Search for the B c Meson in Hadronic Z 0 Decays

A search for decays of the B c meson was performed using data collected from 1990–1995 with the OPAL detector on or near the Z 0 peak at LEP. The decay channels B +c → J /ψπ + , B +c → J /ψ a +1 and B +c → J /ψℓ + ν were investigated, where ℓ denotes an electron or a muon. Two candidates are observed in the mode B +c → J /ψπ + , with an estimated background of (0 . 63 ± 0 . 20) events. The weighted mean of the masses of the two candidates is (6 . 32 ± 0 . 06) GeV /c 2 , which is consistent with the predicted mass of the B c meson. One candidate event is observed in the mode B +c → J /ψℓ + ν , with an estimated background of (0 . 82 ± 0 . 19) events. No candidate events are observed in the B +c → J /ψ a +1 decay mode, with an estimated background of (1 . 10 ± 0 . 22) events. Upper bounds at the 90% conﬁdence level are set on the production rates for these processes.


Introduction
The ground-state pseudoscalar mesons containing a b quark have all been observed, by experiments at CESR, DORIS, LEP and the TEVATRON, except for the beauty-charm meson B c (bc). The B c meson can be produced at LEP in hadronic Z 0 decays. Using the non-relativistic potential model for heavy quark bound states, the mass of the B c meson is predicted to be in the range 6.24 to 6.31 GeV/c 2 [1]. The production mechanism for thebc bound states differs from that of the B d , B u and B s mesons, since the soft fragmentation process, involving spontaneous creation of bb or cc, is severely suppressed. The predicted dominant production mechanism shown in figure 1 involves the emission and splitting to cc of a hard gluon in the process Z 0 → bb [2]. Perturbative QCD calculations predict a production rate of 10 −5 to 10 −4 B c per hadronic Z 0 decay, with a momentum spectrum that is considerably softer than that of the lighter B hadrons [3] (see figure 2). The decay of the B c meson is governed by the weak interaction; strong decay into a lower mass beauty meson and a charmed hadron is forbidden by energy conservation. There is a large spread in the predictions for the B c lifetime, although it is generally agreed that it is shorter than the lifetime of the light B mesons. Theoretical calculations predict a significant branching ratio into modes involving the J/ψ meson [4].
In this article we report on a search for B c decays in a data sample of 4.2 × 10 6 hadronic Z 0 decays collected with the OPAL detector at LEP. A previous article by the OPAL collaboration [5] reported on a study of J/ψ meson production in hadronic Z 0 decays, and the reconstruction of exclusive decays of B hadrons into modes containing a J/ψ meson. This analysis included a candidate for the decay 1 B + c → J/ψπ + . The analysis of the B c decays is extended to include searches for the decay modes B + c → J/ψa + 1 and B + c → J/ψℓ + ν, as well as B + c → J/ψπ + , where ℓ denotes an electron or a muon.

The OPAL Detector
The OPAL detector is described in detail elsewhere [6]. Here we briefly describe the components which are relevant to this analysis. The OPAL coordinate system is defined with the z-axis following the electron beam direction, the x-axis pointing towards the center of the LEP ring and the y-axis pointing upwards, forming a right-handed coordinate system. The polar angle θ is defined relative to the z-axis, and r and φ are the standard cylindrical polar coordinates. Charged particle tracking is performed by the central detector system that is located in a solenoidal magnetic field of 0.435 T. The central tracking system consists of a two layer silicon microvertex detector, installed before the 1991 run [7], a high precision vertex drift chamber, a large volume jet chamber and a set of planar drift z-chambers measuring track coordinates along z. The momentum resolution of the central detector in the x-y plane is (δp xy /p xy ) 2 = (2%) 2 + (0.15% · p xy ) 2 , where p xy is in GeV/c. Particle identification is provided by the measurement of specific ionization, dE/dx, in the jet chamber. The dE/dx resolution for tracks with the maximum of 159 samplings in the jet chamber is 3.5% [8]. The central detector is surrounded by a lead glass electromagnetic calorimeter with a pre-sampler. The magnet yoke is instrumented with layers of streamer tubes that serve as a hadron calorimeter and provide additional information for muon identification. Four layers of planar drift chambers surrounding the detector provide tracking for muons.

