at RHIC as we had done at the CERN-ISR and that the PHENIX detector had actually been designed to make such measurements. 



 §.§ Measurements relevant to   in A+A collisions at RHIC and LHC

Measuring and understanding the properties of nuclear matter under extreme conditions and possibly 
the  requires knowledge of Statistical Physics, Thermo- and Hydro- dynamics without much  input. However, there were several important discoveries and measurements which did involve .


  §.§.§ Baryon chemical potential measured without particle identification

In an equilibrated thermal medium, particles should follow a Boltzmann distribution in the local rest frame <cit.>

    d^2σdp_L p_T dp_T=d^2σdp_L m_T dm_T∝1e^(E-μ)/T± 1∼ e^-(E-μ)/T     ,

where m_T=√(p_T^2+m^2) and μ is a chemical potential. In fact,   the ratios of particle abundances (which are dominated by low p_T particles) for central Au+Au collisions at RHIC, even for strange and multi-strange particles, 
are well described <cit.> by fits to a thermal distribution, 
          
    d^2σdp_L p_T dp_T∼ e^-(E-μ)/T→p̅ p=e^-(E+μ_B)/T/e^-(E-μ_B)/T=e^-(2μ_B)/T     ,

 with similar expressions for strange particles. μ_B (and μ_S) are chemical potentials associated with each conserved quantity: baryon number, μ_B,  (and strangeness, μ_S). 

However for this problem there is also Lattice  thermodynamics which can calculate μ_B from the net electric charge distributions of non-identified charged particles (n^+ -n^-) <cit.>.
The theoretical analyses are made by a Taylor expansion of the free energy F=-Tln Z around the  freezeout temperature T_f where Z is the partition function, or sum over states, which is of the form 


    Z∝ e^-(E-∑_i μ_i Q_i)/kT
 and μ_i are chemical potentials associated with conserved charges Q_i.  The terms of the Taylor expansion, which are obtained by differentiation, are called susceptibilities, denoted χ. 

The only connection of this method to mathematical statistics is that the Cumulant generating function in mathematical statistics for a random variable x is also a Taylor expansion of the ln of an exponential:

    g_x (t)=lne^tx=∑_n=1^∞κ_n t^n/n!    κ_m =.d^m g_x (t)/dt^m|_t=0     .

Thus, the susceptibilities are Cumulants in mathematical statistics terms.  
The first four Cumulants are κ_1=μ≡x,  
κ_2=(x-μ)^2≡σ^2, κ_3=(x-μ)^3, . Two so-called normalized or standardized Cumulants are common in this field, the skewness, S≡κ_3/σ^3 and the kurtosis, κ≡κ_4/σ^4. The theoretical results are presented as ratios of Cumulants so that the volume dependences of μ, σ S, κ cancel. 

The measured values of the temperature T_f and μ_B are obtained <cit.> by comparing the measured values of κ_1/κ_2 and κ_3/κ_1 to the Lattice  calculations <cit.>, which are given as functions of T_f and μ_B. Figure <ref> shows that the PHENIX + Lattice results for μ_B from net-charge fluctuations, with no particle identification, are in excellent agreement with the best accepted analysis of μ_B from baryon/anti-baryon ratios <cit.>. Both the μ_B and T_f (not shown) results <cit.> also agree with the more conventional best accepted values, which I believe was a first for measurements plus Lattice   calculations in A+A collisions! 





  §.§.§ Discovery of the  at RHIC by suppression of high p_T particles—2002

The discovery at RHIC  <cit.> that high p_T π^0 produced by hard parton-parton scattering in the colliding Au+Au nuclei are suppressed in central Au+Au collisions by a factor of ∼5 compared to pointlike scaling from p+p collisions is arguably the  major discovery in Relativistic Heavy Ion Physics. 
 
 	
In Fig. <ref>, the suppression of the many identified particles measured by PHENIX at RHIC is presented as the Nuclear Modification Factor, 
R_AA(p_T), the ratio of the yield of e.g. π per central Au+Au collision (upper 10%-ile of observed multiplicity)  to the pointlike-scaled p+p cross section at the same p_T, where T_AA is the average overlap integral of the nuclear thickness functions: 
   
    R_AA(p_T)=(1/N_AA) d^2N^π_AA/dp_T dy/T_AA   d^2σ^π_pp/dp_T dy   .

  
The striking differences of R_AA(p_T) in central Au+Au collisions for the many particles measured by PHENIX  (Fig. <ref>) illustrates the importance of particle identification for understanding the physics of the medium produced at RHIC. The most notable observations are: 


  1. the equal suppression of π^0 and η mesons by a constant factor of 5 (R_AA=0.2) for 4≤ p_T ≤ 15 GeV/c, with suggestion of an increase in R_AA for p_T > 15 GeV/c;

  2. the equality of suppression of direct-single e^±_ HF from heavy flavor (c, b quark) decay, and π^0 at p_T 5 GeV/c; 

  3. the non-suppression of direct-γ for p_T≥ 4 GeV/c. 

For p_T 4 GeV/c, the hard-scattering region,  the fact that all hadrons are suppressed, but direct-γ are not suppressed, indicates that suppression is a medium effect on outgoing color-charged partons, likely due to energy loss by coherent Landau-Pomeranchuk-Migdal radiation of gluons, predicted in p <cit.>. 


  §.§.§ , the perfect liquid, from charm suppression and flow–2007

The measurement of direct single e^± (also called heavy flavor e^± at RHIC) at mid-rapidity by PHENIX <cit.> in p+p collisions at √(s)=200 GeV is shown in Fig. <ref>a,b. The background from internal and external γ conversions was determined by the converter method as in section <ref>. The data are compared to a fixed-order-plus-next-to-leading-log (FONLL) p calculation <cit.> which is in excellent agreement with the measurement and gives the relative contributions of c and b quark decay.    

  
Figure <ref>c shows the R_AA of direct single heavy flavor e^± and π^0 in √(s_NN)=200 GeV Au+Au collisions <cit.> which become equal in the range 4≤ p_T≤7 GeV/c.  Initially this result was a surprise because heavy flavor quarks were predicted to lose less energy than light quarks due to the “dead cone effect” which happens in QED bremsstrahlung <cit.>. Figure <ref>d shows the anisotropic eliptical flow measurement v_2^ HF for the heavy flavor quarks and for π^0 <cit.>. The heavy quarks at p_T≈ 2 GeV/c are actually barely relativistic, because γβ=p_T/m=2.0/1.3≈ 1.5, but have a significant v_2^ HF. 

The v_2^ HF in this region suggested <cit.> that the charm quarks thermalize in the medium  which responds as a thermalized fluid with a small transport mean free path. Thus they treat the heavy quark in the medium as a thermal diffusion problem with diffusion coefficient D=6η/(ϵ+p) where η is the shear viscosity, ϵ is the energy density, and p the pressure. The enthalpy (ϵ +p)=Ts for zero baryon chemical potential, μ_B (a reasonable assumption at √(s_NN)=200 GeV, Fig. <ref>), where T is the temperature and s is the entropy density. Obviously this is a thermodynamic/hydrodynamic problem with some  in the Monte Carlo to get R_AA but the results, shown as the dashes for two different values of D=3/(2π T) and D=12/(2π T) on Fig. <ref>c,d, lead to a spectacular conclusion. Taking D=6η/Ts ≈ (6 to 4)/(2π T) as the most reasonable range that fits both R_AA and v_2^ HF in Fig.  <ref>c,d <cit.>, gives the result:

    η/s=(2 to 4/3)/4π
           
which is intriguingly close to the conjectured <cit.> quantum lower bound, η/s=1/4π. 

