EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-EP-2019-156LHCb-PAPER-2019-018

23 January 2020

Observation of several sources of CPviolation in B+→ π+π+π− decays

LHCb collaboration†

Abstract

Observations are reported of different sources of CP violation from an amplitudeanalysis of B+→ π+π+π− decays, based on a data sample corresponding to anintegrated luminosity of 3 fb−1 of pp collisions recorded with the LHCb detector. Alarge CP asymmetry is observed in the decay amplitude involving the tensor f2(1270)resonance, and in addition significant CP violation is found in the π+π− S-wave atlow invariant mass. The presence of CP violation related to interference betweenthe π+π− S-wave and the P-wave B+→ ρ(770)0π+ amplitude is also established;this causes large local asymmetries but cancels when integrated over the phase spaceof the decay. The results provide both qualitative and quantitative new insightsinto CP -violation effects in hadronic B decays.

Published in Phys. Rev. Lett. 124 (2020) 031801

c© 2020 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence.

†Authors are listed at the end of this Letter.

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Violation of symmetry under the combined charge-conjugation and parity-transformation operations, CP violation, gives rise to differences between matter andantimatter. Violation of CP symmetry can occur in the amplitudes that describe hadrondecay, in neutral hadron mixing, or in the interference between mixing and decay (for areview, see, e.g., Ref. [1]). For charged mesons, only CP violation in decay is possible,where an asymmetry in particle and antiparticle decay rates can arise when two or moredifferent amplitudes contribute to a transition. In particular, the phase of each complexamplitude can be decomposed into a weak phase, which changes sign under CP , and astrong phase, which is CP invariant. Differences in both the weak and strong phases ofthe contributing amplitudes are required for an asymmetry to occur.

In the Standard Model (SM), weak phases arise from the elements of the Cabibbo–Kobayashi–Maskawa matrix [2,3] that are associated with quark-level transition amplitudes.Decays of B hadrons that do not contain any charm quarks in the final state, such asB+→ π+π+π−, are of particular interest as both tree-level and loop-level amplitudesare expected to contribute with comparable magnitudes, so that large CP -violationeffects are possible. Indeed, significant asymmetries have been observed in the two-bodyB0→ K+π− [4–6] and B0→ π+π− [4, 6, 7] decays. In two-body decays, nontrivial strongphases can arise from rescattering or other hadronic effects. In three-body or multibodydecays, variation of the strong phase is also expected due to the intermediate resonancestructure, and hence amplitude analyses can provide additional sensitivity to CP -violationeffects.

Analysis of the distribution of B+→ π+π+π− decays1 across the Dalitz plot [8,9], whichprovides a representation of the two-dimensional phase space for the decays, has beenpreviously performed by the BaBar collaboration [10,11]. A model-independent analysisby the LHCb collaboration, with over an order of magnitude more signal decays andmuch better signal purity compared to the BaBar data sample, subsequently observed anintriguing pattern of CP violation in its phase space, notably in regions not associated toany known resonant structure [12,13]. The observed variation of the CP asymmetry acrossthe Dalitz plot is expected to be related to the changes in strong phase associated withhadronic resonances, but, to date, has not yet been explicitly described with an amplitudemodel. Many phenomenological studies [14–20] have provided possible interpretations ofthe asymmetries. Particular attention has been devoted to whether large CP -violationeffects could arise from the interference between the broad low-mass spin-0 contributionsand the spin-1 ρ(770)0 resonance [21–24], from mixing between the ρ(770)0 and ω(782)resonances [25–27], or from ππ ↔ KK rescattering [21,23,24,28]. Further experimentalstudies are needed to clarify which of these sources are connected to the observed CPasymmetries.

In this Letter, results are reported on the amplitude structure of B+ → π+π+π−decays, obtained by employing decay models that account for CP violation. The resultsare based on a data sample corresponding to 3 fb−1 of pp collisions at centre-of-massenergies of 7 and 8 TeV, collected with the LHCb detector. A more detailed descriptionof the analysis is given in a companion paper [29]. The LHCb detector is a single-armforward spectrometer covering the pseudorapidity range 2 < η < 5, described in detail inRefs. [30, 31]

1The inclusion of charge-conjugated processes is implied throughout this Letter, except where asym-metries are discussed.

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Figure 1: Dalitz-plot distributions for (a) B+ and (b) B− candidate decays to π±π+π−. Depletedregions are due to the D0 veto.

The selection of signal candidates closely follows the procedure used in the model-independent analysis of the same data sample [12], with minor enhancements. Eventscontaining candidates are selected online by a trigger [32] that includes a hardware andsoftware stage. The hardware stage requires either energy deposits in the calorimetersassociated to signal particles or a trigger caused by other particles in the event. Thesoftware triggers require that the signal tracks come from a secondary vertex consistentwith the decay of a b hadron. In the offline selection, two multivariate algorithmsare used to separate the B+→ π+π+π− signal from background formed from randomcombinations of tracks, and from other B decays with misidentified final state particles,such as B+→ K+π+π−. Candidates that originate from B+→ D0π+ with subsequentD0→ π+π− or misidentified K+π− decays are removed with a veto on both π+π− invariantmass combinations.