Data Sample and Event Selection
The data used in this study were collected between 1990 and 1995 using the OPAL detector at LEP. The sample corresponds to approximately 4.2 × 10 6 hadronic Z 0 decays. The selection of hadronic events has been described elsewhere [9]. The selection efficiency for the multihadronic events is (98.1 ± 0.5)%, with a background of less than 0.1%. For this analysis we impose the following additional requirements on charged tracks: the number of hits in the central detector used for the reconstruction of a track must be greater than 40 (this restricts the acceptance to | cos θ| < 0.94); the distance of closest approach to the beam axis in the x-y plane must be less than 0.5 cm; the transverse momentum with respect to the beam direction must exceed 0.25 GeV/c; and the total momentum of the track must exceed 0.5 GeV/c. To obtain accurate polar angle measurements, a barrel (| cos θ| < 0.72) track is required to match with a z-chamber track segment containing at least 3 hits; forward going tracks are constrained to the point where they leave the chamber.
A track is identified as a pion if the dE/dx probability for the pion hypothesis, that is the probability that the specific ionization energy loss in the jet chamber (dE/dx) is compatible with that expected for a pion, exceeds 2.5% if the measured dE/dx is lower than the expected dE/dx for a pion, and 0.1% if it is higher. For the purpose of background rejection, tracks are identified as kaons if the dE/dx probability for the kaon hypothesis is greater than 5%.
Leptons are identified by imposing the following selection criteria. We require the track momentum p > 2.0 GeV/c, and | cos θ| < 0.9. For electron identification we use a neural network algorithm [10] which uses twelve variables containing information from the central tracking system, the electromagnetic calorimeter and its pre-sampler. The overall efficiency for the identification of electrons from B hadron decays is (77 ± 5)%. The error in the electron identification efficiency was determined by comparing the efficiencies in Monte Carlo and data for a pure sample of electrons from photon conversions. For muon identification, two sets of selection criteria are used. For muon candidates combined to form J/ψ candidates in the B + c → J/ψπ + and B + c → J/ψa + 1 modes we employ a "normal" muon selection. In this selection we require a φ-θ match between the extrapolated muon candidate track and a track segment reconstructed in the muon chamber [11]. In addition, we require that the candidate muon track be the best match to the muon segment. When no match to a muon segment is found, we search for a match with a track segment in the hadron calorimeter [12]. The efficiency for this "normal" muon identification is (85 ± 4)%. The errors for the muon identification were determined by comparing the efficiency between Monte Carlo and data for a pure sample of muons from muon pair events. For any muon candidates combined to form B c candidates in the decay B + c → J/ψℓ + ν, where J/ψ → ℓ + ℓ − , we employ a "strong" muon identification [13]. In this selection we use only tracks matched with track segments in the muon detector, reject tracks identified as kaons using dE/dx information, and apply an isolation cut by requiring that there be less than 20 track segments in the muon detector within 0.3 radians of the track. The efficiency for this "strong" muon identification used in the B c → J/ψℓν mode is (76 ± 4)%.
Events are organised into jets of particles which are constructed using charged tracks and neutral clusters that are not associated to any charged track [14]. To form jets we use the scaled invariant mass jet-finding algorithm of JADE with a jet resolution parameter y cut = 0.04.