This is why we claimed the discovery of the , the perfect liquid, at RHIC  <cit.>, <cit.>, <cit.>,<cit.>, <cit.>. 



  §.§.§ J/Ψ enhancement not suppression proves the existence of the  at the LHC

PHENIX measurements of J/Ψ suppression (R_AA) in Au+Au collisions at √(s_NN)=200 GeV  relative to point-like scaling of p+p collisions at mid-rapidity <cit.> Fig. <ref>a turned out to be nearly identical to the NA50 fixed-target measurements in √(s_NN)=17.2 Pb+Pb collisions at CERN <cit.>.

The equality of J/Ψ suppression at √(s_NN)=17.2 and 200 GeV was was elegantly explained as recombination or coalescence of c and c̅ quarks in the  to regenerate J/Ψ <cit.>. 

Miraculously this made the observed R_AA equal at SpS and RHIC c.m. energies. I called this my “Nightmare Scenario” because I thought that nobody would believe it. The good news was that such models are testable because they predicted the reduction of J/Ψ suppression or even an enhancement (R_AA> 1) at LHC energies <cit.>, <cit.>,<cit.>, which would be spectacular, if observed. 

As shown in Fig. <ref>b, the most recent ALICE <cit.> measurement of R_AA for J/ψ at √(s_NN)=2.76 TeV exhibits considerably less suppression for both J/ψ→ e^+ e^- at mid rapidity and J/ψ→μ^+ μ^- at forward rapadity than the PHENIX measurements at √(s_NN)=200 GeV in  Fig. <ref>a. The reduction of J/Ψ suppression at the LHC compared to RHIC is a clear observation of regeneration at LHC which directly proves the existence of the , since it is evidence that the large number of c and c̅ quarks produced (with their color charge hidden by Debye screening) freely traversed the medium (with a large density of similarly screened color charges) until they met another quark close enough within the screening radii to form J/Ψ's.   

However <cit.>, these beautiful results do not prove that J/Ψ are deconfined in the . According to Satz, the crucial issue is whether the medium modifies the fraction of produced cc̅ pairs which form J/Ψ. Dissociation of J/Ψ in the medium would reduce the observed J/Ψ/cc̅ ratio in A+A compared to p+p collisions, i.e R_AA^J/Ψ/R_AA^cc̅≪ 1. Personally, I think that Debye screening which is the basis of suppression of J/Ψ in the  is proved by Fig. <ref> but Satz's requirement may be important to find how low in √(s_NN) the  is formed.


  §.§.§ jet quenching at the LHC

Although nobody at RHIC had claimed to measure the quenching of fully reconstructed jets in √(s_NN)=200 GeV Au+Au collisions, because the multiparticle background is too large, as soon as the LHC started its 2760 GeV run, unbalanced jets were visibile on the event displays for both ATLAS <cit.> and CMS (Fig. <ref>) <cit.>
 



§ SUMMARY AND CONCLUSIONS

In the years 1972-1982 experiments at Hadron Colliders made major contributions to the theory of  which was developed in this same period. More recently, Heavy Ion Colliders have opened up a new field of the study of superdense nuclear matter in the laboratory, leading to the discovery of the Quark Gluon Plasma which can be analyzed with lattice .  Highlights of these achievements can be summarized as follows.



 §.§ Hadron Colliders and  

The CERN Intersecting Storage Rings (ISR), Geneva, SZ, 1971–1983.
 
This was the first hadron collider, with p+p collisions at c.m. energy √(s)=23.5-62.4 GeV. Also d+d α+α p+α and p+p̅ experiments were performed. The largest contributions for the development of  were from the ISR.


  * Discovery of particle production at high p_T≥ 3 GeV/c, 1972.

  * Discovery of charm particles by direct single e^± production in 1974, but not understood until 1976.

  * First application of  theory to ISR π^± and π^0 spectra with 3≤ p_T≤ 14 GeV/c, 1978.

  * Discovery of direct-γ production 1979-1980 as predicted by  in 1977. 

  * Observation of the di-jet structure of hard-scattering via two-particle correlations including discovery and measurements of k_T, the transverse momentum of a parton in a nucleon, and measurement of j_T the average momentum of jet fragments transverse to the jet axis, 1977-1979.

  * First measurement of the cosθ^* distribution of elementary  subprocesses including the increase of the  coupling constant α_s(Q^2) with decreasing Q^2 at more forward angles, 1982.

  * First direct measurement of the gluon structure function G(x,Q^2), 1987. 

 

The CERN Sp̅pS Collider 1981–1991. Nobel Prize winning hadron collider with p̅+p collisions at √(s)=546-630 GeV.


  * First definitive observation of jets in hadron collisions, 1982.

  * Discovery of the W^± `intermediate boson' of weak interactions, 1983.

  * Discovery of the Z^0 boson of weak interactions, 1983.

 

ISABELLE at BNL, Upton, NY, USA, 1978–1983 (cancelled)

ISABELLE was designed as p+p collider with √(s)=800 GeV. This was the first collider with superconducting magnets, which led to problems during construction. Eventually greatly improved superconducting accelerator magnets were developed and tested, known as the Palmer Magnet <cit.>. This design has been used by all following colliders except for the Fermilab Tevatron Collider. 


Tevatron Collider at Fermilab, Batavia, Illinois, USA, 1986–2011

This was a √(s)=1.8 TeV p̅+p collider with a different superconducting magnet design than ISABELLE. However, the Palmer Magnet developed at ISABELLE was based on the superconducting cable developed for the Tevatron.
 

  * Discovery of the top quark, 1995

  * Measurement of jet cross sections over a wide range of p_T and rapidity in agreement with  .

 

Superconducting Super Collider (SSC), Waxahachie, Texas, USA, 1990–1993 (cancelled) 

The SSC was designed as a √(s)=40 TeV p+p collider. Its demise hurt High Energy Physics in the U.S.A; but on the positive side, in 1994, the U.S. High Energy Physics Advisory Panel recommended that the U.S. siginificantly participate in the CERN Large Hadron Collider to help maintain U.S. involvement in High Energy Physics. In 1997 the DOE recommended spending a total of more than $531 million for U.S. contributions to both the accelerator and the experiments, the first agreement between CERN and the U.S. government. This allowed CERN to build the LHC in a single stage of √(s)=14 GeV rather than the originally approved two stage construction with missing magnets <cit.>.


The CERN Large Hadron Collider, LHC, 2008–present.

The largest and highest energy p+p collider with √(s)=7-13 TeV. Also Pb+Pb and p+Pb collisions.
 

  * Measurement of jet cross sections over a wide range of p_T and rapidity in agreement with  .

