Evidence for an ηc(1S)π− resonance in B0 → ηc(1S)K+π− decays

Eur. Phys. J. C (2018) 78:1019 https://doi.org/10.1140/epjc/s10052-018-6447-z Regular Article - Experimental Physics Evidence for an ηc(1S)π−resonance in B0→ηc(1S)K+π−decays LHCb Collaboration CERN, 1211 Geneva 23, Switzerland Received: 21 September 2018 / Accepted: 13 November 2018 / Published online: 17 December 2018 © CERN for the benefit of the LHCb collaboration 2018 Abstract A Dalitz plot analysis of B0→ηc(1S)K+π− decays is performed using data samples of pp collisions collected with the LHCb detector at centre-of-mass energies of √s=7,8 and 13 TeV, corresponding to a total integrated luminosity of 4.7fb −1. A satisfactory description of the data is obtained when including a contribution representing an exotic ηc(1S)π−resonant state. The significance of this exotic resonance is more than three standard deviations, while its mass and width are 4096 ±20 +18 −22 MeV and 152±58 +60 −35 MeV, respectively. The spin-parity assignments JP=0+and JP=1−are both consistent with the data. In addition, the first measurement of the B0→ηc(1S)K+π− branching fraction is performed and gives B(B0→ηc(1S)K+π−)=(5.73 ±0.24 ±0.13 ±0.66)×10−4, where the first uncertainty is statistical, the second systematic, and the third is due to limited knowledge of external branching fractions. 1 Introduction Since the discovery of the X(3872)state in 2003 [1], several exotic hadron candidates have been observed, as reported in recent reviews [2–7].1The decay modes of these states indicate that they must contain a heavy quark–antiquark pair in their internal structure; however, they cannot easily be accommodated as an unassigned charmonium or bottomonium state due to either their mass, decay properties or electric charge, which are inconsistent with those of pure charmonium or bottomonium states. Different interpretations have been proposed about their nature [2–4], including their quark composition and binding mechanisms. In order to improve the understanding of these hadrons, it is important to search for new exotic candidates, along with new production mechanisms and decay modes of already observed unconventional states. 1The X(3872)state has been recently renamed χc1(3872)in Ref. [8]. ae-mail: giovanni.cav[email protected] The Zc(3900)−state, discovered by the BESIII collaboration in the J/ψ π −final state [9], and confirmed by the Belle [10] and CLEO [11] collaborations, can be interpreted as a hadrocharmonium state, where the compact heavy quark–antiquark pair interacts with the surrounding light quark mesonic excitation by a QCD analogue of the van der Waals force [12]. This interpretation of the Zc(3900)− state predicts an as-yet-unobserved charged charmoniumlike state with a mass of approximately [3800]MeV whose dominant decay mode is to the ηcπ−system.2Alternatively, states like the Zc(3900)−meson could be interpreted as analogues of quarkonium hybrids, where the excitation of the gluon field (the valence gluon) is replaced by an isospin1 excitation of the gluon and light-quark fields [13]. This interpretation, which is based on lattice QCD, predicts different multiplets of charmonium tetraquarks, comprising states with quantum numbers allowing the decay into the ηcπ− system. The ηcπ−system carries isospin I=1, G-parity G=−1, spin J=Land parity P=(−1)L, where Lis the orbital angular momentum between the ηcand the π−mesons. Lattice QCD calculations [14,15] predict the mass and quantum numbers of these states, comprising aIG(JP)=1−(0+)state of mass [4025 ±49]MeV,a IG(JP)=1−(1−)state of mass [3770 ±42]MeV, and a IG(JP)=1−(2+)state of mass [4045 ±44]MeV.The Zc(4430)−resonance, discovered by the Belle collaboration [16] and confirmed by LHCb [17,18], could also fit into this scenario. Another prediction of a possible exotic candidate decaying to the ηcπ−system is provided by the diquark model [19], where quarks and diquarks are the fundamental units to build a rich spectrum of hadrons, including the exotic states observed thus far. The diquark model predicts aJP=0+candidate below the open-charm threshold that could decay into the ηcπ−final state. Therefore, the discovery of a charged charmonium-like meson in the ηcπ−sys2Natural units with ¯ h=c=1 and the simplified notation ηcto refer to the ηc(1S)state are used throughout. In addition, the inclusion of charge-conjugate processes is always implied. 123 1019 Page 2 of 23 Eur. Phys. J. C (2018) 78 :1019 (a) (b) Fig. 1 Feynman diagrams for aB0→ηcK∗0and bB0→Z− cK+decay sequences tem would provide important input towards understanding the nature of exotic hadrons. In this article, the B0→ηcK+π−decay is studied for the first time, with the ηcmeson reconstructed using the ppdecay mode. The decay is expected to proceed through K∗0→K+π−intermediate states, where K∗0refers to any neutral kaon resonance, following the diagram shown in Fig. 1a. If the decay also proceeds through exotic resonances in the ηcπ−system, denoted by Z− cstates in the following, a diagram like that shown in Fig. 1b would contribute. The B0→ηcK+π−decay involves only pseudoscalar mesons, hence it is fully described by two independent kinematic quantities. Therefore, the Dalitz plot (DP) analysis technique [20] can be used to completely characterise the decay. The data sample used corresponds to an integrated luminosity of 4.7fb −1of pp collision data collected with the LHCb detector at centre-of-mass energies of √s=7,8 and 13 TeV in 2011, 2012 and 2016, respectively. Data collected in 2011 and 2012 are referred to as Run 1 data, while data collected in 2016 are referred to as Run 2 data. This paper is organised as follows. A brief description of the LHCb detector as well as the reconstruction and simulation software is given in Sect. 2. The selection of B0→ppK+π−candidates is described in Sect. 3, and the first measurement of the B0→ηcK+π−branching fraction is presented in Sect. 4. An overview of the DP analysis formalism is given in Sect. 5. Details of the implementation of the DP fit are presented in Sect. 6. The evaluation of systematic uncertainties is given in Sect. 7. The results are summarised in Sect. 8. 