After application of all selection requirements, the B+-candidate mass distribution isfitted to obtain signal and background yields. The fit function includes components forsignal decays, combinatorial background and misidentified B+→ K+π+π− decays. Thesignal region in the B+ candidate mass, 5.249 < m(π+π+π−) < 5.317 GeV/c2, which isused for the Dalitz-plot analysis, is estimated to contain 20 600±1 600 signal, 4 400±1 600combinatorial background, and 143± 11 B+→ K+π+π− decays, where the uncertaintiesreflect the combination of statistical and systematic effects. The Dalitz-plot distributionsof selected B+ and B− candidates are displayed in Fig. 1, where the phase space is foldedby ordering the π+π− pairs by their invariant mass, mlow < mhigh.

Given the large number of broad overlapping resonances and decay-channel thresholds,it is particularly challenging to model the B+ → π+π+π− decay phenomenologically.Therefore, on top of the conventional “isobar” model using a coherent sum of all non-zero spin resonances, three complementary approaches are used to describe the S-waveamplitude. The first continues in the isobar approach, comprising the coherent sumof a σ pole [33] together with a ππ ↔ KK rescattering term [34]; the second uses theK-matrix formalism with parameters obtained from scattering data [35–37]; and the thirdimplements a “quasi-model-independent” (QMI) approach, inspired by previous QMIanalyses [38], where the dipion mass spectrum is divided into bins with independentmagnitudes and phases that are free to vary in the amplitude fit.

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The amplitude for B+ and B− signal decays is constructed as the sum over N resonantcontributions and the S-wave component,

A±(m213,m223) =

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where m13 and m23 denote the π+π− invariant mass combinations. Bose symmetry is

accounted for by enforcing the amplitude to be identical under interchange of the twolike-sign pions, making the labelling of the two combinations arbitrary. The Fj term is thenormalised dynamical amplitude of resonance j, represented by a mass lineshape multipliedby the spin-dependent angular distribution using the Zemach tensor formalism [39, 40]and Blatt–Weisskopf barrier factors [41]. The complex coefficients, c±j , give the relativecontribution of each resonance, and A±S is the S-wave amplitude (isobar, K-matrix or QMI).The amplitude models account for CP -violating differences between the distributions ofB+ and B− decays by allowing the c±j coefficients, and relevant parameters in A

±S , to take

different values in the two cases. A likelihood function is constructed from the squaredmagnitude of the signal amplitude, accounting for efficiency effects and normalisation, andincluding background contributions modelled from data sidebands and simulation. Thesignal parameters are evaluated in the fit by minimising the negative logarithm of the totallikelihood, calculated for all candidates in the signal region. The Laura++ package [42]is used for the isobar and K-matrix approaches, while a GPU-accelerated version of theMint2 fitter [43] is used for the QMI approach.

With the exception of the S-wave, the included components are identical in eachapproach and consist of the ρ(770)0 and ω(782) resonances described by a coherent ρ–ωmixing model [44], and the f2(1270), ρ(1450)

0, and ρ3(1690)0 resonances. These latter

three resonances are all described by relativistic Breit–Wigner lineshapes. The choiceof which resonances to include is made starting from the model obtained in the BaBaranalysis [11], with additional contributions included if they cause a significant improvementin the fit to data.

In each approach, model coefficients for B+ and B− decays are obtained simultaneously.The amplitude coefficients extracted from the fit, c±j = (x± δx) + i(y± δy), where positive(negative) signs are used for B+ (B−) decays, are defined such that CP violation ispermitted. For the dominant ρ–ω mixing component, the magnitude of the coefficient inthe B+ amplitude is fixed to unity to set the scale, while both B+ and B− coefficients arealigned to the real axis as the absolute phase carries no physical meaning.

Good overall agreement between the data and the model is obtained for all threeS-wave approaches, with some localised discrepancies that are discussed below. Moreover,the values for the CP -averaged fit fractions and quasi-two-body CP asymmetries (rateasymmetries between a quasi-two-body decay and its CP conjugate), derived from the fitcoefficients and given in Table 1, show good agreement between the three approaches.

Projections of the data and the fit models are shown in regions of the data withm(π+π−) < 1 GeV/c2 in Fig. 2. The ρ(770)0 resonance is found to be the dominantcomponent in all models, with a fit fraction of around 55% and a quasi-two-body CPasymmetry that is consistent with zero. The effect of ρ–ω mixing is very clear in thedata (Fig. 2(b)) and is well described by the models. Contrary to some theoreticalpredictions [25–27], there is no evident CP -violation effect associated with ρ–ω mixing.However, a clear CP asymmetry is seen at values of m(π+π−) below the ρ(770)0 resonance,

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Table 1: Results for CP -conserving fit fractions, quasi-two-body CP asymmetries, and phases foreach component relative to the combined ρ(770)0–ω(782) model, given for each S-wave approach.The ρ(770)0 and ω(782) values are extracted from the combined ρ(770)0–ω(782) mixing model.The first uncertainty is statistical while the second is systematic.

