## Top quark: a short history – part I November 15, 2007

Posted by dorigo in physics, science.

Because part of the course in particle physics I am preparing deals with top quark physics, I have been unearthing old material on that topic, which I used in the past in a few seminars. I think some readers of this blog may be interested to be reminded about (or read for the first time) how the top quark entered the scene of subnuclear physics in the last thirty-five years. It is a story starred by spectacular discoveries and amazing technological breakthroughs, and indeed many of these were awarded a Nobel prize.

Preludes and the existence of quarks

The hypothesis that hadrons are composed of quarks dates back to 1962, when Murray Gell-Mann cooked up his “eightfold way” to catalog known resonances and particles into multiplets of the SU(3) group (Yuval Ne’eman independently formulated the same theory more or less at the same time). Basically, known mesons (baryons) could fit in a very elegant scheme where they were represented as different arrangements of pairs (triplets) of three kinds of constituent particles -which he called quarks inspired by an obscure phrase in “Finnegan’s Wake”, the novel by James Joyce-, satisfying certain symmetry rules. A sketch of the arrangement of nine spin-zero mesons ($3 \times \bar 3$) within a SU(3) octet and a singlet is shown in the plot above.

The need for more than Gell-mann’s original three quarks – the u (up) and d (down) which could make up protons and neutrons, and the s (for strange) with which strange particles could be built – only came about when it was realized that the neutral kaon $K^0$, a meson made by a d and anti-s quark, never decayed into pairs of muons. Now, everything that is not forbidden is compulsory in the subatomic world, but that decay was exceedingly rare, argued Glashow Iliopoulos and Maiani in 1970, because a fourth quark existed, with a large mass: a massive charm quark c canceled the unbalanced effect of the other three, and explained the failure to observe a $K^0 \to \mu \mu$ decay. This neat cancellation was called “GIM mechanism”.

Meanwhile, quarks had been given a chance to show their dynamical properties in the phenomenology of collisions of beams of hadrons with fixed targets at higher and higher energy. The proton had to have a complex structure to produce the observed behavior when torn apart: James Bjorken and Richard Feynman described its constituents with the generic name of “partons” and suggested computational ways to deal with them, but partons remained a rather abstract description of the unknown structure of hadrons.

It was only in November of 1974 that the discovery of the $J/ \psi$ meson – a m=3.1 GeV particle immediately recognized as a charm-anticharm bound state- convinced particle physicists that the quark model of hadrons was not a mathematical construct but a truthful description of reality (in the plot on the left you see the reconstructed invariant mass of pairs of electrons produced by the reaction $p + Be \to J/psi X \to e^+ e^-X$ in the Brookhaven experiment). Even disregarding the interpretation of the $J/\psi$ and its excited state $\psi (2S)$ as bound states of charmed quark pairs, the rise in the relative frequency of electron-positron annihilations yielding hadronic final states as the energy was pushed above the $J/ \psi$ threshold could only mean that a new massive quark was contributing. Below you can see a present-day compilation of measurements of the ratio R between the rate of hadronic final states and leptonic final states in electron-positron collisions: the jumps as the thresholds for new quark pairs is crossed are evident above 6 and 10 GeV. Also notice the various resonances that appear as the collision energy is increase: the $\omega$, the $\phi$, the $\rho '$, and then the $\psi$ and $\Upsilon$ family. And then of course, the Z.

It is clear that November 1974 marked the start of a new era in particle physics. However, well before that – in 1972 – two japanese theoreticians, Kobajashi and Maskawa, had seen way further, and they had in truth hypothesized the existence of as many as six quarks, not just four! To explain their vision we need to make a further jump backwards.

Eight years before, in 1964, the brilliant experiment by Christensen, Cronin, Fitch and Turlay had established that in a small but non-zero fraction of cases, the same $K^0$ particle mentioned above could be seen to decay in a way that violated a symmetry of nature called CP. CP is the product of two symmetry operations, C which exchanges particle with antiparticle, and P which inverts the sign of space coordinates. Weak interactions were known to violate both C and P symmetry, but their product had been thought to be strictly conserved: change each particle with its antimatter partner, switch space coordinates, and any particle reaction would occur in exactly the same way and with the same frequency. Not for $K^0$ mesons: weak interactions could violate the rule, and this demanded the inclusion of some small CP-violating term in the theoretical description of weak processes.

Kobayashi and Maskawa considered the violation of CP invariance in the context of the quark model, and they concluded that the phenomenon could be best accommodated theoretically by inserting a complex phase in the “flavor matrix”, a square of numbers which dictated the relative strength of transitions between quarks of different flavor. With four quarks, one could arrange their transition amplitudes in a $2 \times 2$ matrix, and explain the relative frequency of different weak decays of hadrons with a single parameter, the Cabibbo angle $\theta_c$: a real number. Only with six quarks, however, a $3 \times 3$ matrix could arise, and it would then have four parameters, one of them a complex number: for the $n \times n$ flavor matrix had to be unitary – to conserve probability and fulfil the necessary requirements of the theory – and the number of meaningful parameters of such a matrix is $(n-1)^2$, of which only $(n-1)(n-2)/2$ can be complex phases. With n=3 generations – six quarks – CP violation was possible!

The speculation by Kobayashi and Maskawa was a really risky bet: it built on the unproven existence of quarks, positing that there existed not just those three whose phenomenology had been in some way already explored, but as many as six. And they were right! A rare instance of Occam’s razor being successfully abused: in fact, the need to accommodate CP violation proved stronger than the economy of the quark families.