2 Detector and simulation The LHCb detector [21,22] is a single-arm forward spectrometer covering the pseudorapidity range 2 <η<5, designed for the study of particles containing bor cquarks. 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 the momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV. The minimum distance of a track to a primary vertex (PV), the impact parameter, is measured with a resolution of (15 + 29/pT)µm, where pTis the component of the momentum transverse to the beam, in GeV. Different types of charged hadrons are distinguished using information from two ringimaging Cherenkov (RICH) 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 [23], 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. At the hardware trigger stage, events are required to have a hadron with high transverse energy in the calorimeters. The software trigger requires a two-, threeor four-tracks secondary vertex 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 [24,25] is used to identify secondary vertices that are consistent with b-hadron decays. Simulated events, generated uniformly in the phase space of the B0→ppK+π−or B0→ηcK+π−decay modes, are used to develop the selection, to validate the fit models and to evaluate the efficiencies entering the branching fraction measurement and the DP analysis. In the simulation, pp collisions are generated using Pythia [26,27] with a specific LHCb configuration [28]. Decays of hadronic particles 123 Eur. Phys. J. C (2018) 78 :1019 Page 3 of 23 1019 are described by EvtGen [29], in which final-state radiation is generated using Photos [30]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [31,32] as described in Ref. [33]. 3 Selection An initial offline selection comprising loose criteria is applied to reconstructed particles, where the associated trigger decision was due to the B0candidate. The final-state tracks are required to have p>[1500]MeV,pT>[300]MeV, and to be inconsistent with originating from any PV in the event. Loose particle identification (PID) criteria are applied, requiring the particles to be consistent with either the proton, kaon or pion hypothesis. All tracks are required to be within the acceptance of the RICH detectors (2.0<η<4.9). Moreover, protons and antiprotons are required to have momenta larger than [8]GeV ([11]GeV) to avoid kinematic regions where proton-kaon separation is limited for Run 1 (Run 2) data. The B0candidates are required to have a small χ2 IP with respect to a PV, where χ2 IP is defined as the difference in the vertex-fit χ2of a given PV reconstructed with and without the candidate under consideration. The PV providing the smallest χ2 IP value is associated to the B0candidate. The B0 candidate is required to be consistent with originating from this PV by applying a criterion on the direction angle (DIRA) between the B0candidate momentum vector and the distance vector between the PV to the B0decay vertex. When building the B0candidates, the resolution on kinematic quantities such as the m(pp)distribution, and the Dalitz variables that will be defined in Sect. 5, is improved by performing a kinematic fit [34] in which the B0candidate is constrained to originate from its associated PV, and its reconstructed invariant mass is constrained to the known B0mass [8]. A boosted decision tree (BDT) [35,36] algorithm is used to further suppress the combinatorial background that arises when unrelated particles are combined to form a B0candidate. The training of the BDT is performed using simulated B0→ppK+π−decays as the signal sample and candidates from the high-mass data sideband as the background sample, defined as the 5450 <m(ppK+π−)<5550 MeV range. The input variables to the BDT classifiers are the same for Run 1 and 2 samples and comprise typical discriminating variables of b-hadron decays: the vertex-fit χ2 vtx,χ2 IP,DIRA and flight distance significance of the reconstructed B0candidates; the maximum distance of closest approach between final-state particles; and the maximum and minimum pand pTof the proton and antiproton. The requirements placed on the output of the BDT algorithm and PID variables are simultaneously optimised to maximise the figure of merit defined as S/√S+B.Here Sis the observed B0→ppK+π−yield before any BDT selection multiplied by the efficiency of the BDT requirement evaluated using simulated decays, while Bis the the combinatorial background yield. The training of the BDT and the optimisation of the selection are performed separately for Run 1 and 2 data to accommodate for differences in the two data-taking periods. 4 Branching fraction measurement The measurement of the B0→ηcK+π−branching fraction is performed relative to that of the B0→J/ψ K+π−normalisation channel, where the J/ψ meson is also reconstructed in the ppdecay mode. A two-stage fit procedure to the combined Run 1 and 2 data sample is used. In the first stage, an extended unbinned maximum-likelihood (UML) fit is performed to the m(ppK+π−)distribution in order to separate the B0→ppK+π−and background contributions. The RooFit package [37] is used to perform the fit, and the sPlot technique [38] is applied to assign weights for each candidate to subtract the background contributions. In the second stage, a weighted UML fit to the ppinvariant-mass spectrum is performed to disentangle the ηc,J/ψ , and nonresonant (NR) contributions. The efficiency-corrected yield ratio is R=Nηc NJ/ψ ×J/ψ ηc ,(1) where Nηcand NJ/ψ are the observed ηcand J/ψ yields, while ηcand J/ψ are the total efficiencies, which are obtained from a combination of simulated and calibration samples. The B0→ηcK+π−branching fraction is determined as B(B0→ηcK+π−)=R×B(B0→J/ψ K+π−) ×B(J/ψ →pp) B(ηc→p p),(2) where B(B0→J/ψ K+π−)=(1.15 ±0.05)×10−3, B(J/ψ →pp)=(2.121 ±0.029)×10−3and B(ηc→ pp)=(1.52 ±0.16)×10−3are the external branching fractions taken from Ref. [8]. 