Observation of the decay $B_{s}^{0} \to η_{c} φ$ and evidence for $B_{s}^{0} \to η_{c} π^{+} π^{-} $
LHCb collaboration R. Aaij B. Adeva M. Adinolfi Z. Ajaltouni S. Akar J. Albrecht F. Alessio M. Alexander S. Ali G. Alkhazov P. Alvarez Cartelle A. A. Alves Jr S. Amato S. Amerio Y. Amhis L. An L. Anderlini G. Andreassi M. Andreotti J. E. Andrews R. B. Appleby F. Archilli P. d'Argent J. Arnau Romeu A. Artamonov M. Artuso E. Aslanides G. Auriemma M. Baalouch I. Babuschkin S. Bachmann J. J. Back A. Badalov C. Baesso S. Baker V. Balagura W. Baldini R. J. Barlow C. Barschel S. Barsuk W. Barter F. Baryshnikov M. Baszczyk V. Batozskaya B. Batsukh V. Battista A. Bay L. Beaucourt J. Beddow F. Bedeschi I. Bediaga L. J. Bel V. Bellee N. Belloli K. Belous I. Belyaev E. Ben-Haim G. Bencivenni S. Benson A. Berezhnoy R. Bernet A. Bertolin C. Betancourt F. Betti M. -O. Bettler M. van Beuzekom Ia. Bezshyiko S. Bifani P. Billoir T. Bird A. Birnkraut A. Bitadze A. Bizzeti T. Blake F. Blanc J. Blouw S. Blusk V. Bocci T. Boettcher A. Bondar N. Bondar W. Bonivento I. Bordyuzhin A. Borgheresi S. Borghi M. Borisyak M. Borsato F. Bossu M. Boubdir T. J. V. Bowcock E. Bowen C. Bozzi S. Braun M. Britsch T. Britton J. Brodzicka E. Buchanan C. Burr A. Bursche J. Buytaert S. Cadeddu R. Calabrese M. Calvi M. Calvo Gomez A. Camboni P. Campana D. H. Campora Perez L. Capriotti A. Carbone G. Carboni R. Cardinale A. Cardini P. Carniti L. Carson K. Carvalho Akiba G. Casse L. Cassina L. Castillo Garcia M. Cattaneo G. Cavallero R. Cenci D. Chamont M. Charles Ph. Charpentier G. Chatzikonstantinidis M. Chefdeville S. Chen S. -F. Cheung V. Chobanova M. Chrzaszcz X. Cid Vidal G. Ciezarek P. E. L. Clarke M. Clemencic H. V. Cliff J. Closier V. Coco J. Cogan E. Cogneras V. Cogoni L. Cojocariu P. Collins A. Comerma-Montells A. Contu A. Cook G. Coombs S. Coquereau G. Corti M. Corvo C. M. Costa Sobral B. Couturier G. A. Cowan D. C. Craik A. Crocombe M. Cruz Torres S. Cunliffe R. Currie C. D'Ambrosio F. Da Cunha Marinho E. Dall'Occo J. Dalseno P. N. Y. David A. Davis K. De Bruyn S. De Capua M. De Cian J. M. De Miranda L. De Paula M. De Serio P. De Simone C. T. Dean D. Decamp M. Deckenhoff L. Del Buono M. Demmer A. Dendek D. Derkach O. Deschamps F. Dettori B. Dey A. Di Canto H. Dijkstra F. Dordei M. Dorigo A. Dosil Suárez A. Dovbnya K. Dreimanis L. Dufour G. Dujany K. Dungs P. Durante R. Dzhelyadin A. Dziurda A. Dzyuba N. Déléage S. Easo M. Ebert U. Egede V. Egorychev S. Eidelman S. Eisenhardt U. Eitschberger R. Ekelhof L. Eklund S. Ely S. Esen H. M. Evans T. Evans A. Falabella N. Farley S. Farry R. Fay D. Fazzini D. Ferguson A. Fernandez Prieto F. Ferrari F. Ferreira Rodrigues M. Ferro-Luzzi S. Filippov R. A. Fini M. Fiore M. Fiorini M. Firlej C. Fitzpatrick T. Fiutowski F. Fleuret K. Fohl M. Fontana F. Fontanelli D. C. Forshaw R. Forty V. Franco Lima M. Frank C. Frei J. Fu W. Funk E. Furfaro C. Färber A. Gallas Torreira D. Galli S. Gallorini S. Gambetta M. Gandelman P. Gandini Y. Gao L. M. Garcia Martin J. García Pardiñas J. Garra Tico L. Garrido P. J. Garsed D. Gascon C. Gaspar L. 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Koliiev M. Kolpin I. Komarov R. F. Koopman P. Koppenburg A. Kosmyntseva A. Kozachuk M. Kozeiha L. Kravchuk K. Kreplin M. Kreps P. Krokovny F. Kruse W. Krzemien W. Kucewicz M. Kucharczyk V. Kudryavtsev A. K. Kuonen K. Kurek T. Kvaratskheliya D. Lacarrere G. Lafferty A. Lai G. Lanfranchi C. Langenbruch T. Latham C. Lazzeroni R. Le Gac J. van Leerdam A. Leflat J. Lefrançois R. Lefèvre F. Lemaitre E. Lemos Cid O. Leroy T. Lesiak B. Leverington T. Li Y. Li T. Likhomanenko R. Lindner C. Linn F. Lionetto X. Liu D. Loh I. Longstaff J. H. Lopes D. Lucchesi M. Lucio Martinez H. Luo A. Lupato E. Luppi O. Lupton A. Lusiani X. Lyu F. Machefert F. Maciuc O. Maev K. Maguire S. Malde A. Malinin T. Maltsev G. Manca G. Mancinelli P. Manning J. Maratas J. F. Marchand U. Marconi C. Marin Benito M. Marinangeli P. Marino J. Marks G. Martellotti M. Martin M. Martinelli D. Martinez Santos F. Martinez Vidal D. Martins Tostes L. M. Massacrier A. Massafferri R. Matev A. Mathad Z. Mathe C. Matteuzzi A. Mauri E. Maurice B. Maurin A. Mazurov M. McCann A. McNab R. McNulty B. Meadows F. Meier M. Meissner D. Melnychuk M. Merk A. Merli E. Michielin D. A. Milanes M. -N. Minard D. S. Mitzel A. Mogini J. Molina Rodriguez I. A. Monroy S. Monteil M. Morandin P. Morawski A. Mordà M. J. Morello O. Morgunova J. Moron A. B. Morris R. Mountain F. Muheim M. Mulder M. Mussini D. Müller J. Müller K. Müller V. Müller P. Naik T. Nakada R. Nandakumar A. Nandi I. Nasteva M. Needham N. Neri S. Neubert N. Neufeld M. Neuner T. D. Nguyen C. Nguyen-Mau S. Nieswand R. Niet N. Nikitin T. Nikodem A. Nogay A. Novoselov D. P. O'Hanlon A. Oblakowska-Mucha V. Obraztsov S. Ogilvy R. Oldeman C. J. G. Onderwater J. M. Otalora Goicochea A. Otto P. Owen A. Oyanguren P. R. Pais A. Palano M. Palutan A. Papanestis M. Pappagallo L. L. Pappalardo W. Parker C. Parkes G. Passaleva A. Pastore G. D. Patel M. Patel C. Patrignani A. Pearce A. Pellegrino G. Penso M. Pepe Altarelli S. Perazzini P. Perret L. Pescatore K. Petridis A. Petrolini A. Petrov M. Petruzzo E. Picatoste Olloqui B. Pietrzyk M. Pikies D. Pinci A. Pistone A. Piucci V. Placinta S. Playfer M. Plo Casasus T. Poikela F. Polci A. Poluektov I. Polyakov E. Polycarpo G. J. Pomery A. Popov D. Popov B. Popovici S. Poslavskii C. Potterat E. Price J. D. Price J. Prisciandaro A. Pritchard C. Prouve V. Pugatch A. Puig Navarro G. Punzi W. Qian R. Quagliani B. Rachwal J. H. Rademacker M. Rama M. Ramos Pernas M. S. Rangel I. Raniuk F. Ratnikov G. Raven F. Redi S. Reichert A. C. dos Reis C. Remon Alepuz V. Renaudin S. Ricciardi S. Richards M. Rihl K. Rinnert V. Rives Molina P. Robbe A. B. Rodrigues E. Rodrigues J. A. Rodriguez Lopez P. Rodriguez Perez A. Rogozhnikov S. Roiser A. Rollings V. Romanovskiy A. Romero Vidal J. W. Ronayne M. Rotondo M. S. Rudolph T. Ruf P. Ruiz Valls J. J. Saborido Silva E. Sadykhov N. Sagidova B. Saitta V. Salustino Guimaraes C. Sanchez Mayordomo B. Sanmartin Sedes R. Santacesaria C. Santamarina Rios M. Santimaria E. Santovetti A. Sarti C. Satriano A. Satta D. M. Saunders D. Savrina S. Schael M. Schellenberg M. Schiller H. Schindler M. Schlupp M. Schmelling T. Schmelzer B. Schmidt O. Schneider A. Schopper K. Schubert M. Schubiger M. -H. Schune R. Schwemmer B. Sciascia A. Sciubba A. Semennikov A. Sergi N. Serra J. Serrano L. Sestini P. Seyfert M. Shapkin I. Shapoval Y. Shcheglov T. Shears L. Shekhtman V. Shevchenko B. G. Siddi R. Silva Coutinho L. Silva de Oliveira G. Simi S. Simone M. Sirendi N. Skidmore T. Skwarnicki E. Smith I. T. Smith J. Smith M. Smith H. Snoek l. Soares Lavra M. D. Sokoloff F. J. P. Soler B. Souza De Paula B. Spaan P. Spradlin S. Sridharan F. Stagni M. Stahl S. Stahl P. Stefko S. Stefkova O. Steinkamp S. Stemmle O. Stenyakin H. Stevens S. Stevenson S. Stoica S. Stone B. Storaci S. Stracka M. Straticiuc U. Straumann L. Sun W. Sutcliffe K. Swientek V. Syropoulos M. Szczekowski T. Szumlak S. T'Jampens A. Tayduganov T. Tekampe G. Tellarini F. Teubert E. Thomas J. van Tilburg M. J. Tilley V. 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Yushchenko K. A. Zarebski M. Zavertyaev L. Zhang Y. Zhang A. Zhelezov Y. Zheng X. Zhu V. Zhukov S. Zucchelli




