Contribution Fit fraction (10−2) ACP (10−2) B+ phase (◦) B− phase (◦)

Isobar model

ρ(770)0 55.5 ± 0.6 ± 2.5 +0.7± 1.1± 1.6 — —ω(782) 0.50± 0.03± 0.05 −4.8± 6.5± 3.8 −19± 6± 1 +8± 6± 1f2(1270) 9.0 ± 0.3 ± 1.5 +46.8± 6.1± 4.7 +5± 3± 12 +53± 2± 12ρ(1450)0 5.2 ± 0.3 ± 1.9 −12.9± 3.3± 35.9 +127± 4± 21 +154± 4± 6ρ3(1690)

0 0.5 ± 0.1 ± 0.3 −80.1± 11.4± 25.3 −26± 7± 14 −47± 18± 25S-wave 25.4 ± 0.5 ± 3.6 +14.4± 1.8± 2.1 — —

Rescattering 1.4 ± 0.1 ± 0.5 +44.7± 8.6± 17.3 −35± 6± 10 −4± 4± 25σ 25.2 ± 0.5 ± 5.0 +16.0± 1.7± 2.2 +115± 2± 14 +179± 1± 95

K-matrix

ρ(770)0 56.5 ± 0.7 ± 3.4 +4.2± 1.5± 6.4 — —ω(782) 0.47± 0.04± 0.03 −6.2± 8.4± 9.8 −15± 6± 4 +8± 7± 4f2(1270) 9.3 ± 0.4 ± 2.5 +42.8± 4.1± 9.1 +19± 4± 18 +80± 3± 17ρ(1450)0 10.5 ± 0.7 ± 4.6 +9.0± 6.0± 47.0 +155± 5± 29 −166± 4± 51ρ3(1690)

0 1.5 ± 0.1 ± 0.4 −35.7± 10.8± 36.9 +19± 8± 34 +5± 8± 46S-wave 25.7 ± 0.6 ± 3.0 +15.8± 2.6± 7.2 — —

QMI

ρ(770)0 54.8 ± 1.0 ± 2.2 +4.4± 1.7± 2.8 — —ω(782) 0.57± 0.10± 0.17 −7.9± 16.5± 15.8 −25± 6± 27 −2± 7± 11f2(1270) 9.6 ± 0.4 ± 4.0 +37.6± 4.4± 8.0 +13± 5± 21 +68± 3± 66ρ(1450)0 7.4 ± 0.5 ± 4.0 −15.5± 7.3± 35.2 +147± 7± 152 −175± 5± 171ρ3(1690)

0 1.0 ± 0.1 ± 0.5 −93.2± 6.8± 38.9 +8± 10± 24 +36± 26± 46S-wave 26.8 ± 0.7 ± 2.2 +15.0± 2.7± 8.1 — —

where only the S-wave amplitude contributes significantly (Fig. 2(a)). A detailed inspectionof the behaviour of the S-wave, given in Ref. [29], shows that this CP asymmetry remainsapproximately constant up to the inelastic threshold 2mK , where it appears to changesign; this is seen in all three approaches to the S-wave description. Estimates of thesignificance of this CP -violation effect give values in excess of ten Gaussian standarddeviations (σ) in all the S-wave models. These estimates are obtained from the change innegative log-likelihood between, for each S-wave approach, the baseline fit and alternativefits where no such CP violation is allowed.

An additional source of CP violation, associated principally with the interferencebetween S- and P-waves, is clearly visible when inspecting the cos θhel distributionsseparately in regions above and below the ρ(770)0 peak (Fig. 3(a) and (b)). Here, θhel isthe angle, evaluated in the π+π− rest frame, between the pion with opposite charge tothe B and the third pion from the B decay. These asymmetries are modelled well in allthree approaches to the S-wave description. Evaluation of the significance of CP violationin the interference between S- and P-waves gives values in excess of 25σ in all the S-wavemodels.

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Figure 2: Projections of data and fits (top) on mlow in (a) the low m(π+π−) region and (b) the

ρ–ω region, with (bottom) the corresponding CP asymmetries in these ranges.

At higher m(π+π−) values, the f2(1270) component is found to have a CP -averagedfit fraction of around 9% and a very large quasi-two-body CP asymmetry of around 40%,as can be seen in Fig. 4 and Table 1. This is the first observation of CP violation in anyprocess involving a tensor resonance. The central value of the CP asymmetry is consistentwith some theoretical predictions [19, 45, 46] that, however, have large uncertainties.The significance of CP violation in the complex amplitude coefficients of the f2(1270)component is in excess of 10σ. This conclusion holds in all the S-wave models and isrobust against variations of the models performed to evaluate systematic uncertainties.

The parameters associated to the ρ(1450)0 and ρ3(1690)0 resonances agree less well,

but are nevertheless broadly consistent, between the different models. The small ρ3(1690)0

contribution exhibits a large quasi-two-body CP asymmetry; however this result is subjectto significant systematic uncertainties, particularly due to ambiguities in the amplitudemodel, and therefore is not statistically significant.

The main sources of experimental systematic uncertainty are related to the signal,combinatorial and peaking background parameterisation in the B+ invariant-mass fit,and the description of the efficiency variation across the Dalitz plot. Also considered,and found to be numerically larger for most results, are systematic uncertainties relatedto the physical amplitude models. These comprise the variation of masses and widths,according to the world averages [47], of established resonances, in addition to the inclusionof more speculative resonant structures. A small contribution from the ρ(1700)0 resonanceis expected by some theory predictions [48] and is considered a source of systematicuncertainty since the inclusion of this term did not significantly improve the models’agreement with data.