4.1 Signal and normalisation yields The first-stage UML fit to the m(ppK+π−)distribution is performed in the 5180 −5430 MeV range. The B0→ ppK+π−signal decays, B0 s→ppK+π−decays and various categories of background are present in this range. In addition to the combinatorial background, partially reconstructed backgrounds are present originating from b-hadron 123 1019 Page 4 of 23 Eur. Phys. J. C (2018) 78 :1019 5.2 5.25 5.3 5.35 5.4 ) [GeV] − π + Kpp(m 0 500 1000 1500 2000 Candidates / (2.5 MeV) LHCb Data Total PDF − π + Kpp→ 0 B − π + Kpp→ s 0 B − K + Kpp→ s 0 B − π + π pp→ 0 B Combinatorial background Fig. 2 Distribution of the ppK+π−invariant mass. The solid blue curve is the projection of the total fit result. The components are shown in the legend decays with additional particles that are not part of the reconstructed decay chain, such as a π0meson or a photon. Another source of background is b-hadron decays where one of the final-state particles has been incorrectly identified, which includes the decays B0→p pπ+π−and B0 s→ ppK+K−.TheD0→K+π−and − c→pK+π−decays are removed by excluding the mass range 1845 −1885 MeV in the m(K+π−)distribution and the range 2236−2336 MeV in the m(pK+π−)distribution, respectively. The latter veto also removes partially reconstructed b-hadron decays. Both the B0→ppK+π−and B0 s→ppK+π−components are modelled by Hypatia functions [39]. The Hypatia distribution is a generalisation of the Crystall Ball function [40], where the Gaussian core of the latter is replaced by a hyperbolic core to take into account the distortion on the measured mass due to different sources of uncertainty. The Hypatia functions share a common resolution parameter, while the tail parameters are fixed to the values obtained from the corresponding simulated sample. The distributions of the misidentified B0→p pπ+π−and B0 s→ppK+K− backgrounds are described by Crystal Ball functions, with parameters fixed to the values obtained from simulation. The combinatorial background is modelled using an exponential function. The masses of the B0and B0 smesons, the resolution parameter of the Hypatia functions, the slope of the exponential function, and all the yields, are free to vary in the fit to the data. Using the information from the fit to the m(ppK+π−) distribution, shown in Fig. 2,B0→ppK+π−signal weights are computed and the background components are subtracted using the sPlot technique [38]. About 3.0×104B0decays are observed. Correlations between the ppand ppK+π− invariant-mass variables for both signal and background are found to be negligible. The second-stage UML fit is then performed to the weighted ppinvariant-mass distribution in the mass range 2700 −3300 MeV, which includes ηc,J/ψ , and NR B0→ ppK+π−contributions. The p p invariant-mass distribution of ηccandidates is described by the convolution of a nonrelativistic Breit–Wigner function and a Gaussian function describing resolution effects. Using simulated samples, the ppinvariant-mass resolution is found to be ≈[5]MeV. Given the width ηc=[32.0±0.8]MeV [8], the impact of the detector resolution on the ηclineshape is small. The J/ψ resonance, having a small natural width, is parametrised using an Hypatia function, with tail parameters fixed to the values obtained from the corresponding simulated sample. The same resolution parameter is used for the ηcand J/ψ contributions, which is free to vary in the fit to the data. The ηcand J/ψ masses are also floating, while the ηcnatural width is Gaussian constrained to the known value [8]. The NR B0→ppK+π−contribution is parametrised with an exponential function with the slope free to vary in the fit. All yields are left unconstrained in the fit. A possible term describing the interference between the ηcresonance and the NR ppS-wave is investigated and found to be negligible. The result of the fit to the weighted ppinvariant-mass distribution is shown in Fig. 3. The yields of the B0→ηcK+π− and B0→J/ψ K+π−fit components, entering Eq. (1), are 2105 ±75 and 5899 ±86, respectively. 4.2 Ratio of efficiencies The ratio of efficiencies of Eq. (1) is obtained from B0→ηcK+π−and B0→J/ψ K+π−simulated samples, both selected using the same criteria used in data. Since these decays have the same final-state particles and similar kinematic distributions, the ratio of efficiencies is expected to be close to unity. The efficiencies are computed as the product of the geometrical acceptance of the LHCb detector, the reconstruction efficiency and the efficiency of the offline selection criteria, including the trigger and PID requirements. The efficiency of the PID requirements is obtained using calibration samples of pions, kaons and protons, as a function of the particle momentum, pseudorapidity and the multiplicity of the event, e.g. the number of charged particles in the event [41]. The final ratio of efficiencies is given by J/ψ ηc=1.000 ±0.013,(3) which is compatible with unity as expected. 