  * Discovery of the Higgs Boson, 2012.

  * Discovery of suppression of jets in Pb+Pb collisions, 2010.

  * Discovery of J/Ψ enhancement compared to measurements at RHIC, evidence for the Quark Gluon Plasma, 2014.

 

RHIC, the Relativistic Heavy Ion Collider at BNL, 2000–present.

RHIC is a Heavy Ion Collider with c.m. energy per nucleon pair, √(s_NN)=19.6-200 GeV, and the first polarized p+p collider with √(s)=500 GeV. RHIC has provided collisions of p+p, p+Au, p+Al, d+Au, ^3He+Au, Cu+Cu, Cu+Au, Au+Au and U+U.


  * Discovery of jet quenching predicted for the , 2002.

  * Discovery of the  as a perfect liquid with shear viscosity/entropy density near the quantum limit, 2005–2007.


 

 §.§ Future Possibilities for 

A remaining problem with  is the need to utilize structure and fragmentation functions, which come from experimental measurements, in the calculations. An excellent possibility for the future is to be able to also calculate the structure and fragmentation functions in . [Thanks to Norman Christ for this suggestion.] 




§ APPENDIX




 §.§ The relativistic longitudinal variable, y, rapidity


Any particle with momentum P and energy E can be represented by its longitudinal momentum P_L, which is subject to a Lorentz transformation, and its transverse momentum P_T which is not affected, so 
E^2=p^2+m^2=p_T^2+p_L^2+m^2 in the nomenclature where the speed of light c≡ 1. The `transverse mass', m_T≡√(p_T^2+m^2)=√(E^2-P_L^2), is invariant under a Lorentz transformation.  
The definition of the rapidity of this particle is:

    cosh y=E/m_T    sinh y=p_L/m_T     dy=dp_L/E


    y=1/2ln(E+P_L/E-P_L)=ln(E+P_L/m_T)      .
 

The advantage of rapidity is that if the rapidity of a particle is y^* in a frame moving with velocity  β=v/c with respect to our system, then the rapidity y of the particle in our system is related to y^* by simple addition, y=Y+y^*, where Y is the rapidity of the moving frame   

    Y=1/2ln(1+β/1-β)      .


Using the rapidity variable, the invariant differential single particle inclusive cross section for a scattered particle with longitudinal momentum p_L along the collision axis, and transverse momentum p_T at azimuthal angle ϕ in cylindrical coordinates, can be written in the Lorentz invariant form:

    E d^3σ/dp^3=Ed^3σ/p_T dp_T dp_L dϕ=d^3σ/p_T dp_T dy dϕ     .



  §.§.§ Pseudorapidity, η

In the limit when (P≫ m) for a particle, E→ P, m_T→ p_T→ E sinθ, p_L→ E cosθ, where θ is the polar angle, the rapidity y (Eq. <ref>) reduces to the pseudorapidity, η :

    coshη=θ    sinhη=θ    tanhη=cosθ


    η=-lntanθ/2      .




 §.§ Parton-parton scattering



In hadron colliders, collisions usually take place with protons of equal and opposite vector momenta P and - P so that the p+p center of mass (c.m.) system is at rest in the laboratory. 

However, the partons in each proton have fractional momenta x_1 and x_2 which are not generally equal so that the parton-parton c.m. system moves longitudinally in the p+p c.m. system (Fig. <ref>). 
For kinematic calculations, the gluon and quark partons are massless; and for simplicity the proton mass M can be ignored because P≫ M for the colliders discussed, so that E^2=P^2+M^2→ P^2 and the particles all have relativistic velocities so that Lorentz Transformations are required.

 The c.m. energy of the p+p collision is given by the Lorentz invariant Mandelstam variable √(s)=2P, where 

    s=-(p_1+p_2)^2=-[(0,0,P,iP)+(0,0,-P,iP)]^2=4P^2      .
 
The partons (with notation  ) are assumed to travel along the longitudinal directions of their protons so that the c.m. energy of the parton-parton collision √(ŝ) is given by:

    ŝ=-(p̂_1+p̂_2)^2   =   -[(0,0,x_1 P,ix_1 P)+(0,0,-x_2 P,ix_2 P)]^2=4P^2x_1x_2 
       =    s x_1 x_2      .
 
The parton-parton c.m. system has longitudinal momentum P_L=(x_1 - x_2)P and total energy E=(x_1 + x_2)P in the p+p  c.m. system, transverse mass =√(ŝ) and thus has rapidity (Eq. <ref>) ŷ:

    ŷ=ln(E + P_L/√(ŝ))=ln√(x_1/x_2)    .

Also, Eqs. <ref>, <ref> can be solved for x_1 and x_2:

    x_1=√(ŝ/s) e^ŷ     x_2=√(ŝ/s) e^-ŷ     .



  §.§.§ Kinematics of parton-parton scattering



Figure <ref> shows the elastic scattering of the two initial partons through angle θ^* in the parton-parton c.m. system, where the two colliding partons have equal and opposite momenta, √(ŝ)/2. 
The scattered parton 3-momenta are equal and opposite, P_3^*=-P_4^*, and their energies are equal, and equal to the magnitude of their 3-momenta,  E_3^*=E_4^*=P_3^*=P_4^*=√(ŝ)/2, because both outgoing partons are assumed to be massless. For the z axis along the direction of the initial partons and the y axis perpendicular to the z axis in the scattering plane,  
the parton 4-momenta in the parton-parton c.m. system can be written as:

    p_1^*=√(ŝ)/2 (0,0,1, i)        p_2^*=√(ŝ)/2 (0,0,-1, i) 
    
    
    p_3^*=√(ŝ)/2 (0,sinθ^*,cosθ^*, i)        p_4^*=√(ŝ)/2 (0,-sinθ^*,-cosθ^*, i)       ,

so that 

    P_L_3^*=-P_L_4^*=√(ŝ)/2cosθ^*       P_T_3^*=-P_T_4^*≡ p_T=m_T=√(ŝ)/2sinθ^*    .
 
 For the outgoing partons, the rapidities are equal and opposite in the parton-parton c.m. system:

    y_3^*=sinh^-1 P_L_3^*/m_T=-y_4^*


The other two Mandelstam invariants of the parton-parton scattering, t̂, the 4-momentum-transfer-squared, and û can be easily computed from Eqs. <ref> and <ref>. 
The invariants are related by the c.m. scattering angle:

    Q̂^2=-t̂=(p_1^* - p_3^*)^2 =ŝ(1-cosθ^*)/2    ;
  
and likewise

    -û=(p_1^* - p_4^* )^2=ŝ(1+cosθ^*)/2    .





§ ACKNOWLEDGEMENTS

 Research supported by U.S. Department of Energy, Contract No. DE-SC0012704.   