A clear discrepancy between all three modelling approaches and the data can beobserved in the f2(1270) region (Fig. 4). This discrepancy can be resolved by freeing

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Figure 3: Projections of the CP asymmetry for data and fits as a function of cos θhel in theregions (a) below and (b) above the ρ(770)0 resonance pole.

the f2(1270) mass parameter in the fit, however, the values obtained are significantlydifferent from the world-average value. The discrepancy could arise from interference withan additional spin-2 resonance in this region, but all well established states are either toohigh in mass or too narrow in width to be likely to cause a significant effect. The inclusionof a second spin-2 component in this region, with free mass and width parameters, resultsin values of the f2(1270) mass consistent with the world average, where parameters of theadditional state are broadly consistent with those of the speculative f2(1430) resonance;however the values obtained for the mass and width of the additional state are inconsistentbetween fits with different approaches to the S-wave description. Subsequent analysisof larger data samples will be required to obtain a more detailed understanding of theππ D-wave in B+ → π+π+π− decays. Variation of the f2(1270) mass with respect to theworld-average value, along with the addition of a second spin-2 resonance in this region,are taken into account in the systematic uncertainties.

In summary, an amplitude analysis of the B+→ π+π+π− decay is performed withdata corresponding to 3 fb−1 of LHCb Run 1 data, using three complementary approachesto describe the large S-wave contribution to this decay. Good agreement is found betweenall three models and the data. In all cases, significant CP violation is observed in thedecay amplitudes associated with the f2(1270) resonance and with the π

+π− S-wave atlow invariant mass, in addition to CP violation characteristic of interference between thespin-1 ρ(770)0 resonance and the spin-0 S-wave contribution. Violation of CP symmetryis previously unobserved in these processes and, in particular, this is the first observationof CP violation in the interference between two quasi-two-body decays. As such, theseresults provide significant new insight into how CP violation manifests in multi-body

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B-hadron decays, and motivate further study into the processes that govern CP violationat low ππ invariant mass.

Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments for theexcellent performance of the LHC. We thank the technical and administrative staff at theLHCb 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); NWO (Netherlands); MNiSWand NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MinECo (Spain); SNSF andSER (Switzerland); NASU (Ukraine); STFC (United Kingdom); DOE NP and NSF (USA).We acknowledge the computing resources that are provided by CERN, IN2P3 (France),KIT and DESY (Germany), INFN (Italy), SURF (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 tothe 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 Sk lodowska-Curie Actions and ERC (European Union); ANR, LabexP2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key Research Programof Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China);RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); theRoyal Society and the Leverhulme Trust (United Kingdom).

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LHCb collaboration