4.3 Systematic uncertainties Table 1summarises the systematic uncertainties on the measurement of the ratio Rof Eq. (1). Since the kinematic distributions of the signal and normalisation channel are similar, the uncertainties corresponding to the reconstruction and 123 Eur. Phys. J. C (2018) 78 :1019 Page 5 of 23 1019 2.9 3 3.1 3.2 ) [GeV]pp(m 0 500 1000 1500 2000 2500 3000 Candidates / (6 MeV) Data Total PDF − π + S)K1( c η → 0 B − π + K ψ /J→ 0 B (NR) − π + Kpp→ 0 B LHCb 2.9 3 3.1 3.2 ) [GeV]pp(m 1 10 2 10 3 10 Candidates / (6 MeV) LHCb Fig. 3 Distribution of the p p invariant mass in (left) linear and (right) logarithmic vertical-axis scale for weighted B0→ppK+π−candidates obtained by using the sPlot technique. The solid blue curve is the projection of the total fit result. The full azure, tight-cross-hatched red and dashed-black line areas show the ηc,J/ψ and NR p p contributions, respectively Table 1 Relative systematic uncertainties on the ratio Rof Eq. (1). The total systematic uncertainty is obtained from the quadratic sum of the individual sources Source Systematic uncertainty (%) Fixed shape parameters 0.8 Resolution model 0.3 NR p¯pmodel 1.7 Efficiency ratio 1.1 Total 2.2 selection efficiencies largely cancel in the ratio of branching fractions. A new value of the ratio Ris computed for each source of systematic uncertainty, and its difference with the nominal value is taken as the associated systematic uncertainty. The overall systematic uncertainty is assigned by combining all contributions in quadrature. The systematic uncertainty arising from fixing the shape parameters of the Hypatia functions used to parametrise the B0and J/ψ components is evaluated by repeating the fits and varying all shape parameters simultaneously. These shape parameters 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. To assign a systematic uncertainty arising from the model used to describe the detector resolution, the fits are repeated for each step replacing the Hypatia functions by Crystal Ball functions, whose parameters are obtained from simulation. The systematic uncertainty associated to the parametrisation of the NR B0→ppK+π−contribution is determined by replacing the exponential function with a linear function. The systematic uncertainty associated to the determination of the efficiency involves contributions arising from the weighting procedure of the calibration samples used to determine the PID efficiencies. The granularity of the binning in the weighting procedure is halved and doubled. The free shape parameters in the first stage UML fit lead to uncertainties that are not taken into account by the sPlot technique. In order to estimate this effect, these parameters are varied within their uncertainties and the signal weights are re-evaluated. The variations on the ratio Rresulting from the second stage UML fit are found to be negligible. 4.4 Results The ratio Ris determined to be R=0.357 ±0.015 ±0.008, where the first uncertainty is statistical and the second systematic. The statistical uncertainty includes contributions from the per-candidate weights obtained using the sPlot technique. The value of Ris used to compute the B0→ηcK+π− branching fraction using Eq. (2) which gives B(B0→ηcK+π−)=(5.73 ±0.24 ±0.13 ±0.66)×10−4, where the first uncertainty is statistical, the second systematic, and the third is due to the limited knowledge of the external branching fractions. 5 Dalitz plot formalism The phase space for a three-body decay involving only pseudoscalar particles can be represented in a DP, where two of the three possible two-body invariant-mass-squared combinations, here m2(K+π−)and m2(ηcπ−), are used to define the DP axes. However, given the sizeable natural width of the ηcmeson, the invariant mass m(p p)is used instead of the known value of the ηcmass [8] to compute the kinematic 123 1019 Page 6 of 23 Eur. Phys. J. C (2018) 78 :1019 quantities such as m2(ηcK+),m2(ηcπ−)and the helicity angles. The isobar model [42–44] is used to write the decay amplitude as a coherent sum of amplitudes from resonant and NR intermediate processes as A[m2(K+π−), m2(ηcπ−)] = N  j=1 cjFj[m2(K+π−), m2(ηcπ−)],(4) where cjare complex coefficients giving the relative contribution of each intermediate process. The Fj[m2(K+π−), m2(ηcπ−)]complex functions describe the resonance dynamics and are normalised such that the integral of their squared magnitude over the DP is unity DP |Fj[m2(K+π−), m2(ηcπ−)]|2 ×dm2(K+π−)dm2(ηcπ−)=1.(5) Each Fj[m2(K+π−), m2(ηcπ−)]contribution is composed of the product of several factors. For a K+π−resonance, for instance, F[m2(K+π−), m2(ηcπ−)] =N×X(|p|rBW)×X(|q|rBW)Z(p,q) ×T[m(K+π−)],(6) where Nis a normalisation constant and pand qare the momentum of the accompanying particle (the ηcmeson in this case) and the momentum of one of the resonance decay products, respectively, both evaluated in the K+π− rest frame. The X(z)terms are the Blatt–Weisskopf barrier factors [45] reported in Appendix A. The barrier radius, rBW, is taken to be [4]GeV−1(corresponding to ∼0.8fm)forall resonances. The Z(p,q)term describes the angular probability distribution in the Zemach tensor formalism [46,47], given by the equations reported in Appendix B. The function T[m(K+π−)]of Eq. (6) is the mass lineshape. Most of the resonant contributions are described by the relativistic Breit–Wigner (RBW) function T(m)=1 m2 0−m2−im0(m),(7) where the mass-dependent width is given by (m)=0|q| q0(2L+1)m0 mX2(|q|rBW)(8) and q0is the value of |q|for m=m0,m0being the pole mass of the resonance. The amplitude parametrisations using RBW functions lead to unitarity violation within the isobar model if there are overlapping resonances or if there is a significant interference with a NR component, both in the same partial wave [48]. This is the case for the K+π−S-wave at low K+π−mass, where the K∗ 0(1430)0resonance interferes strongly with a slowly varying NR S-wave component. Therefore, the K+π−S-wave at low mass is modelled using a modified LASS lineshape [49], given by T(m)=m |q|cot δB−i|q|+e2iδB m00m0 q0 m2 0−m2−im00|q| m m0 q0 , (9) with cot δB=1 a|q|+1 2r|q|,(10) and where m0and 0are the pole mass and width of the K∗ 0(1430)0state, and aand rare the scattering length and the effective range, respectively. The parameters aand rdepend on the production mechanism and hence on the decay under study. The slowly varying part (the first term in Eq. (9)) is not well modelled at high masses and it is set to zero for m(K+π−)values above [1.7]GeV. The probability density function for signal events across the DP, neglecting reconstruction effects, can be written as Psig[m2(K+π−), m2(ηcπ−)] =|A|2 DP |A|2dm2(K+π−)dm2(ηcπ−),(11) where the dependence of Aon the DP position has been suppressed for brevity. The natural width of the ηcmeson is set to zero when