A Monte Carlo simulation is used to determine the reconstruction and selection efficiencies for the various decay modes and for estimating the background level. The process Z 0 → bb → B c X (figure 1) and subsequent B c meson decays are simulated using the JETSET 7.4 program [15]. Figure 2 shows the prediction of reference [2] for the B c momentum spectrum along with the JETSET 7.4 simulation of the B c spectrum. In addition to simulating B c production as described in reference [2], JETSET 7.4 includes contributions from the production of excited states ofbc bound states. The two momentum distributions are similar. Also shown is the distribution for light b hadrons given by the Peterson et al. fragmentation function [16] with its parameter tuned to produce the measured mean energy fraction ( x E = E B /E beam ), indicating that the B c spectrum is predicted to be considerably softer than that for the light b hadrons. The measured mean energy fraction ( x E ) for the light b hadrons is x E = 0.695 ± 0.006 ± 0.008 [17], while for the generated B c meson we find x E = 0.54. Samples of 2000 events were simulated for each of the following decay modes: B + c → J/ψπ + , B + c → J/ψa + 1 , where a + 1 → ρ 0 π + and ρ 0 → π + π − , and the semileptonic mode B + c → J/ψℓ + ν, where ℓ denotes an electron or a muon. In each event the J/ψ decays to ℓ + ℓ − .
A simulated event sample of 4 × 10 6 five-flavor hadronic Z 0 decays, nearly equal in size to the data sample, was used for studying the background processes. A sample of 80,000 hadronic Z 0 decays containing the process B → J/ψX, where a J/ψ → ℓ + ℓ − decay is present in each event, was used to increase the statistical significance of the background study. In addition two samples of 4000 events containing the processes Z 0 → J/ψqq and Z 0 → J/ψcc were produced in order to study background due to prompt J/ψ production from gluon fragmentation and c quark fragmentation, respectively. The JETSET 7.4 parton shower Monte Carlo generator is used for the simulation of the hadronic Z 0 decays. For the fragmentation of heavy quarks into charmed and light b-flavored hadrons, we use the Peterson fragmentation function. JETSET 7.4 parameters and branching ratios were tuned to match experimental results [18] [19]. All simulated events are passed through the full simulation of the OPAL detector [20]. JETSET does not include radiative decay of J/ψ into lepton pairs. The presence of unreconstructed final state radiation (FSR) in the decay J/ψ → ℓ + ℓ − γ produces a tail toward lower masses in the invariant mass distribution. The effect of FSR on the J/ψ mass distribution is included in Monte Carlo events at reconstruction level. The photon energy is calculated using first order perturbative QED [21]. An error is calculated to account for the higher order terms [22]. Excepting the FSR correction for Monte Carlo simulated events, data and Monte Carlo simulated samples are analysed using the same reconstruction program.

Search for B c decays
We search for the decay modes B + c → J/ψπ + , B + c → J/ψa + 1 , where a + 1 → ρ 0 π + and ρ 0 → π + π − , and the semileptonic mode B + c → J/ψℓ + ν. The analysis involves the reconstruction of J/ψ candidates in the leptonic mode J/ψ → ℓ + ℓ − , which are then combined with other tracks to form J/ψπ + , J/ψπ + π − π + , and J/ψℓ + combinations. The J/ψℓ + combination is a partial reconstruction of the mode B + c → J/ψℓ + ν. Candidates are formed from charged tracks which are assigned to the same jet.

Reconstruction of J/ψ Decays
The J/ψ meson decays are reconstructed in the leptonic modes J/ψ → µ + µ − and J/ψ → e + e − . A pair of opposite sign electron or muon candidates in the same jet, with an invariant mass consistent with the J/ψ mass, is considered a J/ψ candidate. Muon candidates combined to form J/ψ candidates in the B + c → J/ψπ + and B + c → J/ψa + 1 modes must satisfy the "normal" muon identification. Muon candidates combined to form J/ψ candidates in the B + c → J/ψℓ + ν mode must satisfy the criteria of the "strong" muon identification. J/ψ candidates are required to have an invariant mass within the range 2.9 to 3.3 GeV/c 2 for the µ + µ − channel, and within the range 2.8 to 3.3 GeV/c 2 for the e + e − channel. The J/ψ → e + e − candidate range is extended to lower masses in order to include the tail in the J/ψ → e + e − invariant mass distribution due to electron bremsstrahlung radiation in the detector and J/ψ radiative decays. Figure 3 shows the lepton pair invariant mass distributions for leptons selected with the "normal" lepton selection in the range 2.5 to 3.5 GeV/c 2 , where the J/ψ peak is clearly visible in both e + e − and µ + µ − modes. The peak position and width are consistent with the J/ψ mass and the expected resolution of the OPAL detector. We find a total of 354 J/ψ → e + e − candidates and 551 J/ψ → µ + µ − candidates using the normal muon selection. We find 391 J/ψ → µ + µ − candidates using the "strong" muon selection.