R. Aaij30, C. Abellán Beteta47, B. Adeva44, M. Adinolfi51, C.A. Aidala78, Z. Ajaltouni8,S. Akar62, P. Albicocco21, J. Albrecht13, F. Alessio45, M. Alexander56, A. Alfonso Albero43,G. Alkhazov36, P. Alvarez Cartelle58, A.A. Alves Jr44, S. Amato2, Y. Amhis10, L. An20,L. Anderlini20, G. Andreassi46, M. Andreotti19, J.E. Andrews63, F. Archilli21, J. Arnau Romeu9,A. Artamonov42, M. Artuso65, K. Arzymatov40, E. Aslanides9, M. Atzeni47, B. Audurier25,S. Bachmann15, J.J. Back53, S. Baker58, V. Balagura10,b, W. Baldini19,45, A. Baranov40,R.J. Barlow59, S. Barsuk10, W. Barter58, M. Bartolini22, F. Baryshnikov74, V. Batozskaya34,B. Batsukh65, A. Battig13, V. Battista46, A. Bay46, F. Bedeschi27, I. Bediaga1, A. Beiter65,L.J. Bel30, V. Belavin40, S. Belin25, N. Beliy4, V. Bellee46, K. Belous42, I. Belyaev37,G. Bencivenni21, E. Ben-Haim11, S. Benson30, S. Beranek12, A. Berezhnoy38, R. Bernet47,D. Berninghoff15, E. Bertholet11, A. Bertolin26, C. Betancourt47, F. Betti18,e, M.O. Bettler52,Ia. Bezshyiko47, S. Bhasin51, J. Bhom32, M.S. Bieker13, S. Bifani50, P. Billoir11, A. Birnkraut13,A. Bizzeti20,u, M. Bjørn60, M.P. Blago45, T. Blake53, F. Blanc46, S. Blusk65, D. Bobulska56,V. Bocci29, O. Boente Garcia44, T. Boettcher61, A. Boldyrev75, A. Bondar41,w, N. Bondar36,S. Borghi59,45, M. Borisyak40, M. Borsato15, M. Boubdir12, T.J.V. Bowcock57, C. Bozzi19,45,S. Braun15, A. Brea Rodriguez44, M. Brodski45, J. Brodzicka32, A. Brossa Gonzalo53,D. Brundu25,45, E. Buchanan51, A. Buonaura47, C. Burr59, A. Bursche25, J.S. Butter30,J. Buytaert45, W. Byczynski45, S. Cadeddu25, H. Cai69, R. Calabrese19,g, S. Cali21,R. Calladine50, M. Calvi23,i, M. Calvo Gomez43,m, P. Camargo Magalhaes51, A. Camboni43,m,P. Campana21, D.H. Campora Perez45, L. Capriotti18,e, A. Carbone18,e, G. Carboni28,R. Cardinale22, A. Cardini25, P. Carniti23,i, K. Carvalho Akiba2, A. Casais Vidal44, G. Casse57,M. Cattaneo45, G. Cavallero22, R. Cenci27,p, M.G. Chapman51, M. Charles11,45,Ph. Charpentier45, G. Chatzikonstantinidis50, M. Chefdeville7, V. Chekalina40, C. Chen3,S. Chen25, S.-G. Chitic45, V. Chobanova44, M. Chrzaszcz45, A. Chubykin36, P. Ciambrone21,X. Cid Vidal44, G. Ciezarek45, F. Cindolo18, P.E.L. Clarke55, M. Clemencic45, H.V. Cliff52,J. Closier45, J.L. Cobbledick59, V. Coco45, J.A.B. Coelho10, J. Cogan9, E. Cogneras8,L. Cojocariu35, P. Collins45, T. Colombo45, A. Comerma-Montells15, A. Contu25, G. Coombs45,S. Coquereau43, G. Corti45, C.M. Costa Sobral53, B. Couturier45, G.A. Cowan55, D.C. Craik61,A. Crocombe53, M. Cruz Torres1, R. Currie55, C.L. Da Silva64, E. Dall’Occo30, J. Dalseno44,51,C. D’Ambrosio45, A. Danilina37, P. d’Argent15, A. Davis59, O. De Aguiar Francisco45,K. De Bruyn45, S. De Capua59, M. De Cian46, J.M. De Miranda1, L. De Paula2,M. De Serio17,d, P. De Simone21, J.A. de Vries30, C.T. Dean56, W. Dean78, D. Decamp7,L. Del Buono11, B. Delaney52, H.-P. Dembinski14, M. Demmer13, A. Dendek33, D. Derkach75,O. Deschamps8, F. Desse10, F. Dettori25, B. Dey6, A. Di Canto45, P. Di Nezza21, S. Didenko74,H. Dijkstra45, F. Dordei25, M. Dorigo27,x, A.C. dos Reis1, A. Dosil Suárez44, L. Douglas56,A. Dovbnya48, K. Dreimanis57, L. Dufour45, G. Dujany11, P. Durante45, J.M. Durham64,D. Dutta59, R. Dzhelyadin42,†, M. Dziewiecki15, A. Dziurda32, A. Dzyuba36, S. Easo54,U. Egede58, V. Egorychev37, S. Eidelman41,w, S. Eisenhardt55, U. Eitschberger13, R. Ekelhof13,S. Ek-In46, L. Eklund56, S. Ely65, A. Ene35, S. Escher12, S. Esen30, T. Evans62, A. Falabella18,C. Färber45, N. Farley50, S. Farry57, D. Fazzini10, M. Féo45, P. Fernandez Declara45,A. Fernandez Prieto44, F. Ferrari18,e, L. Ferreira Lopes46, F. Ferreira Rodrigues2,S. Ferreres Sole30, M. Ferro-Luzzi45, S. Filippov39, R.A. Fini17, M. Fiorini19,g, M. Firlej33,C. Fitzpatrick45, T. Fiutowski33, F. Fleuret10,b, M. Fontana45, F. Fontanelli22,h, R. Forty45,V. Franco Lima57, M. Franco Sevilla63, M. Frank45, C. Frei45, J. Fu24,q, W. Funk45,E. Gabriel55, A. Gallas Torreira44, D. Galli18,e, S. Gallorini26, S. Gambetta55, Y. Gan3,M. Gandelman2, P. Gandini24, Y. Gao3, L.M. Garcia Martin77, J. Garćıa Pardiñas47,B. Garcia Plana44, J. Garra Tico52, L. Garrido43, D. Gascon43, C. Gaspar45, G. Gazzoni8,D. Gerick15, E. Gersabeck59, M. Gersabeck59, T. Gershon53, D. Gerstel9, Ph. Ghez7,