computing the DP normalisation shown in the denominator of Eq. (11). The effect of this simplification is determined when assessing the systematic uncertainties as described in Sect. 7. The complex coefficients, given by cjin Eq. (4), depend on the choice of normalisation, phase convention and amplitude formalism. Fit fractions and interference fit fractions are convention-independent quantities that can be directly compared between different analyses. The fit fraction is defined as the integral of the amplitude for a single component squared divided by that of the coherent matrix element squared for the complete DP, FFi=DP |ciFi[m2(K+π−), m2(ηcπ−)]|2dm2(K+π−)dm2(ηcπ−) DP |A[m2(K+π−), m2(ηcπ−)]|2dm2(K+π−)dm2(ηcπ−). (12) In general, the fit fractions do not sum to unity due to the possible presence of net constructive or destructive interference over the whole DP area. This effect can be described by interference fit fractions defined for i<jby 123 Eur. Phys. J. C (2018) 78 :1019 Page 7 of 23 1019 FFij =DP 2Recic∗ jFiF∗ jdm2(K+π−)dm2(ηcπ−) DP |A|2dm2(K+π−)dm2(ηcπ−), (13) where the dependence of F(∗) iand Aon the DP position is omitted. 6 Dalitz plot fit The Laura++ package [50] is used to perform the unbinned DP fit, with the Run 1 and 2 subsamples fitted simultaneously using the JFIT framework [51]. The free parameters in the amplitude fit are in common between the two subsamples, while the signal and background yields and the maps describing the efficiency variations across the phase space, are different. Within the DP fit, the signal corresponds to B0→ηcK+π−decays, while the background comprises both combinatorial background and NR B0→ppK+π− contributions. The likelihood function is given by L= Nc  i k NkPk[m2 i(K+π−), m2 i(ηcπ−)],(14) where the index iruns over the Nccandidates, kruns over the signal and background components, and Nkis the yield of each component. The procedure to determine the signal and background yields is described in Sect. 6.1. The probability density function for the signal, Psig, is given by Eq. (11) where the |A[m2(K+π−), m2(ηcπ−)]|2term is multiplied by the efficiency function described in Sect. 6.3. In order to avoid problems related to the imperfect parametrisation of the efficiencies at the DP borders, a veto of ±[70]MeV is applied around the DP, i.e. to the phase space boundaries of the m(K+π−),m(ηcπ−)and m(ηcK+)distributions. This veto is used when determining the signal and background yields, and the probability density functions for the background, obtained as described in Sect. 6.2.TheK+π−mass resolution is ≈[5]MeV, which is much smaller than the K∗(892)0meson width K∗(892)0≈[50]MeV, the narrowest contribution to the DP; therefore, the resolution has negligible effects and is not considered further. The amplitude fits are repeated many times with randomised initial values to ensure the absolute minimum is found. 6.1 Signal and background yields There is a non-negligible fraction of NR B0→ppK+π− decays in the region of the ηcmeson. In order to separate the contributions of B0→ηcK+π−and NR B0→ ppK+π−decays, a two-dimensional (2D) UML fit to the m(ppK+π−)and m(p p)distributions is performed in the Table 2 Yields of the components in the 2D mass fit to the joint [m(ppK+π−),m(p p)] distribution for the Run 1 and 2 subsamples Component Run 1 Run 2 B0→ηcK+π−805 ±48 1065 ±56 B0→ppK+π−(NR) 234 ±48 273 ±56 Combinatorial background 409 ±36 498 ±41 domain 5220 <m(ppK+π−)<5340 MeV and 2908 < m(pp)<3058 MeV. These ranges are chosen to avoid the misidentified decays reported in Sect. 4.1, and they also define the DP fit domain. The Run 1 and 2 2D mass fits are performed separately. The m(ppK+π−)distributions of B0→ηcK+π−signal and NR B0→ppK+π−decays are described by Hypatia functions. The m(ppK+π−)distribution of the combinatorial background is parametrised using an exponential function. The m(pp)distribution of B0→ηcK+π−signal decays is described by the same model described in Sect. 4.1. A possible component where genuine ηcmesons are combined with random kaons and pions from the PV is investigated but found to be negligible. The B0meson mass, the m(ppK+π−)resolution, the value of mηc, the slopes of the exponential functions, and the yields, are free to vary in the 2D mass fits. The m(pp)resolution and the ηcmeson natural width are Gaussian constrained to the value obtained in the fit to the weighted m(pp)distribution of Sect. 4.1, and to the known value [8], respectively. The yields of all fit components are reported in Table 2. Figure 4shows the result of the 2D mass fits for the Run 1 and 2 subsamples that yield a total of approximately 2000 B0→ηcK+π−decays. The total yield of the B0→ηcK+π−component is lower than that reported in Sect. 4.1 since the fit ranges are reduced. The goodness of fit is validated using pseudoexperiments to determine the 2D pull, i.e. the difference between the fit model and data divided by the uncertainty. 6.2 Parametrisation of the backgrounds The probability density functions for the combinatorial and NR background categories are obtained from the DP distribution of each background source, represented with a uniformly binned 2D histogram. In order to avoid artefacts related to the curved boundaries of the DP, the histograms are built in terms of the Square Dalitz plot (SDP) parametrised by the variables mand θwhich are defined in the range 0 to 1 and are given by m≡1 πarccos 2m(K+π−)−mmin K+π− mmax K+π−−mmin K+π−−1,(15) 123 1019 Page 8 of 23 Eur. Phys. J. C (2018) 78 :1019 5.25 5.3 ) [GeV] − π + Kpp(m 0 20 40 60 80 100 Candidates / (2.4 MeV) LHCb (a) Data Total PDF − π + S)K1( c η → 0 B (NR) − π + Kpp→ 0 B Combinatorial background 5.25 5.3 ) [GeV] − π + Kpp(m 0 20 40 60 80 100 Candidates / (2.4 MeV) LHCb (c) 2.95 3 3.05 ) [GeV]pp(m 0 10 20 30 40 50 60 70 80 Candidates / (3 MeV) LHCb (b) 2.95 3 3.05 ) [GeV]pp(m 0 20 40 60 80 100 Candidates / (3 MeV) LHCb (d) Fig. 4 Results of the 2D mass fit to the joint [m(ppK+π−),m(p p)] distribution for the aRun 1 m(ppK+π−)projection, bRun 1 m(p p) projection, cRun 2 m(ppK+π−)projection, and dRun 2 m(p p)projection. The legend is shown in the top left plot 0 0.2 0.4 0.6 0.8 1 m' 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ' θ 0 2 4 6 8 10 12 14 16 LHCb (a) 0 0.2 0.4 0.6 0.8 1 m' 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ' θ 0 2 4 6 8 10 12 14 16 18 20 LHCb (b) Fig. 5 SDP distributions used in the DP fit to the Run 2 subsample for acombinatorial background and bNR B0→ppK+π−background θ≡1 πθ(K+π−), (16) where mmax K+π−=mB0−mηc,mmin K+π−=mK++mπ− are the kinematic boundaries of m(K+π−)allowed in the B0→ηcK+π−decay, and θ(K+π−)is the helicity angle of the K+π−system (the angle between the K+and the ηc mesons in the K+π−rest frame). The combinatorial and NR background histograms are filled using the weights obtained by applying the sPlot technique to the joint [m(ppK+π−),m(p p)] distribution, merging the Run 1 and 2 data samples. Each histogram is scaled for the corresponding yield in the two subsamples. The combinatorial and NR background histograms for the Run 2 subsample are shown in Fig. 5. Statistical fluctuations in the histograms due to the limited size of the samples are smoothed by applying a 2D cubic spline interpolation. The 2D mass fit described in Sect. 6.1 is repeated to the combined Run 1 and 2 data sample, and the sPlot technique is applied to determine the background-subtracted DP and SDP distributions shown in Fig. 6. 123 Eur. Phys. J. C (2018) 78 :1019 Page 9 of 23 1019 0 10 20 30 40 50 24 ] 2 ) [GeV − π + K( 2 m 10 15 20 ] 2 ) [GeV − π S) 1 ( c η ( 2 m LHCb 0 10 20 30 40 50 0 0.2 0.4 0.6 0.8 1 m' 0 0.2 0.4 0.6 0.8 1 ' θ LHCb Fig. 6 Background-subtracted (top) DP and (bottom) SDP distributions corresponding to the total data sample used in the analysis. The structure corresponding to the K∗(892)0resonance is evident. The veto of B0→ηcK+π−decays in the D0region is visible in the DP 6.3 Signal efficiency Efficiency variation across the SDP is caused by the detector acceptance and by the trigger and offline selection requirements. The efficiency variation is evaluated with simulated samples generated uniformly across the SDP. Corrections are Table 3 Resonances included in the baseline model, where parameters and uncertainties are taken from Ref. [52]. The LASS lineshape also parametrise the K+π−S-wave in B0→ηcK+π−NR decays Resonance Mass [[]MeV]Width [[]MeV]JPModel K∗(892)0895.55 ±0.20 47.3±0.51 −RBW K∗(1410)01414 ±15 232 ±21 1−RBW K∗ 0(1430)01425 ±50 270 ±80 0+LASS K∗ 2(1430)01432.4±1.3 109 ±52 +RBW K∗(1680)01717 ±27 322 ±110 1−RBW K∗ 0(1950)01945 ±22 201 ±90 0+RBW applied for known differences between data and simulation in PID efficiencies. The effect of the vetoes in the phase space is separately accounted for by the Laura++ package, setting to zero the signal efficiency within the vetoed regions. Therefore, the vetoes corresponding to the D0meson and the phase-space border are not applied when constructing the numerator of the efficiency histogram. The efficiency is studied separately for the Run 1 and 2 subsamples, and the resulting efficiency maps are shown in Fig. 7. Lower efficiency in regions with a low-momentum track is due to geometrical effects. Statistical fluctuations in the histograms due to the limited size of the simulated samples are smoothed by applying a 2D cubic spline interpolation. 6.4 Amplitude model with only K+π−contributions In the absence of contributions from exotic resonances, only K+π−resonances are expected as intermediate states. The established K∗0→K+π−mesons reported in Ref. [8] with m(K∗0)m(B0)−m(ηc), i.e. with masses within or slightly above the phase space boundary in B0→ηcK+π− decays, are used as a guide when building the model. Only those amplitudes providing significant improvements in the description of the data are included. This model is referred to as the baseline model and comprises the resonances shown in Table 3. 0 0.2 0.4 0.6 0.8 1 m' 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ' θ 0.004 0.006 0.008 0.01 0.012 LHCb simulation (a) 0 0.2 0.4 0.6 0.8 1 m' 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ' θ 0.004 0.006 0.008 0.01 0.012 LHCb simulation (b) Fig. 7 B0→ηcK+π−signal efficiency across the SDP for the aRun 1 and bRun 2 samples 123 1019 Page 16 of 23 Eur. Phys. J. C (2018) 78 :1019 Appendix: A Blatt–Weisskopf barrier factors The Blatt–Weisskopf barrier factors [45]X(z), where z= |q|rBW or |p|rBW with rBW being the barrier radius, are given by L=0:X(z)=1,(17) L=1:X(z)=1+z2 0 1+z2,(18) L=2:X(z)=z4 0+3z2 0+9 z4+3z2+9,(19) L=3:X(z)=z6 0+6z4 0+45z2 0+225 z6+6z4+45z2+225,(20) L=4:X(z)=z8 0+10z6 0+135z4 0+1575z2 0+11025 z8+10z6+135z4+1575z2+11025, (21) where z0is the value of zwhen the invariant mass is equal to the pole mass of the resonance and Lis the orbital angular momentum between the resonance children. Since the latter are scalars, Lis equal to the spin of the resonance. Since the B0meson and the accompanying particle in the decay are scalars as well, Lis also equal to the orbital angular momentum between the resonance and the accompanying particle in the decay. B: Angular probability distributions Using the Zemach tensor formalism [46,47], the angular probability distributions Z(p,q)are given by L=0:Z(p,q)=1,(22) L=1:Z(p,q)=−2p·q,(23) L=2:Z(p,q)=4 33(p·q)2−(|p||q|)2,(24) L=3:Z(p,q)=−8 55(p·q)3−3(p·q)(|p||q|)2, (25) L=4:Z(p,q)=16 35 35(p·q)4−30(p·q)2(|p||q|)2 +3(|p||q|)4,(26) 0.5 1 1.5 2 ) [GeV] − π + K(m 0 50 100 150 200 / (40 MeV) 1 U P Data Baseline model Nominal model LHCb (a) 0.5 1 1.5 2 ) [GeV] − π + K(m 0 20 40 60 80 100 120 140 / (40 MeV) 2 U P Data Baseline model Nominal model LHCb (b) 0.5 1 1.5 2 ) [GeV] − π + K(m 10− 0 10 20 30 40 50 / (40 MeV) 3 U P Data Baseline model Nominal model LHCb (c) 0.5 1 1.5 2 ) [GeV] − π + K(m 30− 20− 10− 0 10 / (40 MeV) 4 U P Data Baseline model Nominal model LHCb (d) Fig. 10 Comparison