roman




EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)



pdflatex

        

        


         CERN-EP-2017-026 
  
         LHCb-PAPER-2016-056 
  
         December 30, 2023
 
         









Observation of the decay 
 →ϕ and evidence 
 for → 










The LHCb collaboration[Authors are listed at the end of this paper.]







  A study of →ϕ and → decays is performed using pp collision data corresponding to an integrated luminosity of 3.0, collected with the LHCb detector in Run 1 of the LHC.  
The observation of the decay →ϕ is reported, where the meson is reconstructed in the pp̅, K^+K^-π^+π^-, π^+π^-π^+π^- and K^+K^-K^+K^- decay modes and the ϕ(1020) in the K^+ K^- decay mode.
The decay →ϕ is used as a normalisation channel.
Evidence is also reported for the decay →, where the meson is reconstructed in the pp̅ decay mode, using the decay → as a normalisation channel.
The measured branching fractions are


    ℬ (B^0_s→η_cϕ)   =   (5.01 ± 0.53 ± 0.27 ± 0.63 ) × 10^-4 , 
    ℬ (B^0_s→η_cπ^+ π^-)   =   (1.76 ± 0.59 ± 0.12 ± 0.29 ) × 10^-4 ,


where in each case the first uncertainty is statistical, the second systematic and the third uncertainty is due to the limited knowledge of the external branching fractions.






  Published in JHEP 07 (2017) 021






 CERN on behalf of the collaboration, licence http://creativecommons.org/licenses/by/4.0/CC-BY-4.0.
























plain 

arabic









§ INTRODUCTION



When a meson decays through the b̅→c̅ c s̅ process, interference between the direct decay amplitude, and the amplitude after - oscillation, gives rise to a -violating phase, .
This phase is well predicted within the Standard Model (SM) <cit.> and is sensitive to possible contributions from physics beyond the SM <cit.>.
The phase is best measured using the “golden” channel[The simplified notation ϕ and  are used to refer to the ϕ(1020) and the (1S) mesons throughout this article.] →ϕ <cit.> and the precision of this measurement is expected to be dominated by its statistical uncertainty until the end of LHC running. 
In addition to →ϕ, other modes have been used to constrain :  <cit.>,  <cit.>, and ψ(2S)ϕ <cit.>.  

In this paper, the first study of →η_cϕ and →η_c decays is presented.[The use of charge-conjugate modes is implied throughout this article.] These decays also proceed dominantly through a b̅→c̅ c s̅ tree diagram as shown in Fig. <ref>.
Unlike in decays, the ϕ final state is purely -even, so that no angular analysis is required to measure the mixing phase ϕ_s. 
However, the size of the data sample recorded by the LHCb experiment in LHC Run 1 is not sufficient to perform time-dependent analyses of →η_cϕ and →η_c decays. 
Instead, the first measurement of their branching fractions is performed.
No prediction is available for either (→ϕ) or (→). 
Assuming


    ℬ(→ϕ)/ℬ(→ϕ)= 
    ℬ(→ K^0)/ℬ(→ K^0) =
    ℬ(→)/ℬ(→)


allows (→ϕ) and (→) to be estimated.
From the known values of (→), (→), (→ϕ) and (→) <cit.>, one finds 


    (→ϕ)     =    𝒪(10^-3) ,  
    (→)     =    𝒪(10^-4)  .


The measurements presented in this paper are performed using a dataset corresponding to 3of integrated luminosity collected by the LHCb experiment in pp collisions during 2011 and 2012 at centre-of-mass energies of 7and 8, respectively. 



The paper is organised as follows: Section <ref> describes the LHCb detector and the procedure used to generate simulated events; 
an overview of the strategy for the measurements of (→ϕ) and (→) is given in Sec. <ref>; 
the selection of candidate signal decays is described in Sec. <ref>;
the methods to determine the reconstruction and selection efficiencies are discussed in Sec. <ref>.
Section <ref> describes the fit models. 
The results and associated systematic uncertainties are discussed in Secs. <ref> and <ref>.
Finally, conclusions are presented in Sec. <ref>.







§ DETECTOR AND SIMULATION



The detector <cit.> is a single-arm forward spectrometer covering the  range 2<η <5, designed for the study of particles containing or quarks. 
The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet.
The tracking system provides a measurement of momentum, , of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200.
The minimum distance of a track to a primary vertex (PV), the impact parameter (IP), is measured with a resolution of (15+29/), where is the component of the momentum transverse to the beam, in .
Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. 
Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. 
Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. 

The online event selection is performed by a trigger <cit.>, which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction.

Samples of simulated events are used to determine the effects of the detector geometry, trigger, and selection criteria on the invariant-mass distributions of interest for this paper.
In the simulation, pp collisions are generated using  <cit.> with a specific configuration <cit.>. 
The decay of the meson is described by  <cit.>, which generates final-state radiation using  <cit.>. 
The interaction of the generated particles with the detector, and its response, are implemented using the toolkit <cit.> as described in Ref. <cit.>.
Data-driven corrections are applied to the simulation to account for the small level of mismodelling of the particle identification (PID) performance <cit.>.
In the simulation the reconstructed momentum of every track is smeared by a small amount in order to better match the mass resolution of the data.










§ ANALYSIS STRATEGY



In the analysis of →ϕ decays, the ϕ meson is reconstructed in the  final state and the meson is reconstructed in the pp̅, K^+K^-π^+π^-, π^+π^-π^+π^- and K^+K^-K^+K^- final states. 
For clarity, the three four-body final states are referred to as 4h throughout the paper.  
In determining the branching fraction, the decay →ϕ is used as a normalisation channel, where the  meson is reconstructed in the same decay modes as the meson.
A similar strategy is adopted for the measurement of the branching fraction of → decays. 
However, due to the higher expected level of combinatorial background compared to →ϕ decays, the and mesons are reconstructed only in the p p̅ final state in the measurement of (→). 

In both analyses, a two-stage fit procedure is performed. 
In the first stage, unbinned extended maximum likelihood (UML) fits are performed to separate signal candidates from background contributions. 
For the →(→ pp̅) decay the fit is done to the pp̅ mass distribution, while for the decays →(→ pp̅) ϕ(→) and →(→ 4h) ϕ(→) it is made to the two-dimensional pp̅ versus  or 4h versus  mass distributions, respectively.
The likelihood function is 


    L(𝐍, 𝐚) = e^-∑_j N_j/n!∏_l=1^n  ( ∑_j N_j  P_j(m;a) ) ,


where j stands for the event species, N_j is the corresponding yield and N is the vector of yields N_j, a is the vector of fitted parameters other than yields, n is the total number of candidates in the sample, and P_j(m) is the probability density function (PDF) used to parametrise the set of invariant-mass distributions m considered. 
The package<cit.> is used to construct the negative log-likelihood function (NLL), which is minimised using Minuit <cit.>.
Using information from these fits, signal weights for each candidate, ω_l, are obtained using the _s Plot technique <cit.>.  