99
['t Hooft 1999] tHooft99 't Hooft, G., (Proc. Suppl.)74413–4251999.
[Aad 2010]ATLASPRL105 Aad, G. et al. (ATLAS) 1052523032010.
[Aad 2012]ATLASHiggs Aad. G. et al. (ATLAS) 7161–292012.
[Aamodt 2008]ALICEJINST Aamodt, K. et al. (ALICE) JINST 3S080022008.
[Abachi 1995]D0top Abachi, S. et al. (D0) 742632–26371995.
[Abazov 2008]D0jetPRL101 Abazov, V. M. et al. (D0) 1010620012008.
[Abe 1988] CDF88 Abe, F. et al. (CDF) 611819–18221988.
[Abe 1995] CDFtop Abe, F. et al. (CDF) 742626–26311995.
[Abelev 2014]ALICEPLB734 Abelev, B. et al. (ALICE) 734314–3272014. 
[Abramov 1976]AbramovPLB64 Abramov, V. V. et al. 64365–3681976.    
[Abramowicz 1982]CDHSZPC12Abramowicz, H. et al. (CDHS) 12289–2951982.
[Abrams 1974]Abrams1974 Abrams, G.-S. et al. 331453–14551974.
[Acosta 2005]CDFPRD71 Acosta, D. et al. (CDF). 710320012005. 
[Adamczyk 2014] STARPRL113 Adamczyk, L. et al. (STAR) 1130923012014.
[Adams 2005] STWP Adams, J. et al. NPA757102–1832005.
[Adare 2006]ppg065 Adare, A. et al. (PHENIX) 972520022006.
[Adare 2007a]ppg066 Adare, A. et al. (PHENIX) 981723012007a.
[Adare 2007b]PXPRL98J Adare, A. et al. (PHENIX) 982323012007b.
[Adare 2010]PXPRD82 Adare, A. et al. (PHENIX) 820720012010.
[Adare 2012] ppg136 Adare, A. et al. (PHENIX) 860720082012.
[Adare 2016]ppg179 Adare, A. et al. (PHENIX) 93011910(R)2016.
[Adare 2017]PXPRD95 Adare, A. et al. (PHENIX) 950720022017.
[Adcox 2002a]PHENIXPRL92 Adcox, K. et al. (PHENIX). 881923032002a.
[Adcox 2002b] ppg003 Adcox, K. et al. (PHENIX) 880223012002b.
[Adcox 2005] NPA757PX Adcox, K. et al. (PHENIX) 757184–2832005.
[Adler 2005]ppg019 Adler, S. S. et al. (PHENIX) 710349082005.
[Adler 2006] PXppg029PRD74 Adler, S. S. et al. (PHENIX) 740720022006.
[Adler 2014]AdlerPRC89 Adler, S. S. et al. (PHENIX) 890449052014.
[Akesson 1983] WillisPLB126 Akesson, T. et al. (AFS) 128354–3601983. 
[Akesson 1987]AFSZPC34 Akesson, T. et al. (AFS) 34293–3021987.
[Albrow 1978]BFSNPB145 Albrow, M. G. et al. (BFS) 145305–3481978.
[Alessandro 2005] NA50EPJC39 Alessandro, B. et al. (NA50) 39335–3452005.
[Alper 1973]AlperPLB44 Alper, B. et al. (British-Scandinavian ISR Collaboration). 44521–5261973.
[Alper 1974]BSLondon74Alper, B. et al. p. V-9, Fig. 1 in Ref. <cit.>.
[Alper 1975a] BS2 Alper, B. et al. (British-Scandinavian) 8719–401975a.
[Alper 1975b]AlperNPB100 Alper, B. et al. (BS) 100237–2901975b. 
[Altarelli 1971] GuidoPRL26 Altarelli, G., R. A. Brandt and G. Preparata. 2642–461971.
[Altarelli and Parisi 1977]AltarelliParisiNPB126 Altarelli, G. and G. Parisi. 126298–3181977.
[Althoff 1984]TASSOZPC22 Althoff, M. et al. (TASSO) 22307–3401984.
[Amaldi 1979] YuanAmaldi Amaldi, E. et al. 150326–3441979.
[Anassontzis 1982]WillisZPC13 Anassontzis, E. et al. (R806) 13277–2891982.
[Andronic, Braun-Munzinger, Redlich and Stachel 2007]AndronicNPA789 Andronic, A., p. Braun-Munzinger, K. Redlich and J. Stachel. 789334–3562007.
[Angelis 1978]CCORPLB79 Angelis, A. L. S. et al. (CCOR) 79505–5101978.
[Angelis 1979a]Angelis79 Angelis, A. L. S. et al. (CCOR) Physica Scripta 19116–1231979a. 
[Angelis 1979b]CCORUps Angelis, A. L. S. et al. (CCOR). 87398–4021979b.
[Angelis 1980a]CCORPLB94 Angelis, A. L. S. et al. (CCOR). 94106–1121980a. 
[Angelis 1980b]CCORjTkT Angelis, A. L. S. et al. (CCOR) 97163–1681980b.
[Angelis 1982a]CCORNPB209 Angelis, A. L. S. et al. (CCOR) 209284–3001982a.
[Angelis 1982b]CORPLB116 Angelis, A. L. S. et al. (COR) 116379–3821982b.
[Angelis 1983]ET83 Angelis, A. L. S. et al. (COR) 126132–1361983. 
[Angelis 1987]BCMORPLB185 Angelis, A. L. S. et al. (BCMOR) 185213–2171987. 
[Angelis 1989]CMORNPB327 Angelis, A. L. S. et al. (CMOR). 327541–5681989. 
[Angelis, Tanaka 1984] ETQM83 Angelis, A. L. S., Tanaka, M. et al. (BCMOR) 418321c–326c1984.
[Antreasyan, Cronin 1979] CroninPRD19 Antreasyan, D., J. W. Cronin et al. 19764–7781979.
[Appel 1974]Appel74lepton Appel, J. A.  et al. 33722–7251974. 
[Appel 1986] UA2ZPC30 Appel, J. A. et al. (UA2) 301–221986.
[Appelquist 1975]AppelquistPolitzer Appelquist, T. and H. D. Politzer. 3443–451975. 
[Arnison 1983a] UA1W Arnison, G. et al. (UA1) 122103–1161983a.
[Arnison 1983b] UA1Z Arnison, G. et al. (UA1) 126398–4101983b
[Arnison 1984]UA1PLB136 Arnison, G. et al. (UA1) 136294–3001984.
[Arsene 2005] NPA757B Arsene, I. et al. (BRAHMS) 7571–272005.
[Aubert 1974]Ting1974 Aubert, J. J. et al. 331404–14061974.
[Augustin 1974]Richter1974 Augustin, J.-E. et al. 331406–14081974.
[Aurenche 2006]AurenchePRD73 Aurenche, P., J. Ph. Guillet, E. Pilon, M. Werlen and M. Fontannaz. 730940072006.
[Büsser 1973]CCRPLB46 Büsser, F. W. et al. (CCR). 46471–4761973. 
[Büsser 1974]CCRSPLB53 Büsser, F. W. et al. (CCRS). 53212–2161974. 
[Büsser 1975a] CCRSPLB56 Büsser, F. W. et al. (CCRS). 56482–4861975a. 
[Büsser 1975b]CCRS75 Büsser, F. W. et al. (CCRS). 1975b. Fig. 12a, p. 281 in Ref <cit.>.
[Büsser 1975c] CCRSPLB55eta Büsser, F. W. et al. (CCRS). 55232–22361975c.
[Büsser 1976a]CCRSNPB106 Büsser, F. W. et al. (CCRS). 1061–301976a.
[Büsser 1976b] CCRSNPB113 Büsser, F. W. et al. (CCRS). 113189–2451976b.
[Back 2005] NPA757P Back, B. B.  et al. (PHOBOS). 75728–1012005.
[Bagnaia 1983] UA2Z Bagnaia, P. et al. (UA2) 129130–1401983.
[Baier 1997] BDMPS2 Baier, R., Yu. L. Dokshitzer, A. H. Mueller, S. Peigné and D. Schiff, 483291–3201997.
[Baier 2000]BDMPSZ Baier, R., D. Schiff and B. G. Zakharov. 5037–692000.
[Baier 2003]BaierQM02 Baier, R. 2003. Proceedings of the 16th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions, Nantes, France, July  18–24, 2002,  H. Gutbrod, J. Aichelin and K.Werner (eds.) 715209c–218c2003.