of the first four K+π−Legendre moments determined from background-subtracted data (black points) and from the results of the amplitude fit using the baseline model (red triangles) and nominal model (blue triangles) as a function of m(K+π−) 123 Eur. Phys. J. C (2018) 78 :1019 Page 17 of 23 1019 3 3.5 4 4.5 ) [GeV] − π S)1( c η (m 80− 60− 40− 20− 0 / (40 MeV) 1 U P Data Baseline model Nominal model LHCb (a) 33.544.5 ) [GeV] − π S)1( c η (m 10− 0 10 20 30 40 50 60 70 / (40 MeV) 2 U P Data Baseline model Nominal model LHCb (b) 3 3.5 4 4.5 ) [GeV] − π S)1( c η (m 60− 50− 40− 30− 20− 10− 0 10 / (40 MeV) 3 U P Data Baseline model Nominal model LHCb (c) 33.544.5 ) [GeV] − π S)1( c η (m 10− 0 10 20 30 40 50 60 / (40 MeV) 4 U P Data Baseline model Nominal model LHCb (d) Fig. 11 Comparison of the first four ηcπ−Legendre moments determined from background-subtracted data (black points) and from the results of the amplitude fit using the baseline model (red triangles) and nominal model (blue triangles) as a function of m(ηcπ−) 3.5 4 4.5 5 ) [GeV] + S)K1( c η (m 80− 60− 40− 20− 0 / (40 MeV) 1 U P Data Baseline model Nominal model LHCb (a) 3.5 4 4.5 5 ) [GeV] + S)K1( c η (m 10− 0 10 20 30 40 50 60 70 / (40 MeV) 2 U P Data Baseline model Nominal model LHCb (b) 3.5 4 4.5 5 ) [GeV] + S)K1( c η (m 60− 50− 40− 30− 20− 10− 0 10 / (40 MeV) 3 U P Data Baseline model Nominal model LHCb (c) 3.5 4 4.5 5 ) [GeV] + S)K1( c η (m 10− 0 10 20 30 40 50 / (40 MeV) 4 U P Data Baseline model Nominal model LHCb (d) Fig. 12 Comparison of the first four ηcK+Legendre moments determined from background-subtracted data (black points) and from the results of the amplitude fit using the baseline model (red triangles) and nominal model (blue triangles) as a function of m(ηcK+) 123 1019 Page 18 of 23 Eur. 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Eklund54,S.Ely 62,A.Ene 33, S. Escher10,S.Esen 28, T. Evans60, A. Falabella16,N.Farley 48,S.Farry 55, D. Fazzini21,43,i, L. Federici26, P. Fernandez Declara43, A. Fernandez Prieto42, F. Ferrari16, L. Ferreira Lopes44, F. Ferreira Rodrigues2, M. Ferro-Luzzi43, S. Filippov37,R.A.Fini 15,M.Fiorini 17,g, M. Firlej31, C. Fitzpatrick44, T. Fiutowski31, F. Fleuret8,b, M. Fontana43, F. Fontanelli20,h,R.Forty 43, V. Franco Lima55, M. Frank43,C.Frei 43,J.Fu 22,q, W. Funk43, C. Färber43, M. Féo Pereira Rivello Carvalho28, E. Gabriel53, A. Gallas Torreira42, D. Galli16,e, S. Gallorini24, S. Gambetta53,Y.Gan 3, M. Gandelman2, P. Gandini22,Y.Gao 3, L. M. Garcia Martin75, B. Garcia Plana42, J. García Pardiñas45, J. Garra Tico50, L. Garrido41, D. Gascon41, C. Gaspar43, L. Gavardi11, G. Gazzoni6,D.Gerick 13, E. Gersabeck57, M. Gersabeck57, T. Gershon51, D. Gerstel7, Ph. Ghez5, S. Gianì44,V.Gibson 50,O.G.Girard 44, P. Gironella Gironell41, L. Giubega33, K. Gizdov53, V. V. Gligorov9, D. Golubkov35, A. 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Lopes2, G. H. Lovell50, D. Lucchesi24,o, M. Lucio Martinez42, A. Lupato24, E. Luppi17,g, O. Lupton43, A. Lusiani25,X.Lyu 65, F. Machefert8, F. Maciuc33, V. Macko44, P. Mackowiak11, S. Maddrell-Mander49,O.Maev 34,43, K. Maguire57, D. Maisuzenko34, M.W.Majewski 31, S. Malde58, B. Malecki30, A. Malinin72, T. Maltsev39,w, G. Manca23,f, G. Mancinelli7, D. Marangotto22,q, J. Maratas6,v, J. F. Marchand5, U. Marconi16, C. MarinBenito8, M. Marinangeli44,P.Marino 44, J. Marks13, P. J. Marshall55, G. Martellotti27, M. Martin7, M. Martinelli43, D. Martinez Santos42, F. Martinez Vidal75, A. Massafferri1, M. Materok10,R.Matev 43, A. Mathad51, Z. Mathe43, C. Matteuzzi21, A. Mauri45, E. Maurice8,b, B. Maurin44, A. Mazurov48, M. McCann43,56, A. McNab57, R. McNulty14, J. V. Mead55, B. Meadows60, C. Meaux7, N. Meinert70, D. Melnychuk32,M.Merk 28,A.Merli 22,q, E. Michielin24, D. A. Milanes69, E. Millard51, M.-N. Minard5, L. Minzoni17,g, D. S. Mitzel13, A. Mogini9,R.D.Moise 56, J. Molina Rodriguez1,y, T. 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Simone15,d, I. Skiba17, N. Skidmore13, T. Skwarnicki62, M. W. Slater48, J. G. Smeaton50, E. Smith10, I.T.Smith 53, M. Smith56, M. Soares16, l. Soares Lavra1, M. D. Sokoloff60, F. J. P. Soler54, B. Souza De Paula2, B. Spaan11, E. Spadaro Norella22,q, P. Spradlin54, F. Stagni43, M. Stahl13, S. Stahl43, P. Stefko44,S.Stefkova 56, O. Steinkamp45, S. Stemmle13, O. Stenyakin40, M. Stepanova34, H. Stevens11, A. Stocchi8, S. Stone62, B. Storaci45, S. Stracka25, M. E. Stramaglia44, M. Straticiuc33, U. Straumann45,S.Strokov 74, J. Sun3, L. Sun67, K. Swientek31, A. Szabelski32, T. Szumlak31, M. Szymanski65, S. T’Jampens5, Z. Tang3, A. Tayduganov7, T. Tekampe11, G. Tellarini17, F. Teubert43, E. Thomas43, J. van Tilburg28, M. J. Tilley56, V. Tisserand6, M. Tobin31, S. Tolk43, L. Tomassetti17,g, D. Tonelli25,D.Y.Tou 9, R. Tourinho Jadallah Aoude1, E. Tournefier5, M. Traill54, M. T. Tran44,A.Trisovic 50, A. Tsaregorodtsev7, G. Tuci25,p, A. Tully50, N. Tuning28,43, A. Ukleja32, A. Usachov8, A. Ustyuzhanin38, U. Uwer13, A. Vagner74, V. Vagnoni16, A. Valassi43, S. Valat43, G. Valenti16, R. Vazquez Gomez43, P. Vazquez Regueiro42, S. Vecchi17, M. van Veghel28, J. J. Velthuis49, M. Veltri18,r, G. Veneziano58, A. Venkateswaran62, M. Vernet6, M. Veronesi28, N. V. Veronika14, M. Vesterinen58, J. V. Viana Barbosa43, D. Vieira65, M. Vieites Diaz42, H. Viemann70, X. Vilasis-Cardona41,m, A. Vitkovskiy28, M. Vitti50,V.Volkov 36, A. Vollhardt45, D. Vom Bruch9, B. Voneki43, A. Vorobyev34, V. Vorobyev39,w, J.A.deVries 28, C. Vázquez Sierra28, R. Waldi70,J.Walsh 25, J. Wang62, M. Wang3, Y. Wang68, Z. Wang45, D.R.Ward 50, H.M.Wark 55, N.K.Watson 48, D. Websdale56, A. Weiden45, C. Weisser59, M. Whitehead10, J. Wicht51, G. Wilkinson58, M. Wilkinson62, I. Williams50, M. R. J. Williams57, M. Williams59, T. Williams48, F.F.Wilson 52,M.Winn 8, J. Wishahi11, W. Wislicki32, M. Witek30, G. Wormser8, S. A. Wotton50, K. Wyllie43,D.Xiao 68,Y.Xie 68,A.Xu 3,M.Xu 68,Q.Xu 65,Z.Xu 3,Z.Xu 5, Z. Yang3, Z. Yang61, Y. Yao62, L. E. Yeomans55,H.Yin 