In the second stage, for → pp̅ candidates a weighted UML fit is made to the pp̅ invariant-mass spectrum, and weighted UML fits of the pp̅ and the 4h invariant-mass spectra are done for → pp̅ϕ and → 4h ϕ candidates, respectively, to disentangle  and  candidates from nonresonant (NR) and remaining background contributions, as described in Sec. <ref>.
For the weighted fits, the NLL function is given by


    -  ln L(𝐍, 𝐚)= ζ∑_j N_j -  ζ∑_l ω_l   ln(∑_j N_j  P_j(m;a) ) + ln(n!),


where ζ = ∑_l ω_l / ∑_l ω_l^2 ensures proper uncertainty estimates from the weighted likelihood fit <cit.>.
For the observed numbers of η_c and  candidates in final state f, N_,f and N_,f, the measured branching fraction is


    ℬ(→ X) = N_,f/N_,f×ℬ(→ X)×ℬ(→ f)/ℬ(→ f)×ε()_f/ε()_f  ,


where X refers to either the ϕ meson or the  pair.
The branching fractions ℬ(→ϕ), ℬ(→), ℬ(→ f) and ℬ(→ f) are taken from Ref. <cit.>, and the efficiency correction factors, ε, are obtained from simulation.
In order to maximise the sensitivity to ℬ(→ϕ), a simultaneous fit to the pp̅ and 4h invariant-mass spectra is performed.







§ EVENT SELECTION



A common strategy for the event selection, comprising several stages, is adopted for all final states. 
First, online requirements are applied at the trigger level, followed by an initial offline selection in which relatively loose criteria are applied. 
Boosted decision trees (BDTs) <cit.>, implemented using the TMVA software package <cit.>, are then used to further suppress the combinatorial background arising from random combinations of tracks originating from any PV. 
Finally, the requirements on the output of the BDTs and on the PID variables are simultaneously optimised for each final state, to maximise the statistical significance of the signal yields. 

At the hardware trigger stage, events are required to have a muon with high or a
  hadron with high transverse energy in the calorimeters.
The software trigger requires a two-, three- or four-track secondary vertex (SV) with a significant displacement from any PV. 
At least one charged particle must have a large transverse momentum and be inconsistent with originating from a PV. 
A multivariate algorithm <cit.> is used for the identification of secondary vertices consistent with the decay of a b hadron into charged hadrons. 
In addition, for the 4h final states, an algorithm is used to identify inclusive ϕ→ K^+ K^- production at a secondary vertex, without requiring a decay consistent with a b hadron. 

In the initial stage of the offline selection, candidates for  and  (→ 4h ) decays are required to have four (six) good quality, high-tracks consistent with coming from a vertex that is displaced from any PV in the event. 
Loose PID criteria are applied, requiring the tracks to be consistent with the types of hadrons corresponding to the respective final states.
In addition, the  candidates, formed by the combination of the final-state candidates, are required to originate from a PV by requiring a small angle between the  candidate momentum vector and the vector joining this PV and the  decay vertex, and a small , which is defined as the difference in the vertex-fit of the considered PV reconstructed with and without the candidate.
When forming the  candidates for → pp̅ and → pp̅ decays, the pp̅ mass resolution is improved by performing a kinematic fit <cit.> in which the candidate is constrained to originate from its associated PV (that with the smallest value of  for the ), and its reconstructed invariant mass is constrained to be equal to the known value of the B^0_s mass <cit.>. 
No significant improvement of the 4h mass resolution is observed for → 4h decays.
In order to reduce the combinatorial background, a first BDT, based on kinematic and topological properties of the reconstructed tracks and candidates, is applied directly at the initial stage of the offline selection of candidate → 4h K^+K^- decays. 
It is trained with events from dedicated simulation samples as signal and data from the reconstructed high-mass sidebands of the candidates as background.

In the second step of the selection, the offline BDTs are applied. They are trained using the same strategy as that used for the training of the first BDT. 
The maximum distance of closest approach between final-state particles, the transverse momentum, and the χ^2_ IP of each reconstructed track, as well as the vertex-fit χ^2 per degree of freedom, the χ^2_ IP, and the pointing angle of the candidates are used as input to the BDT classifiers used to select candidate → pp̅ and → pp̅ decays.
For the pp̅ K^+K^- final state, the direction angle, the flight distance significance and the χ^2_ IP of the reconstructed candidate are also used as input to the BDT, while the of the candidate is used for the pp̅π^+π^- final state. The difference in the choice of input variables for the 
p p̅K^+K^- and the p p̅π^+π^- final states is due to different PID requirements applied to pions and kaons in the first stage of the offline selection.
The optimised requirements on the BDT output and PID variables for → pp̅ (→ pp̅) decays retain ∼ 45 % (40 %) of the signal and reject more than 99% (99%) of the combinatorial background, inside the mass-fit ranges defined in Sec. <ref>.


Dedicated BDT classifiers are trained to select candidate → 4h decays using the following set of input variables: the and the IP with respect to the SV of all reconstructed tracks; the vertex-fit χ^2 of the  and ϕ candidates; the vertex-fit χ^2, the , the flight-distance significance with respect to the PV of the candidate, and the angle between the momentum and the vector joining the primary to the secondary vertex of the candidate.
The optimised requirements on the BDT output and PID variables, for each of the 4h modes, retain about 50% of the signal and reject more than 99% of the combinatorial background inside the mass-fit ranges defined in Sec. <ref>.

From simulation, after all requirements for → 4h decays, a significant contamination is expected from → 3h decays, where the  decays to ϕ and 3h is any combination of three charged kaons and pions.
This background contribution has distributions similar to the signal in the 4hK^+K^- and K^+K^- invariant-mass spectra, while its distribution in the 4h invariant-mass spectrum is not expected to exhibit any peaking structure. 
In order to reduce this background contamination, the absolute difference between the known value of the mass <cit.> and the reconstructed invariant mass of the system formed by the combination of the  candidate and any signal candidate track consistent with a pion hypothesis is required to be > 17. 
This requirement is optimised using the significance of → candidates with respect to background contributions. This significance is stable for cut values in the range [9, 25]MeV/c^2, with a maximum at 17MeV/c^2, which removes about 90% of → 3h decays, with no significant signal loss.







§ EFFICIENCY CORRECTION







The efficiency correction factors appearing in Eq. <ref> are obtained from fully simulated events.
Since the signal and normalisation channels are selected based on the same requirements and have the same final-state particles with very similar kinematic distributions, the ratio between the efficiency correction factors for → X and → X decays are expected to be close to unity.
The efficiency correction factors include the geometrical acceptance of the LHCb detector, the reconstruction efficiency, the efficiency of the offline selection criteria, including the trigger and PID requirements.
The efficiencies of the PID requirements are obtained as a function of particle momentum and number of charged tracks in the event using dedicated data-driven calibration samples of pions, kaons, and protons <cit.>.
The overall efficiency is taken as the product of the geometrical acceptance of the LHCb detector, the reconstruction efficiency and the efficiency of the offline selection criteria.
In addition, corrections are applied to account for different lifetime values used in simulation with respect to the known values for the decay channels considered.
The effective lifetime for decays to ϕ () final state, being purely -even (-odd), is obtained from the known value of the decay width of the light (heavy) state <cit.>.
The effective lifetime of →ϕ (→) decays is taken from Ref. <cit.>.
The lifetime correction is obtained after reweighting the signal and normalisation simulation samples.
The final efficiency correction factors, given in Table <ref>, are found to be compatible to unity as expected.







§ FIT MODELS



In this section the fit models used for the measurement of the branching fractions are described, first the model used for → decays in Sec. <ref>, then the model used for →ϕ decays in Sec. <ref>.