[Baier also Tannenbaum 1998]4thQCDWks Baier, R. also M. J. Tannenbaum. Proc. IV Workshop on Quantum Chromodynamics, Paris, France, June 1–6, 1998, H. M. Fried and B. Müller  (eds.) (World Scientific, Singapore, 1999) pp. 272–285. 
[Banner 1973]BannerPLB44 Banner, M. et al. (Saclay-Strasbourg Collaboration). 44537–5401973.
[Banner 1983]UA2W Banner, M. et al. (UA2). 122476–4851983. 
[Basile 1981]Basile81 Basile, M. et al. A65421–4561981.
[Baum 1976] chormn Baum, L. et al. (CHORMN) 60485–4901976.
[Bazavov 2012] BazavovPRL109 Bazavov, A. et al. 1091923022012.
[Berman 1971]BBK Berman, S. M., J. D. Bjorken and J. B. Kogut. 43388–34181971.
[Bernardini 1964]CERNnoW64 Bernardini, G.,  J. K. Bienlein, G. Von Dardel, H. Faissner, F. Ferrerero, J. M. Gaillard, H. J. Gerber, B. Hahn, V. Kaftanov, F. Krienen, C. Manfredotti, M. Reinharz and R. A. Salmeron, 1386–911964.
[Bernstein 1963]BernsteinPR129 Bernstein, J. 1292323–23251963.
[Bilan 1972] SFM Billan, J., R. Perin and V. Sergo, 1972. Proc. 4th International Conference on Magnet Technology, (Upton, NY, 19-22 September, 1972) Y. Winterbottom (editor) (Brookhaven National Laboratory, Upton, NY, 1972) pp. 433–443.  <http://inspirehep.net/record/80276/files/C720919-p433.PDF>
[Bjorken 1964] BJShelly Bjorken, B. J. and S. L. Glashow 11255–2571964. 
[Bjorken 1971] BjCornell Bjorken, J. D, 1971. Proc. 1971 International Symposium on Electron and Photon Interactions at High Energies, (Cornell University, 23-27 August, 1971) N. B. Mistry (editor) (Cornell, Ithaca, NY, 1971) pp. 282–297.  
[Bjorken 1973]BjPRD8 Bjorken, J. D. 84098–41061973. 
[Bjorken 1969]BjPR179 Bjorken, J. D. 1791547–15531969.
[Bjorken 1983] BjorkenPRD27 Bjorken, J. D. 27140–1511983.
[Bjorken and Paschos 1969]BjPaschosPR185 Bjorken, J. D. and E. A. Paschos.  1851975–19821969.
[Blankenbecler 1972]BBG1972 Blankenbecler, R., S. J. Brodsky and J. F. Gunion, 42461–4651972. 
[Borsanyi 2014]BorsanyiPRL113 Borsanyi, S. et al. 1130523012014.
[Bourquin 1976] BG76 Bourquin, M. and J.-M. Gaillard, 114334–3641976.
[Boyarski 1975] BoyarskiPRL35 Boyarski, A. M. et al. 35196–1991975. 
[Boymond 1974]Boymond74Boymond, J. P.  et al. 33112–1151974. 
[Braun-Munzinger and Stachel 2000] PBMPLB490 Braun-Munzinger, P. and J. Stachel. 490196–2022000.  
[Braunschweig 1990]TASSOZPC47 Braunschweig, W. et al. (TASSO) 47187–1981990.
[Breidenbach 1969]DIS Breidenbach, M., J. I. Friedman, H. W. Kendall, E. D. Bloom, D. H. Coward, H. DeStabler, J. Drees, L. W. Mo and R. E. Taylor. 23935–9391969.  
[Brodsky 1970]BrodskyDrellARNPS Brodsky, S. J. and S. D. Drell. 20147–1941970. 
[Bromberg 1978] FoxNPB134 Bromberg, C., G. C. Fox et al. (E260) 134189–2411978.
[Burns 1965a]AGS65 Burns, R., K. Goulianos, E. Hyman, L. Lederman, W. Lee, N. Mistry, J. Rettberg, M. Schwartz, J. Sunderland and G. Danby. 1542–451965a.
[Burns 1965b]BNLnoW65 Burns, R., K. Goulianos, E. Hyman, L. Lederman, W. Lee, N. Mistry, J. Rettberg, M. Schwartz, and J. Sunderland, 15830–8341965b.
[Cahalan 1975]CahalanPRD11 Cahalan, R. F., K. A. Geer, J. Kogut and L. Susskind. 111199–12121975.
[CCOR 1973]CCOR73 CCR Collaboration. 1973. Proposal for a continuation with Increased Sensitivity of the Search for e^±, e^+ e^- pairs, High p_T π^±∘ and multiple pion correlations in collisions with high p_T, CERN/ISRC/73-13, 14 May 1973. <http://cds.cern.ch/record/732024/files/cm-p00048643.pdf> 
[CCOR 1974]CCOR74 CCOR Collaboration. 1974. Proposal for a High Sensitivity Search at the ISR  For High Mass States Decaying Into Two Electrons, CERN/ISRC/74-56, 25 November 1974. <http://cds.cern.ch/record/1004373/files/CM-P00063282.pdf> 
[CCRS 1973] CCRS1973 CCRS Collaboration. 1973. Addendum 2 to Proposal: Measurement of High Transverse Momentum Charged Particles, CERN/ISRC/72-13/Add. 2, April 1973. <http://cds.cern.ch/record/835104/files/CM-P00053349.pdf> 
[CERN-Saclay 1974] CERNSaclay74 CERN-Saclay Collaboration. 1974. Proposal to Search for Charmed Particles and e^+ e^- Pairs at the ISR, CERN/ISRC/74-55, 25 November 1974. <http://cds.cern.ch/record/738399/files/cm-p00047665.pdf> 
[Chatrchyan 2011a]CMSjetPRL107 Chatrchyan, S. et al. (CMS) 1071320012011a.
[Chatrchyan 2011b]CMSPRC84 Chatrchyan, S. et al. (CMS) 840249062011b.
[Chatrchyan 2012]CMSHiggs Chatrchyan, S. et al. (CMS) 71630–612012.
[Chilton 1966] ChiltonPR148 Chilton, F., A. M. Saperstein and E. Shrauner.  1481380–13841966.
[Christenson 1970]LMLPRL25 Christenson, J. H., G. S. Hicks, L. M. Lederman, P. J. Limon, B. G. Pope and E. Zavattini. 251523–15261970.
[Clark 1978] ClarkNPB142 Clark, A. G. et al. (CSZ). 14229–521978.
[Clark 1979]ClarkNPB160 Clark, A. G. et al. (CS) 160397–4251979.
[Cleymans 2006]CleymansOeschler Cleymans, J., H. Oeschler, K. Redlich and S. Wheaton. 730349052006.
[Cobb 1977]BCSYwrong Cobb, J. H. et al. (BCSY). 72273–2771977.
[Cocconi 1961] Cocconi Cocconi, G., L. J. Koester, and D. H. Perkins, Technical Report No. UCRL-
10022 (1961), Lawrence Radiation Laboratory (unpublished), p. 167, <https://www.osti.gov/scitech/biblio/4695660/> as cited by <cit.>. 
[Collins and Perry 1975] CollinsPerry Collins, J. C. and M. J. Perry. 341353–13561975.
[Combridge 1977]CombridgePLB70 Combridge, B. L., J. Kripfganz and J. Ranft. 70234–2381977.
[Contogouris 1981] ContogourisPLB104 Contogouris, A. P., S. Papadopoulos and J. Ralston. 10470–741981.
[Cool 1969]CCRprops Cool, R., L. DiLella, L. Lederman and E. Zavattini. 1969. Intersecting Storage Ring Study Of Dileptons, CERN/ISRC/69-43, 20 June 1969. <http://cds.cern.ch/record/1005387/files/CM-P00062888.pdf>  
[Cool 1973]CoolICHEP72 Cool, R. L. et al. 1973. (CCR) Proc. XVI International Conference on High Energy Physics (Chicago-Batavia,1972). J. D. Jackson and A. Roberts (eds.) (NAL, Batavia, IL,1973) Vol. 3 p. 317. 