Selection of B c Candidates
The dominant background to the sample of B c candidates is from random combinations of J/ψ's produced in b hadron decays with other tracks from b hadron decays or from fragmentation. Given the fact that at best a few events are expected in each channel, it is crucial that the combinatorial background be reduced to below the level of the expected signals. The selection criteria were developed by studying Monte Carlo simulated events containing the signal processes, and the simulated sample of five-flavor Z 0 events (described above). In general, significant background suppression can be achieved by taking advantage of the hard momentum spectrum and the long lifetime of the b hadrons. However, the soft momentum spectrum of the B c weakens the discrimination power of any momentum cut. Furthermore, since there is large uncertainty in the predictions of the B c lifetime, no decay length cut is used. The criteria are summarised below: a. In all decay modes J/ψ candidates are kinematically constrained to the nominal J/ψ mass in order to improve the B c mass resolution.
b. For the exclusive modes, J/ψπ + and J/ψa + 1 , we require that the dE/dx measurement for each pion candidate be "consistent" with the expected value for a pion (as described in section 3).
c. In the semileptonic mode, B + c → J/ψℓ + ν, there is a large background at lower masses involving fake J/ψ or J/ψ combined with fake leptons or leptons from cascade decays. This background is reduced by using the "strong" muon identification for all muon candidates and requiring the ℓ + lepton track momentum p > 4.0 GeV/c. d. For J/ψπ + π − π + combinations, we require that the three-pion combination be consistent with resulting from the decay a + 1 → ρ 0 π + , where ρ 0 → π + π − . The invariant mass of the three pion combination must be consistent with the a 1 mass, (1.0 < M (π + π − π + ) < 1.6) GeV/c 2 , and the invariant mass of at least one of the two π + π − pairs must be in the ρ 0 mass range, (0.65 < M (π + π − ) < 0.90) GeV/c 2 . e. All tracks from the B c must be consistent with originating from the same decay vertex. For each B c candidate we determine the decay vertex from the intersection of the tracks, including the tracks forming the J/ψ candidate, in the x-y plane. We require the χ 2 probability of the vertex fit to exceed 1%.
f. Since the combinatorial backgrounds are largest at low momenta, we impose a minimum momentum cut on the B c candidates. For the J/ψℓ + ν mode, where the full momentum of the candidate is not reconstructed, we require the momentum of the J/ψℓ + combination to exceed 30% of the beam energy. For J/ψπ + combinations we require the momentum of the B c candidate to exceed 55% of the beam energy. For the B + c → J/ψa + 1 candidates, where the combinatorial background is more severe, the candidate momentum is required to exceed 70% of the beam energy. g. For the exclusive modes, we take advantage of the fact that the decay products of a pseudoscalar meson are isotropically distributed in its rest frame. We define θ * as the angle between the B c candidate direction and the direction of the J/ψ in the B c rest frame. Since the combinatorial background mainly peaks near the backward direction (cos θ * = −1.0), we require cos θ * > −0.8.