 §.§ Model for → decays



Candidates are fitted in two stages.
First, an extended UML fit to the pp̅π^+π^- invariant-mass spectrum is performed in the range 5150–5540, to discriminate → pp̅ events from combinatorial background, B^0→ p p̅ decays, and B^0→ p p̅ K π decays, where the kaon is misidentified as a pion.
The p p̅ mass distribution of → p p̅ and B^0→ p p̅ candidates are described by Hypatia functions <cit.>. 
Both Hypatia functions share common core resolution and tail parameters. The latter are fixed to values obtained from simulation.
The distribution of the misidentified B^0→ p p̅ K π background is described by a Crystal Ball function <cit.>, with mode, power-law tail, and core resolution parameters fixed to values obtained from simulation.
The combinatorial background is modelled using an exponential function.
The mode and the common core resolution parameters of the Hypatia functions and the slope of the exponential functions, as well as all the yields, are allowed to vary in the fit to data. 
Using the information from the fit to the pp̅ spectrum, signal weights are then computed and the background components are subtracted using the _s Plot technique <cit.>. 
Correlations between the pp̅ and pp̅ invariant-mass spectra, for both signal and backgrounds, are found to be negligible.

Second, a UML fit to the weighted pp̅ invariant-mass distribution is performed in the mass range 2900–3200.
In this region, three event categories are expected to populate the pp̅ spectrum: the and resonances, as well as a possible contribution from nonresonant → (pp̅)_ NR decays.
The pp̅ mass distribution of candidates is described by the convolution of the square of the modulus of a complex relativistic Breit-Wigner function (RBW) with constant width and a function describing resolution effects. 
The expression of the RBW function is taken as


    R_ res(m;m_ res,Γ_ res) ∝1/m^2_ res - m^2 - i m_ resΓ_ res,


where m_ res and Γ_ res are the pole mass and the natural width, respectively, of the resonance. 
From simulation, in the mass range considered, the pp̅ invariant-mass resolution is found to be a few , while Γ_ = 31.8±0.8 <cit.>. 
Thus, the pp̅ distribution of candidates is expected to be dominated by the RBW, with only small effects on the total lineshape from the resolution.
On the other hand, due to the small natural width of the resonance <cit.>, the corresponding lineshape is assumed to be described to a very good approximation by the resolution function only.
For the and lineshapes, Hypatia functions are used to parametrise the resolution, with tail parameters that are fixed to values obtained from simulation. A single core resolution parameter, σ_ res^cc̅, shared between these two functions, is free to vary in the fit to data.
The pole mass and the mode of the Hypatia function describing the lineshape, which can be approximated by the pole mass of the resonance, are also free to vary, while the η_c natural width is constrained to its known value <cit.>.
The possible contribution from → (pp̅)_ NR decays is parametrised by a constant.

The angular distributions of P- and S-waves are characterised by a linear combination of odd- and even-order Legendre polynomials, respectively.
In the case of a uniform acceptance, after integration over the helicity angles, the interference between the two waves vanishes. 
For a non-uniform acceptance, after integration, only residual effects from the interference between (→ pp̅) and (→ pp̅) amplitudes can arise in the pp̅ invariant mass spectra. 
Due to the limited size of the current data sample, these effects are assumed to be negligible.
Also, given the sample size and the small expected contribution of the NR pp̅ component, interference between the (→ pp̅) and (pp̅)_ NR amplitudes is neglected.


In order to fully exploit the correlation between the yields of and candidates, the former is parametrised in the fit, rearranging Eq. (<ref>), as


    N_ = N_×ℬ(→)/ℬ(→)×ℬ(→ pp̅) /ℬ(→ pp̅)×ε()_pp̅/ε()_pp̅ ,


where (→) and N_ are free parameters. 
The yield of the NR pp̅ component is also free to vary.






 §.§ Model for →ϕ decays



The procedure and the fit model used to measure ℬ( →ϕ ) is based on that described in Sec. <ref>.
However, several additional features are needed to describe the data, as detailed below.

The  invariant mass is added as a second dimension in the first step fit, which here consists of a two-dimensional (2D) fit to the pp̅ or 4h and  invariant mass spectra.
This allows the contributions from ϕ→ decays and nonresonant  pairs to be separated.
Thus, the first step of the fitting procedure consists of four independent two-dimensional UML fits to the pp̅ versus  and 4h versus  invariant-mass spectra in the ranges 5200–5500and 990–1050, respectively.[In order to better constrain the combinatorial background shape, the upper limit of the pp̅ invariant-mass range is extended to 5550.] 

Similar 2D fit models are used for each 4h mode. 
The 4h distributions of → 4h ϕ signal and → 4h ϕ background contributions, as well as those of → 4h and → 4h backgrounds, are described by Hypatia functions.  
The 4h distribution of the combinatorial background is parametrised using two exponential functions, one for when the  pair arises from a random combination of two prompt kaons, and another for when the  pair originates from the decay of a prompt ϕ meson.
The K^+K^- distribution of each contribution including a ϕ in the final state is described by the square of the modulus of a RBW with mass-dependent width convolved with a Gaussian function accounting for resolution effects.
The K^+K^- distributions of the contributions including a nonresonant  pair are parametrised by linear functions.
The expression of the RBW with mass-dependent width describing the ϕ resonance is the analogue of Eq. (<ref>), with the mass-dependent width given by 


    Γ(m) = Γ_ϕ( q/q_ϕ)^3( m_ϕ/m) X^2(qr),


where m_ϕ=1019.461±0.019, Γ_ϕ=4.266±0.031 <cit.>, and q is the magnitude of the momentum of one of the ϕ decay products, evaluated in the resonance rest frame such that


    q = 1/2√(m^2-4m_K^±^2).


with m_K^± = 493.677 ± 0.016 <cit.>.
The symbol q_ϕ denotes the value of q when m = m_ϕ. The X(qr) function is the Blatt-Weisskopf barrier factor <cit.> with a barrier radius of r. 
The value of the parameter r is fixed at 3(GeV/c)^-1.
Defining the quantity z = qr, the Blatt-Weisskopf barrier function for a spin-1 resonance is given by


    X(z) = √(1+z_ϕ^2/1+z^2),


where z_ϕ represents the value of z when m = m_ϕ.

The same 2D fit model is used for the pp̅ mode with an additional component accounting for the presence of misidentified B^0→ p p̅ K π background events. 
The pp̅ and  distributions of B^0→ p p̅ K π candidates are described by a Crystal Ball function and a linear function, respectively.
 
Using the sets of signal weights computed from the 2D fits, the pp̅ and 4h spectra are obtained after subtraction of background candidates from  decays and  decays with nonresonant  pairs as well as combinatorial background.
Correlations between the invariant-mass spectra used in the 2D fits and the pp̅ or 4h spectrum are found to be negligible.
A simultaneous UML fit is then performed to the weighted pp̅ and 4h invariant-mass distributions, with identical mass ranges of 2820–3170.
Different models are used to describe the pp̅ and 4h spectra.

The pp̅ invariant-mass spectrum is modelled similarly to the description in Sec. <ref>.
However, as shown in Sec. <ref>, the fit to the pp̅ spectrum for → pp̅ decays yields a contribution of NR pp̅ decays compatible with zero. 
Thus, here, the contribution of such decays is fixed to zero and only considered as a source of systematic uncertainty, as described in Sec. <ref>.

For the 4h modes, in addition to →ϕ and →ϕ decays, other contributions are expected in the mass range considered:
→ 4h ϕ decays, where the 4h system is in a nonresonant state with a total angular momentum equal to zero, and where decays proceed via intermediate resonant states decaying in turn into two or three particles for instance, → PP^'ϕ decays, where P and P^' could be any resonance such as (892), ρ(770), ϕ(1020), (782), _2(1270), '_2(1525) and _2(1320).
Similarly to →3h decays, all these decays are expected to have smooth distributions in the 4h invariant-mass spectra. 
Therefore, lacking information from previous measurements, all these contributions are merged into one category, denoted (4h)_ bkg. The 4h nonresonant contribution is denoted (4h)_ NR.
The  being a pseudoscalar particle, interference between →(→ 4h) ϕ and → (4h)_ NRϕ amplitudes for each 4h final state are accounted for in the model. 
On the other hand, given the large number of amplitudes contributing to the (4h)_ bkg event category, the net effect of all interference terms is assumed to cancel.
Similarly to the pp̅ fit model, terms describing residual effects of the interference between the and the other fit components are neglected.
The total amplitude for each of the 4h modes, integrated over the helicity angles, is then given by


    |A(m_f;c^f_k,𝐚)|^2 =   ∑_k |c^f_k R_k(m_f;𝐚)|^2 + 2( c^f_R_(m_f;𝐚) c^f∗_ NRR^∗_ NR(m_f;𝐚) )  ,


where R_k(m_f;𝐚) is the line-shape of the component k, 𝐚 represents the line-shape parameters, c_k^f are complex numbers such that c^f_k = α_k^f  e^iφ_k^f where α_k^f and φ_k^f are the magnitude and the strong phase of amplitude k, and m_f is one of the 4h invariant masses. 
The  and the  resonances are described similarly to the pp̅ mode, and the (4h)_ NR and (4h)_ bkg components are described using exponential functions.