[Cooper and Frye 1974] CooperFrye Cooper, F. and G. Frye. 10186–1892010.
[Crease 2008]Crease2008 Crease, R. P. Hist. Stud. Nat. Sci.  38 535–568 2008.
[Cronin 1977]Cronin1977 Cronin, J. W. 1977. Proc. 1977 Int. Symposium on Lepton and Photon Interactions at High Energies, (Hamburg, Germany 25-31 August, 1977), F. Gutbrod (editor) (DESY, Hamburg, 1977) pp. 579–598.
[Cutler 1978]CutlerPRD17 Cutler, R. and D. Sivers. 17196–2111978.
[Danby 1962]Danby62 Danby, G.,  J.-M. Gaillard, K. Goulianos, L. M. Lederman, N. Mistry, M. Schwartz, and J. Steinberger, 936–441962.
[Darriulat 1976a]DarriulatNPB110 Darriulat, P. et al. 110365–3791976a.
[Darriulat 1976b]Darriulatpoutxe Darriulat, P. et al. 107429–4561976b.
[Darriulat 1980]Darriulat1980 Darriulat, P. 1980. Large Transverse Momentum Hadronic Processes, CERN-EP/80-16  <http://cds.cern.ch/record/133947/files/198004343.pdf>
[Darriulat 2012] Darriulat1 Darriulat, P. 2012. 40th Anniversary of the First Proton-Proton Collisions in the CERN Intersecting Storage Rings (ISR), CERN-2012-004, 2012. pp 63–73. <http://cds.cern.ch/record/1456765>
[De Marzo 1982] DeMarzoPLB112 De Marzo, C. et al. (NA5) 112173–1771982.
[De Rujula 1975]AlvaroShelly De Rujula, A. and S. L. Glashow. 3446–491975.
[Della Negra 1977]CCHK Della Negra, M. et al. (CCHK) 1271–421977.
[Di Lella 1974] DiLellaLondon Di Lella, L.  pp. V-13–V20 in Ref. <cit.>.
[Diakonou 1979]WillisPLB87 Diakonou, M. et al. (AABC). 87292–2961979.
[Djhelyadin 1980] Djhelyadin80 Djhelyadin, R. I. et al. 94548–5501980.
[Dokshitzer and Kharzeev 2001] YuriDima2001 Dokshitzer, Yu. L. and D. E. Kharzeev. 519199–2062001.
[Drell and Walecka 1964]DrellWalecka64 Drell, S. D. and J. D. Walecka, Ann. Phys. (NY) 2818–331964.
[Drell and Yan 1970] DrellYanPRL25 Drell, S. D. and T.-M. Yan 25316–3201970.
[Drijard 1979]CCHKPLB81 Drijard, D. et al. (CCHK) 81250–2541979.
[Eichten 1975]Cornell1 Eichten, E. et al. 34369–3721975.
[Eichten 1977]Cornell2 Eichten, E. and K. Gottfried. 66286–2901977.
[Evans and Bryant 2008]LHC2008 Evans, L. and P. Bryant (editors). JINST 3S080012008 <http://dx.doi.org/10.1088/1748-0221/3/08/S08001>. 
[Fabjan 2004]FabjanPLC Fabjan, C. W. and N. McCubbin. 403–404165–1752004.
[Faessler 1979]ISRC79-10 Faessler, M. A. et al. (CHL) p-α and α-α Collisions in the ISR, Proposal to CERN-ISRC,  CERN/ISRC/79-10; ISRC/P101, April 10, 1979. <http://cds.cern.ch/record/719842/files/cm-p00048087.pdf>
[Faissler 1984] FaisslerPLC115 Faissler, M. A. 1151–911984. 
[Farrar 1976] Glennys76 Farrar, G. R. and S. C. Frautschi. 361017–10201976.
[Ferbel 1984]FerbelMolzon Ferbel, T. and W. R. Molzon. 56181–2211984.
[Feynman 1977]FFF1 Feynman, R. P., R. D. Field and G. C. Fox. 1281–651977.
[Feynman 1978] FFFPRD18  Feynman, R. P., R. D. Field and G. C. Fox. 183320–33431978.
[Friedman 1991]FriedmanNobel Friedman, J. I. 63615–6271991. 
[Fritzsch 1977]FritzschPLB69 Fritzsch, H. and P. Minkowski. 69316–3201977.
[Fritzsch and Gell-Mann 1973]QCDbirth Fritzsch, H. and M. Gell-Mann Proc. XVI International Conference on High Energy Physics (Chicago-Batavia,1972). J. D. Jackson and A. Roberts (eds.) (NAL, Batavia, IL,1973) Vol. 2 pp. 135–165. 
[Fritzsch and Gell-Mann and Leutwyler 1973] FGLPLB47 Fritzsch, H., M. Gell-Mann and H. Leutwyler, 47365–3681973.
[Gell-Mann 1964]GellMannQ Gell-Mann, M. 8214–2151964.
[Gell-Mann 2013]Gell-Mann2013 Gell-Mann, M. 2813300162013.
[Glashow 1970]GIM Glashow, S. L., J. Iliopoulos and L. Maiani. 21285–12921970.
[Goldhaber 1958] GGSPR109 Goldhaber, M., L. Grodzins and A. W. Sunyar. 1091015–10171958. 
[Goldhaber 1976] OpenCharm Goldhaber, G. et al. 37255–2591976.
[Greenberg 1964]Greenberg1964 Greenberg, O. W. 13598–6021964.
[Gross and Wilczek 1973] GrossWilczekPRL30 Gross, D. J. and F. Wilczek, 301343–13461973.
[Hagedorn 1994]Hagedorn1994 Hagedorn, R. NATO Sci.Ser.B34613–461995. <https://link.springer.com/chapter/10.1007%2F978-3-319-17545-4_17>
[Harrison 2003]NIMA499 Harrison, M., T. Ludlam and S. Ozaki (eds.). 2003. “The Relativistic Heavy Ion Collider Project: RHIC and its Detectors”, 499235–8802003.
[Herb 1977]HerbPRL39 Herb, S. W. et al. (CFS). 39252–2551977.
[Hinchliffe 1976a]HLLSPLB Hinchliffe, I. and C. H. Llewellyn Smith. 61472–4761976a.
[Hinchliffe 1976b] HLLSNPB Hinchliffe, I. and C. H. Llewellyn Smith. 11445–601976b.
[Hom 1976a]HomPRL36 Hom, D. C. et al. (CFS). 361236–12391976a.
[Hom 1976b]HomPRL37 Hom, D. C. et al. (CFS). 371374–13771976b.
[Jacob 1976]JacobNPB113 Jacob, M. and P. V. Landshoff. 113395–4121976.
[Jacob 1978]JacobPLC48 Jacob, M. and P. V. Landshoff. 48285–3501978.
[Jacob 1979] JacobEPS79 Jacob, M. Proc. EPS International Conference on High Energy Physics, (Geneva, 27 June-4 July 1979)  (CERN, Geneva, SZ, 1980) pp. 473–522.  <http://inspirehep.net/record/141851/files/19399_473-522.pdf>
[Jacob 1984]Jacob1984 Jacob, M. 1984. HISTORY OF ISR PHYSICS, Ref.TH.3807-CERN  <http://cds.cern.ch/record/150654/files/CM-P00062099.pdf>
[Jane 1975] JanePLB59 Jane, M. R.  et al. 59103–1051975. Erratum 735031978. 
[Jarlskog and Pilkuhn 1967]JarkskogNPB1 Jarlskog, C. and H. Pilkuhn. 1264–2681967.
[Koch, Müller and Rafelski 1986]PLC142 Koch, P., B. Müller and J. Rafelski. 142167–2621986.
[Kourkoumelis 1979a]WillisPLB84 Kourkoumelis, C. et al. (ABCS) 84271–2761979a.
[Kourkoumelis 1979b]WillisPLB86 Kourkoumelis, C. et al. (ABCS) 86391–3941979b.
[Kourkoumelis 1979c]WillisNPB158 Kourkoumelis, C. et al. (ABCS) 15839–561979c.
[Kourkoumelis 1980a] WillisPLB91J Kourkoumelis, C. et al. (ABCSY). 91481–4861980a.
[Kourkoumelis 1980b]ABCSYDY Kourkoumelis, C. et al. (ABCSY) 91475–4801980b.
[Kovtun, Son and Starinets 2005] QuantumBound Kovtun, P. K., D. T. Son and A. O. Starinets. 941116012005.