68,J.Yu 68,aa, X. Yuan62, O. Yushchenko40, K. A. Zarebski48, M. Zavertyaev12,c, D. Zhang68, L. Zhang3, W. C. Zhang3,z, Y. Zhang8, A. Zhelezov13, Y. Zheng65,X.Zhu 3, V. Zhukov10,36, J. B. Zonneveld53, S. Zucchelli16 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 4Institute Of High Energy Physics (IHEP), Beijing, China 5Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France 6Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France 7Aix-Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France 8LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France 9LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France 10 I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany 11 Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany 12 Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany 13 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 14 School of Physics, University College Dublin, Dublin, Ireland 123 1019 Page 22 of 23 Eur. Phys. J. C (2018) 78 :1019 15 INFN Sezione di Bari, Bari, Italy 16 INFN Sezione di Bologna, Bologna, Italy 17 INFN Sezione di Ferrara, Ferrara, Italy 18 INFN Sezione di Firenze, Firenze, Italy 19 INFN Laboratori Nazionali di Frascati, Frascati, Italy 20 INFN Sezione di Genova, Genoa, Italy 21 INFN Sezione di Milano-Bicocca, Milan, Italy 22 INFN Sezione di Milano, Milan, Italy 23 INFN Sezione di Cagliari, Monserrato, Italy 24 INFN Sezione di Padova, Padua, Italy 25 INFN Sezione di Pisa, Pisa, Italy 26 INFN Sezione di Roma Tor Vergata, Rome, Italy 27 INFN Sezione di Roma La Sapienza, Rome, Italy 28 Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands 29 Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands 30 Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland 31 Faculty of Physics and Applied Computer Science, AGH-University of Science and Technology, Kraków, Poland 32 National Center for Nuclear Research (NCBJ), Warsaw, Poland 33 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania 34 Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia 35 Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia 36 Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia 37 Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS), Moscow, Russia 38 Yandex School of Data Analysis, Moscow, Russia 39 Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia 40 Institute for High Energy Physics (IHEP), Protvino, Russia 41 ICCUB, Universitat de Barcelona, Barcelona, Spain 42 Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain 43 European Organization for Nuclear Research (CERN), Geneva, Switzerland 44 Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland 45 Physik-Institut, Universität Zürich, Zürich, Switzerland 46 NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine 47 Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 48 University of Birmingham, Birmingham, UK 49 H.H. Wills Physics Laboratory, University of Bristol, Bristol, UK 50 Cavendish Laboratory, University of Cambridge, Cambridge, UK 51 Department of Physics, University of Warwick, Coventry, UK 52 STFC Rutherford Appleton Laboratory, Didcot, UK 53 School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK 54 School of Physics and Astronomy, University of Glasgow, Glasgow, UK 55 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK 56 Imperial College London, London, UK 57 School of Physics and Astronomy, University of Manchester, Manchester, UK 58 Department of Physics, University of Oxford, Oxford, UK 59 Massachusetts Institute of Technology, Cambridge, MA, USA 60 University of Cincinnati, Cincinnati, OH, USA 61 University of Maryland, College Park, MD, USA 62 Syracuse University, Syracuse, NY, USA 63 Laboratory of Mathematical and Subatomic Physics, Constantine, Algeria, associated to2 64 Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to2 65 University of Chinese Academy of Sciences, Beijing, China, associated to3 66 South China Normal University, Guangzhou, China, associated to3 123 Eur. Phys. J. C (2018) 78 :1019 Page 23 of 23 1019 67 School of Physics and Technology, Wuhan University, Wuhan, China, associated to3 68 Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China, associated to3 69 Departamento de Fisica, Universidad Nacional de Colombia, Bogotá, Colombia, associated to9 70 Institut für Physik, Universität Rostock, Rostock, Germany, associated to13 71 Van Swinderen Institute, University of Groningen, Groningen, Netherlands, associated to28 72 National Research Centre Kurchatov Institute, Moscow, Russia, associated to35 73 National University of Science and Technology “MISIS”, Moscow, Russia, associated to35 74 National Research Tomsk Polytechnic University, Tomsk, Russia, associated to35 75 Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia-CSIC, Valencia, Spain, associated to41 76 University of Michigan, Ann Arbor, USA, associated to62 77 Los Alamos National Laboratory (LANL), Los Alamos, USA, associated to62 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, Genoa, Italy iUniversità di Milano Bicocca, Milan, Italy jUniversità di Roma Tor Vergata, Rome, Italy kUniversità di Roma La Sapienza, Rome, 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, Vietnam oUniversità di Padova, Padua, Italy pUniversità di Pisa, Pisa, Italy qUniversità degli Studi di Milano, Milan, Italy rUniversità di Urbino, Urbino, Italy sUniversità della Basilicata, Potenza, Italy tScuola Normale Superiore, Pisa, Italy uUniversità di Modena e Reggio Emilia, Modena, Italy vMSU-Iligan Institute of Technology (MSU-IIT), Iligan, Philippines wNovosibirsk State University, Novosibirsk, Russia xSezione INFN di Trieste, Trieste, Italy yEscuela Agrícola Panamericana, San Antonio de Oriente, Honduras zSchool of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi’an, China aa Physics and Micro Electronic College, Hunan University, Changsha, China ab National Research University Higher School of Economics, Moscow, Russia †Deceased 123