Finally, taking into account the detector resolution, the total function, ℱ_ tot, used to describe the invariant-mass spectra m_f is given by


    ℱ_ tot(m_f;c^f_k,𝐚,𝐚^')     = |A(m_f;c^f_k,𝐚)|^2  ⊗ℛ(𝐚^' (m_f)) 
       =  ξ^f_ℱ_(m_f)/∫_m_fℱ_(m_f)  dm_f + ξ^f_ℱ_(m_f)/∫_m_fℱ_(m_f)  dm_f
          + ξ^f_ NRℱ_ NR(m_f)/∫_m_fℱ_ NR(m_f)  dm_f + ξ^f_ bkgℱ_ bkg(m_f)/∫_m_fℱ_ bkg(m_f)  dm_f
          + 2 √(ξ^f_ξ^f_ NR)ℱ_ I(m_f)/∫_m_f√(ℱ_(m_f)ℱ_ NR(m_f)) dm_f ,








with ξ^f_k = (α_k^f)^2 and where the expressions for ℱ_k(m_f) are


    ℱ_(m_f)     =   |R_(m_f;𝐚)|^2⊗ℛ(𝐚^' (m_f)) , 
    ℱ_(m_f)     =   ℛ(𝐚^' (m_f)) , 
    ℱ_ NR(m_f)     =    e^κ_ NR m_f⊗ℛ(𝐚^' (m_f)) , 
    ℱ_ bkg(m_f)     =    e^κ_ bkg m_f⊗ℛ(𝐚^' (m_f)) , 
    ℱ_ I(m_f)     =   ( e^κ_ NR m_f/2[R_(m_f;𝐚)e^iδφ] ) ⊗ℛ(𝐚^' (m_f)) ,


where δφ is the difference between the strong phases of (4h)_ NRϕ and (→ 4h) ϕ amplitudes. 
The integrals in Eq. (<ref>) are calculated over the mass range in which the fit is performed.
Only the and components are used in the expression for ℱ_ tot(m_pp̅).
The fit fractions FF_k measured for each component, as well as the interference fit fraction FF_ I between the  and the NR amplitudes for the 4h modes, are calculated as:


    FF_k^f    =   ∫_m_fξ^f_kℱ_k(m_f)/ℱ_tot(m_f) ∫_m_fℱ_k(m_f)  dm_f dm_f , 
    FF^f_ I   =   ∫_m_f2 √(ξ^f_ξ^f_ NR)ℱ_ I(m_f)/ℱ_tot(m_f)∫_m_f√(ℱ_(m_f)ℱ_ NR(m_f)) dm_f dm_f .



The resolution, ℛ(𝐚^' (m_f)), is described by a Hypatia function, with parameters 𝐚^' (m_f) that depend on the final state and the invariant-mass region.
They are estimated using dedicated simulation samples in two mass regions: a high-mass region around the resonance, and a low-mass region around the resonance.

As in the model for → pp̅ decays, the branching fraction ℬ(→ϕ) is directly determined in the fit.
In this configuration, the squared magnitudes of the amplitudes, ξ^f_, are parametrised as 


    ξ^f_ = ξ^f_×ℬ(→ϕ)/ℬ(→ϕ)×ℬ(→ f) /ℬ(→ f)×ε()_f/ε()_f .



In the simultaneous fit to the pp̅ and 4h invariant-mass spectra several parameters are allowed to take different values depending on the final state: the intensities ξ^f_k (free to vary), the slopes κ_ bkg and κ_ NR of the (4h)_ bkg and (4h)_ NR exponentials, respectively, (free to vary), the relative strong phase between the (4h)_ NR and amplitudes (free to vary) as well as the low and high mass resolution parameters (fixed).
The pole mass, the mode of the Hypatia function describing the and the branching fraction ℬ(→ϕ) are common parameters across all final states and are free to vary in the fit. 
The width is fixed to the world average value taken from Ref. <cit.>.
For each mode, ξ_ and φ_ are fixed as reference to 1 and 0, respectively. 







§ RESULTS












The yields of the various decay modes determined by the UML fit to the pp̅ invariant mass distribution, and from the 2D fits to the pp̅(4h) versus  invariant mass planes, are summarised in Table <ref>.
The mass distributions and the fit projections are shown in Appendix <ref>.
The pp̅ and 2D fit models are validated using large samples of pseudoexperiments, from which no significant bias is observed. 







The pp̅ invariant-mass distribution for → pp̅ candidates, and the projection of the fit are shown in Fig. <ref>. 
The values of the and shape parameters as well as the yields are given in Table <ref>. 
The branching fraction for the → decay mode is found to be

    ℬ (B^0_s→η_cπ^+π^-) =  (1.76 ± 0.59 ± 0.12 ± 0.29) × 10^-4 ,

 where the two first uncertainties are statistical and systematic,
 respectively, and the third uncertainty is due to the limited
 knowledge of the external branching fractions. The systematic
 uncertainties on the branching fraction are discussed in
 Sec. <ref>. The significance of the presence of
 → decays in the pp̅ invariant-mass
 spectrum is estimated, as √(-2 Δln L), from the
   difference between the log-likelihood (ln L) values for N_ = 0 and the value
   of N_ that minimises ln L.
For the estimation of the significance, N_ is not parametrised as a function of (→), but is a free parameter in the fit.
As shown in Fig. <ref>, the significance of the component in the fit to the pp̅ invariant-mass distribution is 5.0 standard deviations (σ) with statistical uncertainties and 4.6σ when including systematic uncertainties.
The latter is obtained by adding Gaussian constraints to the likelihood function.
This result is the first evidence for → decays.

















The pp̅ and 4h invariant-mass distributions for → pp̅ϕ and → 4hϕ candidates, and the projection of the simultaneous fit are shown in Fig. <ref>. 
The values of the shape parameters, of the magnitudes and of the relative strong phases are given in Table <ref>. 
The statistical correlation matrix of the simultaneous fit is given in Appendix <ref>. 
The fit fractions are given in Table <ref>.
The measured branching fraction for the →ϕ decay mode is


    ℬ (B^0_s→η_cϕ) = (5.01 ± 0.53 ± 0.27 ± 0.63) × 10^-4 ,


where the two first uncertainties are statistical and systematic, respectively, and the third uncertainty is due to the limited knowledge of the external branching fractions.
This measurement corresponds to the first observation of →ϕ decays.

As a cross-check, individual fits to the pp̅ and to each of the 4h invariant-mass spectra give compatible values of ℬ (B^0_s→η_cϕ) within statistical uncertainties.
The precision of the ℬ (B^0_s→η_cϕ)
measurement obtained using each of the 4h modes is limited compared to the pp̅ mode.
This is expected due to the presence of additional components below the and resonance in the 4h invariant-mass spectra, and due to the interference between →(→ 4h)ϕ and → (4h)_ NRϕ amplitudes.
The measurement of ℬ (B^0_s→η_cϕ) from the simultaneous fit is largely dominated by the pp̅ mode.















§ SYSTEMATIC UNCERTAINTIES



As the expressions for ℬ(→) and ℬ(→ϕ) are based on the ratios of observed quantities, only sources of systematic uncertainties inducing different biases to the number of observed and candidates are considered. 
The dominant source of systematic uncertainties is due to the knowledge of the external branching fractions. 
These are estimated by adding Gaussian constraints on the external branching fractions in the fits, with widths corresponding to their known uncertainties <cit.>. 
A summary of the systematic uncertainties can be found in Table <ref>. 

To assign systematic uncertainties due to fixing of PDF parameters, the fits are repeated by varying all of them simultaneously. 
The resolution parameters, estimated from simulation, are varied according to normal distributions, taking into account the correlations between the parameters and with variances related to the size of the simulated samples.
The external parameters are varied within a normal distribution of mean and width fixed to their known values and uncertainties <cit.>.
This procedure is repeated 1000 times, and for each iteration a new value of the branching fraction is obtained.
The systematic uncertainties on the branching fraction are taken from the variance of the corresponding distributions. 