[Kroll and Wada]KrollWada Kroll, N. M. and W. Wada. 981355–13591955.
[Lamb 1965] ZGS65 Lamb, R. C., R. A. Lundy, T. B. Novey, D. D. Yovanovitch, M. L. Good, R. Hartung, M. W. Peters and A. Subramanian. 15800–8021965.
[Landsberg 1985] LandsbergPLC Landsberg, L. G. 128301–3761985.
[Landshoff and Polkinghorne 1978] LandshoffPRD18 Landshoff, P. V. and J. C. Polkinghorne 183344–33521978.
[Lebedev 1973]Lebedev1973 Lebedev, V. et al. pp. 328–335 in Ref. <cit.>.
[Lederman 1970]E70prop Lederman, L. M., W. Lee, J. Appel, M. Tannenbaum, L. Read, J. Sculli, T. White and T. Yamanouchi, Study of Lepton Pairs From Proton-Nuclear Interactions; Search For Intermediate Bosons and Lee-Wick Structure, June 17, 1970, NAL PROPOSAL No. 70 <http://lss.fnal.gov/archive/test-proposal/0000/fermilab-proposal-0070.pdf>. 
[Lederman 1974]LMLLondon74 Lederman, L. M. p. V-55 in Ref. <cit.>.
[Lederman 1975]LMLSLAC75 Lederman, L. M. 1975. Proc. 1975 International Symposium on Lepton and Photon Interactions at High Energies, (Stanford University, 21-27 August, 1975) W. T. Kirk (editor) (SLAC, Stanford CA,1975) pp. 265–316.  
[Lederman 1976]LMLPLC76 Lederman, L. M. 26149–1811976.
[Lederman and Weneser 1975]BearMountain Lederman, L. and J. Weneser (eds.) Report of the Workshop on BeV/Nucleon Collisions of Heavy Ions–How and Why (Bear Mountain, NY, 29 November–1 December, 1974) (BNL 50445, Upton, NY, 1975).
[Lee 1961]LeeCERN61 Lee, T. D. CERN SEMINARS 1961,  CERN 61-30, 1961, pp. 65–72. <http://cds.cern.ch/record/285663/files/CERN-61-30.pdf>
[Lee 2005]NPA740 Lee, T. D. et al. 7501–1712005.
[Lee and Yang 1960]LYW60 Lee, T. D. and C. N. Yang. 1191410–14191960.
[Levin 1975] LevinRyskin75 Levin, E. M. and M G. Ryskin Sov. Phys.-JETP 42783–7891975. <http://www.jetp.ac.ru/cgi-bin/dn/e_042_05_0783.pdf> 
[Matsui 1987]MatsuiLBL24604Matsui, T. 1987. "On the Charm Production in Ultra-relativistic Heavy Ion Collisions", Proc. 2nd Workshop on Experiments and detectors for RHIC, Berkeley, CA, May 1987, eds. H. G. Ritter, A. Shor, LBL-24604. <http://www.osti.gov/scitech/biblio/5302565>
[Matsui and Satz 1986] MatsuiSatz86 Matsui, T. and H. Satz 17416–4221986. 
[Moore and Teaney 2005]MooreTeaneyPRC71 Moore, G. D. and D. Teaney. 710649042005.
[Nearing 1963]Nearing1963 Nearing, J. 1322323-23241963.
[Nearing 1964] Nearing64 Nearing, J. 135AB21964.
[Orear 1964]Orear64 Orear, J. 12112–1131964.
[Owens 1978a]OwensPRD18 Owens, J. F., E. Reya and M. Glück. 181501–15141978a
[Owens 1978b] OwensKimel Owens, J. F. and J. D. Kimel. 183313–33191978b.
[Owens 1987] OwensRMP59 Owens, J. F. 59465–5031987.
[Palmer 1985]PalmerMagnet Palmer, R. B., E. J. Bleser et al. 235435–4631985.
[Panofsky 1968]Pief-Vienna Panofsky, W. K. H. 1968. Proc. 14^ th International Conference on High Energy Physics, Vienna, Austria, 28 Aug.–5 Sept,1968. J. Prentki and J. Steinberger (eds.) (CERN, Geneva, 1968) pp. 23–39. 
[Perkins 1973]PerkinsICHEP72 Perkins, D. H.  Proc. XVI International Conference on High Energy Physics ,Chicago-Batavia,1972. J. D. Jackson and A. Roberts (eds.) (NAL, Batavia, IL,1973) Vol. 4 pp. 189–247. 
[Piccioni 1966]GoodPiccioni64 Piccioni, O., R. Good, W. Melhop and R. Swanson. 1966. Proc. XII International Conference on High Energy Physics, (Dubna, 1964). Ya. A. Smorodinskii (editor-in-chief) (Atomizdat, Moscow, 1966), Vol. 2, p. 32–36. <http://inspirehep.net/record/1376999/files/C64-08-05-p032.pdf>
[Politzer 1973] HDPPRL30 Politzer, H. D., 301346–13491973.
[Pontecorvo 1959]Pontecorvo59 Pontecorvo, B. JETP 371751–17571959.
[Pope 1978]PopeCCORPrelim Pope, B. G. et al. (CCOR) AIP Conf. Proc. 43239–2421978.
[Pretzl 1980] PretzlICHEP80 Pretzl, K., C. Favuzzi et al. (NA5) Proc. XX International Conference on High Energy Physics (Madison, WI 1980). L. Durand and L. G. Pondrom (editors) (AIP,New York, 1980), pp. 435–468. <http://aip.scitation.org/doi/pdf/10.1063/1.32442>
[Prino 2001]PrinoISMD2000 Prino, F. et al. (NA50) Proc. XXX International Symposium  on Multiparticle Dynamics (ISMD2000), Tihany, Hungary, October 9–15,2000, T. Csorgo, S. Hegy and W. Kittel  (eds.) (World Scientific, New Jersey, 2001). <https://arxiv.org/pdf/hep-ex/0101052.pdf>.
[Rak and Tannenbaum 2013]RATCUP Rak, J. and M. J. Tannenbaum. 2013. High p_T Physics in the Heavy Ion Era, (Cambridge University Press, 2013).
[Repellin 1982]RepellinParis Repellin, J.-P. 1982 (UA2) Proc. 21st International Conference on High Energy Physics (ICHEP), Paris, France, July 26–31, 1982 P. Petiau and M. Porneuf  (eds.) J. Phys. Colloques. 43: C3-571–C3-578. <https://doi.org/10.1051/jphyscol:1982376> 
[Russell 1971]Trident-PRL Russell, J. J., R. C. Sah, M. J. Tannenbaum, W. E. Cleland, D. G. Ryan and D. G. Stairs. 2646–501971.
[Russo 1996]Russo Russo, A. 1996. History of CERN, Volume 3, J. Krige (editor) (North Holland, Elsevier Science, Amsterdam, 1996), pp. 97–170.
[Russo 1996a]Russoa Russo, A. 1996a. pp. 151–152 in Ref. <cit.>.
[Satz 1976] seagull Satz, H. and Y. Zarmi Lett.Nuovo Cim. 15421-4281976.
[Satz 2000] SatzRPP63 Satz, H. 631511–15742000.
[Satz 2013] Satz2013 Satz, H. 2013. Adv. High Energy Phys. 2013 242918.  <http://inspirehep.net/record/1223872/files/242918.a.pdf>.
[Schwartz 1960]MS60 Schwartz, M. 4306–307 1960. 
[Segler 1974]CCRSLondon74 Segler, S. et al. (CCRS). Proc. XVII International Conference on High Energy Physics (London,1974). J. R. Smith (editor) (Rutherford Laboratory, Chilton, Didcot, UK, 1974), pp. V-41–V-43. 
[Shuryak 1980] Shuryak80 Shuryak, E. V. 6171–1581980.
[Soltz 2015]SoltzARNPS65 Soltz, R. A., C. DeTar, F. Karsch, S. Mukherjee and P. Vranas. 65379–4022015.