11

V. Gibson52, A. Gioventù44, O.G. Girard46, P. Gironella Gironell43, L. Giubega35, K. Gizdov55,V.V. Gligorov11, C. Göbel67, D. Golubkov37, A. Golutvin58,74, A. Gomes1,a, I.V. Gorelov38,C. Gotti23,i, E. Govorkova30, J.P. Grabowski15, R. Graciani Diaz43, L.A. Granado Cardoso45,E. Graugés43, E. Graverini46, G. Graziani20, A. Grecu35, R. Greim30, P. Griffith25, L. Grillo59,L. Gruber45, B.R. Gruberg Cazon60, C. Gu3, E. Gushchin39, A. Guth12, Yu. Guz42,45, T. Gys45,T. Hadavizadeh60, C. Hadjivasiliou8, G. Haefeli46, C. Haen45, S.C. Haines52, P.M. Hamilton63,Q. Han6, X. Han15, T.H. Hancock60, S. Hansmann-Menzemer15, N. Harnew60, T. Harrison57,C. Hasse45, M. Hatch45, J. He4, M. Hecker58, K. Heijhoff30, K. Heinicke13, A. Heister13,K. Hennessy57, L. Henry77, M. Heß71, J. Heuel12, A. Hicheur66, R. Hidalgo Charman59,D. Hill60, M. Hilton59, P.H. Hopchev46, J. Hu15, W. Hu6, W. Huang4, Z.C. Huard62,W. Hulsbergen30, T. Humair58, M. Hushchyn75, D. Hutchcroft57, D. Hynds30, P. Ibis13,M. Idzik33, P. Ilten50, A. Inglessi36, A. Inyakin42, K. Ivshin36, R. Jacobsson45, S. Jakobsen45,J. Jalocha60, E. Jans30, B.K. Jashal77, A. Jawahery63, F. Jiang3, M. John60, D. Johnson45,C.R. Jones52, C. Joram45, B. Jost45, N. Jurik60, S. Kandybei48, M. Karacson45, J.M. Kariuki51,S. Karodia56, N. Kazeev75, M. Kecke15, F. Keizer52, M. Kelsey65, M. Kenzie52, T. Ketel31,B. Khanji45, A. Kharisova76, C. Khurewathanakul46, K.E. Kim65, T. Kirn12, V.S. Kirsebom46,S. Klaver21, K. Klimaszewski34, S. Koliiev49, M. Kolpin15, A. Kondybayeva74,A. Konoplyannikov37, P. Kopciewicz33, R. Kopecna15, P. Koppenburg30, I. Kostiuk30,49,O. Kot49, S. Kotriakhova36, M. Kozeiha8, L. Kravchuk39, M. Kreps53, F. Kress58,S. Kretzschmar12, P. Krokovny41,w, W. Krupa33, W. Krzemien34, W. Kucewicz32,l,M. Kucharczyk32, V. Kudryavtsev41,w, G.J. Kunde64, A.K. Kuonen46, T. Kvaratskheliya37,D. Lacarrere45, G. Lafferty59, A. Lai25, D. Lancierini47, G. Lanfranchi21, C. Langenbruch12,T. Latham53, C. Lazzeroni50, R. Le Gac9, R. Lefèvre8, A. Leflat38, F. Lemaitre45, O. Leroy9,T. Lesiak32, B. Leverington15, H. Li68, P.-R. Li4,aa, X. Li64, Y. Li5, Z. Li65, X. Liang65,T. Likhomanenko73, R. Lindner45, F. Lionetto47, V. Lisovskyi10, G. Liu68, X. Liu3, D. Loh53,A. Loi25, J. Lomba Castro44, I. Longstaff56, J.H. Lopes2, G. Loustau47, G.H. Lovell52,D. Lucchesi26,o, M. Lucio Martinez44, Y. Luo3, A. Lupato26, E. Luppi19,g, O. Lupton53,A. Lusiani27, X. Lyu4, F. Machefert10, F. Maciuc35, V. Macko46, P. Mackowiak13,S. Maddrell-Mander51, O. Maev36,45, A. Maevskiy75, K. Maguire59, D. Maisuzenko36,M.W. Majewski33, S. Malde60, B. Malecki45, A. Malinin73, T. Maltsev41,w, H. Malygina15,G. Manca25,f , G. Mancinelli9, D. Marangotto24,q, J. Maratas8,v, J.F. Marchand7, U. Marconi18,C. Marin Benito10, M. Marinangeli46, P. Marino46, J. Marks15, P.J. Marshall57, G. Martellotti29,L. Martinazzoli45, M. Martinelli45,23,i, D. Martinez Santos44, F. Martinez Vidal77,A. Massafferri1, M. Materok12, R. Matev45, A. Mathad47, Z. Mathe45, V. Matiunin37,C. Matteuzzi23, K.R. Mattioli78, A. Mauri47, E. Maurice10,b, B. Maurin46, M. McCann58,45,A. McNab59, R. McNulty16, J.V. Mead57, B. Meadows62, C. Meaux9, N. Meinert71,D. Melnychuk34, M. Merk30, A. Merli24,q, E. Michielin26, D.A. Milanes70, E. Millard53,M.-N. Minard7, O. Mineev37, L. Minzoni19,g, D.S. Mitzel15, A. Mödden13, A. Mogini11,R.D. Moise58, T. Mombächer13, I.A. Monroy70, S. Monteil8, M. Morandin26, G. Morello21,M.J. Morello27,t, J. Moron33, A.B. Morris9, R. Mountain65, H. Mu3, F. Muheim55,M. Mukherjee6, M. Mulder30, D. Müller45, J. Müller13, K. Müller47, V. Müller13,C.H. Murphy60, D. Murray59, P. Naik51, T. Nakada46, R. Nandakumar54, A. Nandi60,T. Nanut46, I. Nasteva2, M. Needham55, N. Neri24,q, S. Neubert15, N. Neufeld45,R. Newcombe58, T.D. Nguyen46, C. Nguyen-Mau46,n, S. Nieswand12, R. Niet13, N. Nikitin38,N.S. Nolte45, A. Oblakowska-Mucha33, V. Obraztsov42, S. Ogilvy56, D.P. O’Hanlon18,R. Oldeman25,f , C.J.G. Onderwater72, J. D. Osborn78, A. Ossowska32, J.M. Otalora Goicochea2,T. Ovsiannikova37, P. Owen47, A. Oyanguren77, P.R. Pais46, T. Pajero27,t, A. Palano17,M. Palutan21, G. Panshin76, A. Papanestis54, M. Pappagallo55, L.L. Pappalardo19,g,W. Parker63, C. Parkes59,45, G. Passaleva20,45, A. Pastore17, M. Patel58, C. Patrignani18,e,A. Pearce45, A. Pellegrino30, G. Penso29, M. Pepe Altarelli45, S. Perazzini18, D. Pereima37,