The systematic uncertainty due to the fixing of the values of the efficiencies is estimated by adding Gaussian constraints to the likelihood functions, with widths that are taken from the uncertainties quoted in Table <ref>.

The presence of intrinsic biases in the fit models is studied using parametric simulation. 
For this study, 1000 pseudoexperiments are generated and fitted using the nominal PDFs, where the generated parameter values correspond to those obtained in the fits to data. 
The biases on the branching fractions are then calculated as the difference between the generated values and the mean of the distribution of the fitted branching fraction values. 

To assign a systematic uncertainty from the model used to describe the detector resolution, the fits are repeated for each step replacing the Hypatia functions by bifurcated Crystal Ball functions, the parameters of which are obtained from simulation. 
The difference from the nominal branching fraction result is assigned as a systematic uncertainty. 

The Blatt-Weisskopf parameter r of the ϕ is arbitrarily set to 3()^-1.
To assign a systematic uncertainty due to the fixed value of this r parameter, the fits are repeated for different values taken in the range 1.5–5.0()^-1.
The maximum differences from the nominal branching fraction result are assigned as systematic uncertainties.

To assign a systematic uncertainty due to the assumption of a uniform acceptance, the simultaneous fit is repeated after correcting the 4h invariant-mass distributions for acceptance effects. 
A histogram describing the acceptance effects in each of the 4h invariant-mass spectra is constructed from the ratio of the normalised 4h invariant-mass distributions taken from simulated samples of → (4h) ϕ phase space decays, obtained either directly from , or after processing through the full simulation chain.     
The simultaneous fit is repeated after applying weights for each event from the central value of its bin in the 4h invariant-mass distribution.
The difference from the nominal branching fraction result is assigned as a systematic uncertainty. 
No significant dependence on the binning choice was observed.

The systematic uncertainty due to neglecting the presence of a nonresonant pp̅ contribution in the pp̅ spectrum for → pp̅ϕ candidates is estimated by repeating the simultaneous fit with an additional component described by an exponential function, where the slope and the yield are allowed to vary.
The difference from the nominal branching fraction result is assigned as a systematic uncertainty.








§ CONCLUSIONS



This paper reports the observation of →ϕ decays and the first evidence for → decays. 
The branching fractions are measured to be


    ℬ (B^0_s→η_cϕ)   =   (5.01 ± 0.53 ± 0.27 ± 0.63 ) × 10^-4 , 
    ℬ (B^0_s→η_cπ^+ π^-)   =   (1.76 ± 0.59 ± 0.12 ± 0.29 ) × 10^-4 ,


where in each case the two first uncertainties are statistical and systematic, respectively, and the third uncertainties are due to the limited knowledge of the external branching fractions.
The significance of the → decay mode, including systematic uncertainties, is 4.6σ.
The results for (→) and (→ϕ) are in agreement with expectations based on Eqs. (<ref>), (<ref>) and (<ref>).

The data sample recorded by the LHCb experiment in Run 1 of the LHC is not sufficiently large to allow a measurement of the -violating phase from time-dependent analysis of →ϕ or → decays.
However, in the future with significant improvement of the hadronic trigger efficiencies <cit.>, these decay modes may become of interest to add sensitivity to the measurement of . 









§ ACKNOWLEDGEMENTS











 
We express our gratitude to our colleagues in the CERN
accelerator departments for the excellent performance of the LHC. We
thank the technical and administrative staff at the LHCb
institutes. We acknowledge support from CERN and from the national
agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China);
CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy);
FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland);
NASU (Ukraine); STFC (United Kingdom); NSF (USA).
We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities behind the multiple open
source software packages on which we depend.
Individual groups or members have received support from AvH Foundation (Germany),
EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union),
Conseil Général de Haute-Savoie, Labex ENIGMASS and OCEVU,
Région Auvergne (France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust (United Kingdom).




Appendix






§ FIT PROJECTIONS

 

The pp̅ invariant mass distribution and the fit projection are shown in Fig. <ref>.
The four pp̅(4h) and  invariant-mass distributions and the corresponding two-dimensional fit projections are shown in Figs. <ref> to <ref>.































§ CORRELATION MATRIX

 

The statistical correlation matrix for the simultaneous fit to the pp̅ and 4h invariant-mass distributions for → pp̅ϕ and → 4hϕ candidates is given in Table <ref>.