[Tannenbaum 1977]MJT1977comment Tannenbaum, M. J. 1977. p. 598 in Ref. <cit.>.
[Tannenbaum 1982] TannenbaumParis Tannenbaum, M. J. 1982. (CCOR) pp. C3-134–C3-139 in Ref. <cit.> <https://doi.org/10.1051/jphyscol:1982331>
[Tannenbaum 1985] MJTQM1984 Tannenbaum, M. J. et al. 1985. (BCMOR) Proceedings of the Fourth International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions, Helsinki, Finland, June  17–21, 1984,  K. Kajantie (editor) Lecture Notes in Physics 221 (Springer-Verlag, Berlin, Heidelberg, 1985) <https://www.osti.gov/scitech/servlets/purl/6174559> 
[Tannenbaum 1989]MJTIJMPA4 Tannenbaum, M. J. 43377–34761989.
[Tannenbaum 1996]MJT96 Tannenbaum, M. J. Heavy Ion Physics 4139–1481996.
[Tannenbaum 2006]MJTRPP69 Tannenbaum, M. J. 692005–20592006.
[Tannenbaum 2008]MJTBuffalo Tannenbaum, M. J. 17771–8012008.
[Tannenbaum 2014]MJTErice52 Tannenbaum, M. J. 2014. Proceedings of the International School of Subnuclear Physics, ISSP 2014, 52nd Course, Erice, Sicily, Italy, June 24–July 3, 2014, Antonino Zichichi (editor) The Subnuclear Series: Volume 52 (World Scientific, Singapore, 2017). arXiv:1504.02771.
[Tannenbaum 2016] MJTW Tannenbaum, M. J. Eur. Phys. J. H 41 303–3252016.
[Tavernier 1987]Tavernier Tavernier, S. P. K. 501439–14891987.
[Thews, Schroedter and Rafelski 2001]ThewsPRC63 Thews, R. L., M. Schroedter and J. Rafelski. 630549052001.
[van Hees, Greco and Rapp 2006]van Hees van Hees, H., V. Greco and R. Rapp, 730349132006.
[Vogt, Cacciari and Nason 2006] FONNL Vogt, R., M. Cacciari and P. Nason. 774661–6642006.
[Wolf 1982]WolfParis Wolf, G. pp. C3-525–C3-568 in Ref. <cit.> <https://doi.org/10.1051/jphyscol:1982374>
[Yamaguchi 1966] YamaguchiNC43 Yamaguchi, Y. Nuovo Cimento A43193–1991966. 
[Zichichi 1966] Nino64 Zichichi, A. Comment in discussion <cit.> p. 35.
[Zhao and Rapp 2008]RappPLB664 Zhao, X. and R. Rapp 664253–2572008. 
[Zweig 2010]ZweigA Zweig, G. 253863–38772010.