After the November revolution in 1974, the hunt was set on for a third family of elementary fermions: because as some say, there’s no two without a three, and on the other hand, Kobayashi and Maskawa’s arrangement had proven to be economical after all. A third charged lepton, the tau, was soon discovered by Perl’s team in 1975, and a third d-type fermion, the bottom quark, was found by Leon Lederman and collaborators in 1977 at Fermilab, where evidence of the Upsilon meson family -three $b \bar b$ bound states of narrow width- was seen in the collisions of 400-GeV protons with a beryllium target. Upsilon mesons decayed to muon pairs, which were seen as resonance peaks in the rapidly falling invariant mass spectrum (see plot on the right, showing with a red arrow the enhancement in the cross section plotted as a function of dimuon invariant mass).

[To be continued…]

1. Alejandro Rivero - November 16, 2007

eta’ is a risky bussiness for an introductory course if you are forced to explain how the singlet gets to mix with the octet.

2. Kea - November 16, 2007

Ooooh, I like posts with hexagons and lattices in them. And I thought you were away wandering in the mountains with your family…

3. dorigo - November 16, 2007

Hi Alejandro, you are right. I do not plan to mess around with the subtleties of mixing of those states, axial U(1) etcetera. If a student asks a non-pertinent question, it will backfire 😉

Hi Kea, 🙂 I should have known and pleased you some more with the decuplet and maybe some SU(4) three-dimensional diagrams. Next time! Oh, btw I have been on a plane for most of today… I am at Fermilab now.

Cheers,
T.

4. David Heffernan - November 16, 2007

Kobayashi, not Kobajashi.

5. dorigo - November 16, 2007

That’s right David … I tend to mix j’s and y’s in names, I should be more careful.

6. Andrea Giammanco - November 16, 2007

Since you are there: do you know some easy way to extract the Cabibbo angle from baryon (not meson) properties?
Last monday I gave a lesson of particle physics (to 4th year students) about the J/psi discovery, and I started by a theoretical introduction: first introducing the Cabibbo angle, then the K0->mu+mu- problem, and how the charm solves it, etc.
Since I had been asked by their regular professor to assign them some homework, I thought that it would have been easy and motivating, at the same time, to extract theta by the comparison of the decay rates of the neutron and of the sigma- into proton and neutron respectively. The only difference at quark level is that in one case you have d->u, in the other s->u, so in principle the ratio (taking into account branching ratio and phase space) should be the square of the tangent.
Well, maybe I messed up the phase space (Perkins suggests E0^5 where E0 is the maximum energy allowed to the electron, considering it relativistic and neglecting the baryon recoil) but I get something quite wrong: 2 degrees instead of 13.
I assume that the reason is that the spectator quarks contribute to the amplitude in a different way for different masses, so the cancellation in the ratio is bad.
I did the exercise again with K->munu versus pi->munu, which is what I wanted to avoid because the calculation of the phase space is now much more complicated (I cannot neglect the muon mass), and taking into account the form factors, which are not so different after all (I found a ratio of 1.29 between f_K and f_pi), I get 12 degrees which is quite close to reality.
Probably the form factors are even more messy for baryon (which would not be a surprise).
So probably I will explain the exercise with kaons versus pions, but I am a bit unhappy, because Perkins (the textbook), without demonstration, says that the ratio between sigma and neutron widths is ~1/20 and from this he deduces the Cabibbo angle. And in one of the exercises at the end of the chapter it even propose to extract it from sigma->lambda+e+nu over sigma->neutron+pion, which seems to be even messier from the point of view on non-perturbative QCD contributions to the amplitude.

7. dorigo - November 16, 2007

Hi Andrea,

good question. I think the reason why for didactical purposes the Cabibbo angle is always extracted from the k/pi ratio of widths rather than using baryons has to do with the fact that in the latter case there are strong contributions from axial vector currents as well as vector ones: the Ademollo-Gatto theorem does not apply to hyperons, and SU(3) breaking terms occur at first order. The ratio in fact depends on the different values of gv/ga which are thus listed in the PDG:

$n \to p e \nu$: $g_A/g_V=-1.2695$
$\Sigma^- \to n e \nu$: $g_A/g_V=0.340$
$\Lambda^0 \to p e \nu$: $g_A/g_V=-0.718$

It is interesting to note that because of the mentioned contribution from axial vector terms, the PDG itself does not use hyperon decays to quote results for V_us…

You can try to shed more light in the issue by reading the following two old papers, which tried to understand whether the Cabibbo angle was “universal” studying baryonic decays:

http://prola.aps.org/pdf/PR/v172/i5/p1694_1

http://prola.aps.org/abstract/PR/v152/i4/p1433_1

Cheers,
T.

8. nc - November 17, 2007

Thank you very much for this post, which is a very useful historical background.

9. kwameantonio - November 17, 2007

Thank you that was well written. To refresh knowledge is nice, especially in our immediate time/space/spirit.

10. Top quark: a short history - part II « A Quantum Diaries Survivor - November 17, 2007

[…] spectacular experimental results mentioned in the first section of this multi-part post were the preludes to the searches of the top quark which were forthcoming […]

11. dorigo - November 18, 2007

Nc, antonio, thank you for your support. Writing these posts is a good way for me to prepare my course without feeling I am really working 🙂

Cheers,
T.

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