12

P. Perret8, L. Pescatore46, K. Petridis51, A. Petrolini22,h, A. Petrov73, S. Petrucci55,M. Petruzzo24,q, B. Pietrzyk7, G. Pietrzyk46, M. Pikies32, M. Pili60, D. Pinci29, J. Pinzino45,F. Pisani45, A. Piucci15, V. Placinta35, S. Playfer55, J. Plews50, M. Plo Casasus44, F. Polci11,M. Poli Lener21, M. Poliakova65, A. Poluektov9, N. Polukhina74,c, I. Polyakov65, E. Polycarpo2,G.J. Pomery51, S. Ponce45, A. Popov42, D. Popov50, S. Poslavskii42, K. Prasanth32, E. Price51,C. Prouve44, V. Pugatch49, A. Puig Navarro47, H. Pullen60, G. Punzi27,p, W. Qian4, J. Qin4,R. Quagliani11, B. Quintana8, N.V. Raab16, B. Rachwal33, J.H. Rademacker51, M. Rama27,M. Ramos Pernas44, M.S. Rangel2, F. Ratnikov40,75, G. Raven31, M. Ravonel Salzgeber45,M. Reboud7, F. Redi46, S. Reichert13, F. Reiss11, C. Remon Alepuz77, Z. Ren3, V. Renaudin60,S. Ricciardi54, S. Richards51, K. Rinnert57, P. Robbe10, A. Robert11, A.B. Rodrigues46,E. Rodrigues62, J.A. Rodriguez Lopez70, M. Roehrken45, S. Roiser45, A. Rollings60,V. Romanovskiy42, A. Romero Vidal44, J.D. Roth78, M. Rotondo21, M.S. Rudolph65, T. Ruf45,J. Ruiz Vidal77, J.J. Saborido Silva44, N. Sagidova36, B. Saitta25,f , V. Salustino Guimaraes67,C. Sanchez Gras30, C. Sanchez Mayordomo77, B. Sanmartin Sedes44, R. Santacesaria29,C. Santamarina Rios44, M. Santimaria21,45, E. Santovetti28,j , G. Sarpis59, A. Sarti21,k,C. Satriano29,s, A. Satta28, M. Saur4, D. Savrina37,38, S. Schael12, M. Schellenberg13,M. Schiller56, H. Schindler45, M. Schmelling14, T. Schmelzer13, B. Schmidt45, O. Schneider46,A. Schopper45, H.F. Schreiner62, M. Schubiger30, S. Schulte46, M.H. Schune10, R. Schwemmer45,B. Sciascia21, A. Sciubba29,k, A. Semennikov37, E.S. Sepulveda11, A. Sergi50,45, N. Serra47,J. Serrano9, L. Sestini26, A. Seuthe13, P. Seyfert45, M. Shapkin42, T. Shears57, L. Shekhtman41,w,V. Shevchenko73, E. Shmanin74, B.G. Siddi19, R. Silva Coutinho47, L. Silva de Oliveira2,G. Simi26,o, S. Simone17,d, I. Skiba19, N. Skidmore15, T. Skwarnicki65, M.W. Slater50,J.G. Smeaton52, E. Smith12, I.T. Smith55, M. Smith58, M. Soares18, L. Soares Lavra1,M.D. Sokoloff62, F.J.P. Soler56, B. Souza De Paula2, B. Spaan13, E. Spadaro Norella24,q,P. Spradlin56, F. Stagni45, M. Stahl15, S. Stahl45, P. Stefko46, S. Stefkova58, O. Steinkamp47,S. Stemmle15, O. Stenyakin42, M. Stepanova36, H. Stevens13, A. Stocchi10, S. Stone65,S. Stracka27, M.E. Stramaglia46, M. Straticiuc35, U. Straumann47, S. Strokov76, J. Sun3,L. Sun69, Y. Sun63, K. Swientek33, A. Szabelski34, T. Szumlak33, M. Szymanski4, Z. Tang3,T. Tekampe13, G. Tellarini19, F. Teubert45, E. Thomas45, M.J. Tilley58, V. Tisserand8,S. T’Jampens7, M. Tobin5, S. Tolk45, L. Tomassetti19,g, D. Tonelli27, D.Y. Tou11,E. Tournefier7, M. Traill56, M.T. Tran46, A. Trisovic52, A. Tsaregorodtsev9, G. Tuci27,45,p,A. Tully52, N. Tuning30, A. Ukleja34, A. Usachov10, A. Ustyuzhanin40,75, U. Uwer15,A. Vagner76, V. Vagnoni18, A. Valassi45, S. Valat45, G. Valenti18, M. van Beuzekom30,H. Van Hecke64, E. van Herwijnen45, C.B. Van Hulse16, J. van Tilburg30, M. van Veghel30,R. Vazquez Gomez45, P. Vazquez Regueiro44, C. Vázquez Sierra30, S. Vecchi19, J.J. Velthuis51,M. Veltri20,r, A. Venkateswaran65, M. Vernet8, M. Veronesi30, M. Vesterinen53,J.V. Viana Barbosa45, D. Vieira4, M. Vieites Diaz44, H. Viemann71, X. Vilasis-Cardona43,m,A. Vitkovskiy30, M. Vitti52, V. Volkov38, A. Vollhardt47, D. Vom Bruch11, B. Voneki45,A. Vorobyev36, V. Vorobyev41,w, N. Voropaev36, R. Waldi71, J. Walsh27, J. Wang3, J. Wang5,M. Wang3, Y. Wang6, Z. Wang47, D.R. Ward52, H.M. Wark57, N.K. Watson50, D. Websdale58,A. Weiden47, C. Weisser61, M. Whitehead12, G. Wilkinson60, M. Wilkinson65, I. Williams52,M. Williams61, M.R.J. Williams59, T. Williams50, F.F. Wilson54, M. Winn10, W. Wislicki34,M. Witek32, G. Wormser10, S.A. Wotton52, K. Wyllie45, Z. Xiang4, D. Xiao6, Y. Xie6,H. Xing68, A. Xu3, L. Xu3, M. Xu6, Q. Xu4, Z. Xu7, Z. Xu3, Z. Yang3, Z. Yang63, Y. Yao65,L.E. Yeomans57, H. Yin6, J. Yu6,z, X. Yuan65, O. Yushchenko42, K.A. Zarebski50,M. Zavertyaev14,c, M. Zeng3, D. Zhang6, L. Zhang3, S. Zhang3, W.C. Zhang3,y, Y. Zhang45,A. Zhelezov15, Y. Zheng4, Y. Zhou4, X. Zhu3, V. Zhukov12,38, J.B. Zonneveld55, S. Zucchelli18,e.