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C. D'Ambrosio^40,
F. Da Cunha Marinho^2,
E. Dall'Occo^43,
J. Dalseno^48,
P.N.Y. David^43,
A. Davis^3,
K. De Bruyn^6,
S. De Capua^56,
M. De Cian^12,
J.M. De Miranda^1,
L. De Paula^2,
M. De Serio^14,d,
P. De Simone^19,
C.T. Dean^53,
D. Decamp^4,
M. Deckenhoff^10,
L. Del Buono^8,
M. Demmer^10,
A. Dendek^28,
D. Derkach^35,
O. Deschamps^5,
F. Dettori^40,
B. Dey^22,
A. Di Canto^40,
H. Dijkstra^40,
F. Dordei^40,
M. Dorigo^41,
A. Dosil Suárez^39,
A. Dovbnya^45,
K. Dreimanis^54,
L. Dufour^43,
G. Dujany^56,
K. Dungs^40,
P. Durante^40,
R. Dzhelyadin^37,
A. Dziurda^40,
A. Dzyuba^31,
N. Déléage^4,
S. Easo^51,
M. Ebert^52,
U. Egede^55,
V. Egorychev^32,
S. Eidelman^36,w,
S. Eisenhardt^52,
U. Eitschberger^10,
R. Ekelhof^10,
L. Eklund^53,
S. Ely^61,
S. Esen^12,
H.M. Evans^49,
T. Evans^57,
A. Falabella^15,
N. Farley^47,
S. Farry^54,
R. Fay^54,
D. Fazzini^21,i,
D. Ferguson^52,
A. Fernandez Prieto^39,
F. Ferrari^15,40,
F. Ferreira Rodrigues^2,
M. Ferro-Luzzi^40,
S. Filippov^34,
R.A. Fini^14,
M. Fiore^17,g,
M. Fiorini^17,g,
M. Firlej^28,
C. Fitzpatrick^41,
T. Fiutowski^28,
F. Fleuret^7,b,
K. Fohl^40,
M. Fontana^16,40,
F. Fontanelli^20,h,
D.C. Forshaw^61,
R. Forty^40,
V. Franco Lima^54,
M. Frank^40,
C. Frei^40,
J. Fu^22,q,
W. Funk^40,
E. Furfaro^25,j,
C. Färber^40,
A. Gallas Torreira^39,
D. Galli^15,e,
S. Gallorini^23,
S. Gambetta^52,
M. Gandelman^2,
P. Gandini^57,
Y. Gao^3,
L.M. Garcia Martin^69,
J. García Pardiñas^39,
J. Garra Tico^49,
L. Garrido^38,
P.J. Garsed^49,
D. Gascon^38,
C. Gaspar^40,
L. Gavardi^10,
G. Gazzoni^5,
D. Gerick^12,
E. Gersabeck^12,
M. Gersabeck^56,
T. Gershon^50,
Ph. Ghez^4,
S. Gianì^41,
V. Gibson^49,
O.G. Girard^41,
L. Giubega^30,
K. Gizdov^52,
V.V. Gligorov^8,
D. Golubkov^32,
A. Golutvin^55,40,
A. Gomes^1,a,
I.V. Gorelov^33,
C. Gotti^21,i,
R. Graciani Diaz^38,
L.A. Granado Cardoso^40,
E. Graugés^38,
E. Graverini^42,
G. Graziani^18,
A. Grecu^30,
P. Griffith^16,
L. Grillo^21,40,i,
B.R. Gruberg Cazon^57,
O. Grünberg^67,
E. Gushchin^34,
Yu. Guz^37,
T. Gys^40,
C. Göbel^62,
T. Hadavizadeh^57,
C. Hadjivasiliou^5,
G. Haefeli^41,
C. Haen^40,
S.C. Haines^49,
B. Hamilton^60,
X. Han^12,
S. Hansmann-Menzemer^12,
N. Harnew^57,
S.T. Harnew^48,
J. Harrison^56,
M. Hatch^40,
J. He^63,
T. Head^41,
A. Heister^9,
K. Hennessy^54,
P. Henrard^5,
L. Henry^8,
E. van Herwijnen^40,
M. Heß^67,
A. Hicheur^2,
D. Hill^57,
C. Hombach^56,
H. Hopchev^41,
W. Hulsbergen^43,
T. Humair^55,
M. Hushchyn^35,
D. Hutchcroft^54,
M. Idzik^28,
P. Ilten^58,
R. Jacobsson^40,
A. Jaeger^12,
J. Jalocha^57,
E. Jans^43,
A. Jawahery^60,
F. Jiang^3,
M. John^57,
D. Johnson^40,
C.R. Jones^49,
C. Joram^40,
B. Jost^40,
N. Jurik^57,
S. Kandybei^45,
M. Karacson^40,
J.M. Kariuki^48,
S. Karodia^53,
M. Kecke^12,
M. Kelsey^61,
M. Kenzie^49,
T. Ketel^44,
E. Khairullin^35,
B. Khanji^12,
C. Khurewathanakul^41,
T. Kirn^9,
S. Klaver^56,
K. Klimaszewski^29,
S. Koliiev^46,
M. Kolpin^12,
I. Komarov^41,
R.F. Koopman^44,
P. Koppenburg^43,
A. Kosmyntseva^32,
A. Kozachuk^33,
M. Kozeiha^5,
L. Kravchuk^34,
K. Kreplin^12,
M. Kreps^50,
P. Krokovny^36,w,
F. Kruse^10,
W. Krzemien^29,
W. Kucewicz^27,l,
M. Kucharczyk^27,
V. Kudryavtsev^36,w,
A.K. Kuonen^41,
K. Kurek^29,
T. Kvaratskheliya^32,40,
D. Lacarrere^40,
G. Lafferty^56,
A. Lai^16,
G. Lanfranchi^19,
C. Langenbruch^9,
T. Latham^50,
C. Lazzeroni^47,
R. Le Gac^6,
J. van Leerdam^43,
A. Leflat^33,40,
J. Lefrançois^7,
R. Lefèvre^5,
F. Lemaitre^40,
E. Lemos Cid^39,
O. Leroy^6,
T. Lesiak^27,
B. Leverington^12,
T. Li^3,
Y. Li^7,
T. Likhomanenko^35,68,
R. Lindner^40,
C. Linn^40,
F. Lionetto^42,
X. Liu^3,
D. Loh^50,
I. Longstaff^53,
J.H. Lopes^2,
D. Lucchesi^23,o,
M. Lucio Martinez^39,
H. Luo^52,
A. Lupato^23,
E. Luppi^17,g,
O. Lupton^40,
A. Lusiani^24,
X. Lyu^63,
F. Machefert^7,
F. Maciuc^30,
O. Maev^31,
K. Maguire^56,
S. Malde^57,
A. Malinin^68,
T. Maltsev^36,
G. Manca^16,f,
G. Mancinelli^6,
P. Manning^61,
J. Maratas^5,v,
J.F. Marchand^4,
U. Marconi^15,
C. Marin Benito^38,
M. Marinangeli^41,
P. Marino^24,t,
J. Marks^12,
G. Martellotti^26,
M. Martin^6,
M. Martinelli^41,
D. Martinez Santos^39,
F. Martinez Vidal^69,
D. Martins Tostes^2,
L.M. Massacrier^7,
A. Massafferri^1,
R. Matev^40,
A. Mathad^50,
Z. Mathe^40,
C. Matteuzzi^21,
A. Mauri^42,
E. Maurice^7,b,
B. Maurin^41,
A. Mazurov^47,
M. McCann^55,40,
A. McNab^56,
R. McNulty^13,
B. Meadows^59,
F. Meier^10,
M. Meissner^12,
D. Melnychuk^29,
M. Merk^43,
A. Merli^22,q,
E. Michielin^23,
D.A. Milanes^66,
M.-N. Minard^4,
D.S. Mitzel^12,
A. Mogini^8,
J. Molina Rodriguez^1,
I.A. Monroy^66,
S. Monteil^5,
M. Morandin^23,
P. Morawski^28,
A. Mordà^6,
M.J. Morello^24,t,
O. Morgunova^68,
J. Moron^28,
A.B. Morris^52,
R. Mountain^61,
F. Muheim^52,
M. Mulder^43,
M. Mussini^15,
D. Müller^56,
J. Müller^10,
K. Müller^42,
V. Müller^10,
P. Naik^48,
T. Nakada^41,
R. Nandakumar^51,
A. Nandi^57,
I. Nasteva^2,
M. Needham^52,
N. Neri^22,
S. Neubert^12,
N. Neufeld^40,
M. Neuner^12,
T.D. Nguyen^41,
C. Nguyen-Mau^41,n,
S. Nieswand^9,
R. Niet^10,
N. Nikitin^33,
T. Nikodem^12,
A. Nogay^68,
A. Novoselov^37,
D.P. O'Hanlon^50,
A. Oblakowska-Mucha^28,
V. Obraztsov^37,
S. Ogilvy^19,
R. Oldeman^16,f,
C.J.G. Onderwater^70,
J.M. Otalora Goicochea^2,
A. Otto^40,
P. Owen^42,
A. Oyanguren^69,
P.R. Pais^41,
A. Palano^14,d,
M. Palutan^19,
A. Papanestis^51,
M. Pappagallo^14,d,
L.L. Pappalardo^17,g,
W. Parker^60,
C. Parkes^56,
G. Passaleva^18,
A. Pastore^14,d,
G.D. Patel^54,
M. Patel^55,
C. Patrignani^15,e,
A. Pearce^40,
A. Pellegrino^43,
G. Penso^26,
M. Pepe Altarelli^40,
S. Perazzini^40,
P. Perret^5,
L. Pescatore^41,
K. Petridis^48,
A. Petrolini^20,h,
A. Petrov^68,
M. Petruzzo^22,q,
E. Picatoste Olloqui^38,
B. Pietrzyk^4,
M. Pikies^27,
D. Pinci^26,
A. Pistone^20,
A. Piucci^12,
V. Placinta^30,
S. Playfer^52,
M. Plo Casasus^39,
T. Poikela^40,
F. Polci^8,
A. Poluektov^50,36,
I. Polyakov^61,
E. Polycarpo^2,
G.J. Pomery^48,
A. Popov^37,
D. Popov^11,40,
B. Popovici^30,
S. Poslavskii^37,
C. Potterat^2,
E. Price^48,
J.D. Price^54,
J. Prisciandaro^39,40,
A. Pritchard^54,
C. Prouve^48,
V. Pugatch^46,
A. Puig Navarro^42,
G. Punzi^24,p,
W. Qian^50,
R. Quagliani^7,48,
B. Rachwal^27,
J.H. Rademacker^48,
M. Rama^24,
M. Ramos Pernas^39,
M.S. Rangel^2,
I. Raniuk^45,†,
F. Ratnikov^35,
G. Raven^44,
F. Redi^55,
S. Reichert^10,
A.C. dos Reis^1,
C. Remon Alepuz^69,
V. Renaudin^7,
S. Ricciardi^51,
S. Richards^48,
M. Rihl^40,
K. Rinnert^54,
V. Rives Molina^38,
P. Robbe^7,40,
A.B. Rodrigues^1,
E. Rodrigues^59,
J.A. Rodriguez Lopez^66,
P. Rodriguez Perez^56,†,
A. Rogozhnikov^35,
S. Roiser^40,
A. Rollings^57,
V. Romanovskiy^37,
A. Romero Vidal^39,
J.W. Ronayne^13,
M. Rotondo^19,
M.S. Rudolph^61,
T. Ruf^40,
P. Ruiz Valls^69,
J.J. Saborido Silva^39,
E. Sadykhov^32,
N. Sagidova^31,
B. Saitta^16,f,
V. Salustino Guimaraes^1,
C. Sanchez Mayordomo^69,
B. Sanmartin Sedes^39,
R. Santacesaria^26,
C. Santamarina Rios^39,
M. Santimaria^19,
E. Santovetti^25,j,
A. Sarti^19,k,
C. Satriano^26,s,
A. Satta^25,
D.M. Saunders^48,
D. Savrina^32,33,
S. Schael^9,
M. Schellenberg^10,
M. Schiller^53,
H. Schindler^40,
M. Schlupp^10,
M. Schmelling^11,
T. Schmelzer^10,
B. Schmidt^40,
O. Schneider^41,
A. Schopper^40,
K. Schubert^10,
M. Schubiger^41,
M.-H. Schune^7,
R. Schwemmer^40,
B. Sciascia^19,
A. Sciubba^26,k,
A. Semennikov^32,
A. Sergi^47,
N. Serra^42,
J. Serrano^6,
L. Sestini^23,
P. Seyfert^21,
M. Shapkin^37,
I. Shapoval^45,
Y. Shcheglov^31,
T. Shears^54,
L. Shekhtman^36,w,
V. Shevchenko^68,
B.G. Siddi^17,40,
R. Silva Coutinho^42,
L. Silva de Oliveira^2,
G. Simi^23,o,
S. Simone^14,d,
M. Sirendi^49,
N. Skidmore^48,
T. Skwarnicki^61,
E. Smith^55,
I.T. Smith^52,
J. Smith^49,
M. Smith^55,
H. Snoek^43,
l. Soares Lavra^1,
M.D. Sokoloff^59,
F.J.P. Soler^53,
B. Souza De Paula^2,
B. Spaan^10,
P. Spradlin^53,
S. Sridharan^40,
F. Stagni^40,
M. Stahl^12,
S. Stahl^40,
P. Stefko^41,
S. Stefkova^55,
O. Steinkamp^42,
S. Stemmle^12,
O. Stenyakin^37,
H. Stevens^10,
S. Stevenson^57,
S. Stoica^30,
S. Stone^61,
B. Storaci^42,
S. Stracka^24,p,
M. Straticiuc^30,
U. Straumann^42,
L. Sun^64,
W. Sutcliffe^55,
K. Swientek^28,
V. Syropoulos^44,
M. Szczekowski^29,
T. Szumlak^28,
S. T'Jampens^4,
A. Tayduganov^6,
T. Tekampe^10,
G. Tellarini^17,g,
F. Teubert^40,
E. Thomas^40,
J. van Tilburg^43,
M.J. Tilley^55,
V. Tisserand^4,
M. Tobin^41,
S. Tolk^49,
L. Tomassetti^17,g,
D. Tonelli^40,
S. Topp-Joergensen^57,
F. Toriello^61,
E. Tournefier^4,
S. Tourneur^41,
K. Trabelsi^41,
M. Traill^53,
M.T. Tran^41,
M. Tresch^42,
A. Trisovic^40,
A. Tsaregorodtsev^6,
P. Tsopelas^43,
A. Tully^49,
N. Tuning^43,
A. Ukleja^29,
A. Ustyuzhanin^35,
U. Uwer^12,
C. Vacca^16,f,
V. Vagnoni^15,40,
A. Valassi^40,
S. Valat^40,
G. Valenti^15,
R. Vazquez Gomez^19,
P. Vazquez Regueiro^39,
S. Vecchi^17,
M. van Veghel^43,
J.J. Velthuis^48,
M. Veltri^18,r,
G. Veneziano^57,
A. Venkateswaran^61,
M. Vernet^5,
M. Vesterinen^12,
J.V. Viana Barbosa^40,
B. Viaud^7,
D.  Vieira^63,
M. Vieites Diaz^39,
H. Viemann^67,
X. Vilasis-Cardona^38,m,
M. Vitti^49,
V. Volkov^33,
A. Vollhardt^42,
B. Voneki^40,
A. Vorobyev^31,
V. Vorobyev^36,w,
C. Voß^9,
J.A. de Vries^43,
C. Vázquez Sierra^39,
R. Waldi^67,
C. Wallace^50,
R. Wallace^13,
J. Walsh^24,
J. Wang^61,
D.R. Ward^49,
H.M. Wark^54,
N.K. Watson^47,
D. Websdale^55,
A. Weiden^42,
M. Whitehead^40,
J. Wicht^50,
G. Wilkinson^57,40,
M. Wilkinson^61,
M. Williams^40,
M.P. Williams^47,
M. Williams^58,
T. Williams^47,
F.F. Wilson^51,
J. Wimberley^60,
J. Wishahi^10,
W. Wislicki^29,
M. Witek^27,
G. Wormser^7,
S.A. Wotton^49,
K. Wraight^53,
K. Wyllie^40,
Y. Xie^65,
Z. Xing^61,
Z. Xu^4,
Z. Yang^3,
Y. Yao^61,
H. Yin^65,
J. Yu^65,
X. Yuan^36,w,
O. Yushchenko^37,
K.A. Zarebski^47,
M. Zavertyaev^11,c,
L. Zhang^3,
Y. Zhang^7,
A. Zhelezov^12,
Y. Zheng^63,
X. Zhu^3,
V. Zhukov^33,
S. Zucchelli^15.