1Centro Brasileiro de Pesquisas F́ısicas (CBPF), Rio de Janeiro, Brazil2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil3Center for High Energy Physics, Tsinghua University, Beijing, China

13

4University of Chinese Academy of Sciences, Beijing, China5Institute Of High Energy Physics (ihep), Beijing, China6Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China7Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France8Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France9Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France10LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France11LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France12I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany13Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany14Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany15Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany16School of Physics, University College Dublin, Dublin, Ireland17INFN Sezione di Bari, Bari, Italy18INFN Sezione di Bologna, Bologna, Italy19INFN Sezione di Ferrara, Ferrara, Italy20INFN Sezione di Firenze, Firenze, Italy21INFN Laboratori Nazionali di Frascati, Frascati, Italy22INFN Sezione di Genova, Genova, Italy23INFN Sezione di Milano-Bicocca, Milano, Italy24INFN Sezione di Milano, Milano, Italy25INFN Sezione di Cagliari, Monserrato, Italy26INFN Sezione di Padova, Padova, Italy27INFN Sezione di Pisa, Pisa, Italy28INFN Sezione di Roma Tor Vergata, Roma, Italy29INFN Sezione di Roma La Sapienza, Roma, Italy30Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands31Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam,Netherlands32Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland33AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,Kraków, Poland34National Center for Nuclear Research (NCBJ), Warsaw, Poland35Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania36Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI), Gatchina, Russia37Institute of Theoretical and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI), Moscow,Russia, Moscow, Russia38Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS), Moscow, Russia40Yandex School of Data Analysis, Moscow, Russia41Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia42Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI), Protvino, Russia,Protvino, Russia43ICCUB, Universitat de Barcelona, Barcelona, Spain44Instituto Galego de F́ısica de Altas Enerx́ıas (IGFAE), Universidade de Santiago de Compostela,Santiago de Compostela, Spain45European Organization for Nuclear Research (CERN), Geneva, Switzerland46Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland47Physik-Institut, Universität Zürich, Zürich, Switzerland48NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine49Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine50University of Birmingham, Birmingham, United Kingdom51H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom52Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom53Department of Physics, University of Warwick, Coventry, United Kingdom54STFC Rutherford Appleton Laboratory, Didcot, United Kingdom

14

55School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom56School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom57Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom58Imperial College London, London, United Kingdom59School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom60Department of Physics, University of Oxford, Oxford, United Kingdom61Massachusetts Institute of Technology, Cambridge, MA, United States62University of Cincinnati, Cincinnati, OH, United States63University of Maryland, College Park, MD, United States64Los Alamos National Laboratory (LANL), Los Alamos, United States65Syracuse University, Syracuse, NY, United States66Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria, associated to 267Pontif́ıcia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 268South China Normal University, Guangzhou, China, associated to 369School of Physics and Technology, Wuhan University, Wuhan, China, associated to 370Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia, associated to 1171Institut für Physik, Universität Rostock, Rostock, Germany, associated to 1572Van Swinderen Institute, University of Groningen, Groningen, Netherlands, associated to 3073National Research Centre Kurchatov Institute, Moscow, Russia, associated to 3774National University of Science and Technology “MISIS”, Moscow, Russia, associated to 3775National Research University Higher School of Economics, Moscow, Russia, associated to 4076National Research Tomsk Polytechnic University, Tomsk, Russia, associated to 3777Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain,associated to 4378University of Michigan, Ann Arbor, United States, associated to 65

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, BrazilbLaboratoire Leprince-Ringuet, Palaiseau, FrancecP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, RussiadUniversità di Bari, Bari, ItalyeUniversità di Bologna, Bologna, ItalyfUniversità di Cagliari, Cagliari, ItalygUniversità di Ferrara, Ferrara, ItalyhUniversità di Genova, Genova, ItalyiUniversità di Milano Bicocca, Milano, ItalyjUniversità di Roma Tor Vergata, Roma, ItalykUniversità di Roma La Sapienza, Roma, ItalylAGH - University of Science and Technology, Faculty of Computer Science, Electronics andTelecommunications, Kraków, PolandmLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, SpainnHanoi University of Science, Hanoi, VietnamoUniversità di Padova, Padova, ItalypUniversità di Pisa, Pisa, ItalyqUniversità degli Studi di Milano, Milano, ItalyrUniversità di Urbino, Urbino, ItalysUniversità della Basilicata, Potenza, ItalytScuola Normale Superiore, Pisa, ItalyuUniversità di Modena e Reggio Emilia, Modena, ItalyvMSU - Iligan Institute of Technology (MSU-IIT), Iligan, PhilippineswNovosibirsk State University, Novosibirsk, RussiaxSezione INFN di Trieste, Trieste, ItalyySchool of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi’an, ChinazPhysics and Micro Electronic College, Hunan University, Changsha City, ChinaaaLanzhou University, Lanzhou, China

†Deceased

15

References