^1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil

^2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil

^3Center for High Energy Physics, Tsinghua University, Beijing, China

^4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France

^5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France

^6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France

^7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France

^8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France

^9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany

^10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany

^11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany

^12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

^13School of Physics, University College Dublin, Dublin, Ireland

^14Sezione INFN di Bari, Bari, Italy

^15Sezione INFN di Bologna, Bologna, Italy

^16Sezione INFN di Cagliari, Cagliari, Italy

^17Sezione INFN di Ferrara, Ferrara, Italy

^18Sezione INFN di Firenze, Firenze, Italy

^19Laboratori Nazionali dell'INFN di Frascati, Frascati, Italy

^20Sezione INFN di Genova, Genova, Italy

^21Sezione INFN di Milano Bicocca, Milano, Italy

^22Sezione INFN di Milano, Milano, Italy

^23Sezione INFN di Padova, Padova, Italy

^24Sezione INFN di Pisa, Pisa, Italy

^25Sezione INFN di Roma Tor Vergata, Roma, Italy

^26Sezione INFN di Roma La Sapienza, Roma, Italy

^27Henryk Niewodniczanski Institute of Nuclear Physics  Polish Academy of Sciences, Kraków, Poland

^28AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland

^29National Center for Nuclear Research (NCBJ), Warsaw, Poland

^30Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania

^31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia

^32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia

^33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia

^34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia

^35Yandex School of Data Analysis, Moscow, Russia

^36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia

^37Institute for High Energy Physics (IHEP), Protvino, Russia

^38ICCUB, Universitat de Barcelona, Barcelona, Spain

^39Universidad de Santiago de Compostela, Santiago de Compostela, Spain

^40European Organization for Nuclear Research (CERN), Geneva, Switzerland

^41Institute of Physics, Ecole Polytechnique  Fédérale de Lausanne (EPFL), Lausanne, Switzerland

^42Physik-Institut, Universität Zürich, Zürich, Switzerland

^43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands

^44Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands

^45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine

^46Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine

^47University of Birmingham, Birmingham, United Kingdom

^48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom

^49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom

^50Department of Physics, University of Warwick, Coventry, United Kingdom

^51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom

^52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom

^53School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom

^54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom

^55Imperial College London, London, United Kingdom

^56School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom

^57Department of Physics, University of Oxford, Oxford, United Kingdom

^58Massachusetts Institute of Technology, Cambridge, MA, United States

^59University of Cincinnati, Cincinnati, OH, United States

^60University of Maryland, College Park, MD, United States

^61Syracuse University, Syracuse, NY, United States

^62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to ^2

^63University of Chinese Academy of Sciences, Beijing, China, associated to ^3

^64School of Physics and Technology, Wuhan University, Wuhan, China, associated to ^3

^65Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China, associated to ^3

^66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia, associated to ^8

^67Institut für Physik, Universität Rostock, Rostock, Germany, associated to ^12

^68National Research Centre Kurchatov Institute, Moscow, Russia, associated to ^32

^69Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain, associated to ^38

^70Van Swinderen Institute, University of Groningen, Groningen, The Netherlands, associated to ^43

^aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil

^bLaboratoire Leprince-Ringuet, Palaiseau, France

^cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia

^dUniversità di Bari, Bari, Italy

^eUniversità di Bologna, Bologna, Italy

^fUniversità di Cagliari, Cagliari, Italy

^gUniversità di Ferrara, Ferrara, Italy

^hUniversità di Genova, Genova, Italy

^iUniversità di Milano Bicocca, Milano, Italy

^jUniversità di Roma Tor Vergata, Roma, Italy

^kUniversità di Roma La Sapienza, Roma, Italy

^lAGH - University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland

^mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain

^nHanoi University of Science, Hanoi, Viet Nam

^oUniversità di Padova, Padova, Italy

^pUniversità di Pisa, Pisa, Italy

^qUniversità degli Studi di Milano, Milano, Italy

^rUniversità di Urbino, Urbino, Italy

^sUniversità della Basilicata, Potenza, Italy

^tScuola Normale Superiore, Pisa, Italy

^uUniversità di Modena e Reggio Emilia, Modena, Italy

^vIligan Institute of Technology (IIT), Iligan, Philippines

^wNovosibirsk State University, Novosibirsk, Russia

^†Deceased