h. For the exclusive modes, the invariant mass of the B c candidates must be in the mass interval 6.0 to 6.5 GeV/c 2 (hereafter referred to as the signal region) which is centered around the predicted B c mass, with a width which is about three times the B c mass resolution (≃ 80 MeV/c 2 ) on each side. The mass window includes the entire range of predictions for the B c mass. For the semileptonic mode, where the full invariant mass cannot be calculated, the invariant mass of the J/ψℓ + combination is used to define the signal region. The rarity of random combinations of three leptons in hadronic Z 0 decays combined with the high mass of the B c produces a natural separation point between the signal and the background combinations. Figure 4 shows the invariant mass distribution for J/ψℓ + combinations from a sample of simulated B + c → J/ψℓ + ν decays, along with the distribution of the combinatorial background from simulated samples of the B → J/ψX and prompt J/ψ events (see the following section for detail). The signal distribution peaks above 4.0 GeV/c 2 and the background combinations are mostly at lower masses. Hence we restrict the signal region to the mass interval 4.0 to 6.5 GeV/c 2 .
i. B + → J/ψK + decays can fake B + c → J/ψℓ + ν decays if the kaon is misidentified as a lepton. For the semileptonic mode we reject candidates that have a reconstructed mass within 3σ in mass resolution (σ ≃ 60 MeV/c 2 ) of the measured B + mass when the third lepton candidate is assigned the kaon mass.

Estimation of Reconstruction Efficiencies and the Background Levels
The reconstruction efficiencies are calculated from Monte Carlo generated event samples, with the B c meson simulated at a mass of 6.25 GeV/c 2 . In the J/ψπ + mode the leptons from the J/ψ decay are expected to have a sin 2 θ angular distribution with respect to the J/ψ direction in the B c rest-frame. In order to simulate this distribution, which was not included in the Monte Carlo generator, the selected events in the J/ψπ + mode were reweighted. For the decay B + c → J/ψa + 1 we conservatively assume an a + 1 width of 400 MeV. Each sample is composed of events with the appropriate B c decay and subsequent J/ψ → ℓ + ℓ − decay. The mass resolution is found to be about 80 MeV/c 2 in the modes J/ψπ + and J/ψa + 1 . The reconstruction efficiencies for these modes are (10.0 ± 0.7)% and (1.8 ± 0.3)%, respectively, and (5.5 ± 0.5)% for the semileptonic mode B + c → J/ψℓ + ν, where the errors are due to Monte Carlo statistics. The reconstruction efficiency is sensitive to the B c momentum distribution. An estimate of this sensitivity is found by comparing the efficiencies obtained using the distribution predicted by JETSET 7.4 with those obtained assuming the theoretical calculations of reference [2]. Values of m b = (4.9 ± 0.2) GeV/c 2 and m c = (1.5 ± 0.2) GeV/c 2 were used for the input quark masses [3]. In the J/ψπ + mode the difference is 16.3%. For the J/ψa + 1 mode, where a harder cut of x E > 0.7 is applied, a difference of 37.9% is found. In the semileptonic mode the difference is 5.7%. We take the systematic errors on the efficiencies to be one half of the difference for each mode.
The expected background level in each channel is determined by searching for B c decays in the simulated hadronic Z 0 event sample. According to Monte Carlo simulations the background combinations at masses below the signal region are dominated by the combinations of a real J/ψ with random tracks from b hadron decays or from the fragmentation processes. The J/ψ mesons originate dominantly from the decays of b hadrons, with a small fraction, (4.8 ± 1.7 ± 1.7)% [23], of prompt J/ψ (J/ψ resulting from the fragmentation processes). In total, the simulated hadronic event sample contains 2800 events containing a leptonic J/ψ decay. To improve the statistical significance of the background studies we apply the B c search to a sample of 80,000 hadronic Z 0 decays containing the process B → J/ψX, where a J/ψ → ℓ + ℓ − decay is present in each event. This Monte Carlo sample is equivalent to 30 times the size of the data sample. In addition, the B c search was applied to two samples of 4000 events containing the processes Z 0 → J/ψqq and Z 0 → J/ψcc in order to study background due to prompt J/ψ production from gluon fragmentation and c quark fragmentation, respectively, which are the predicted dominant production mechanisms for prompt J/ψ [24]. The predicted branching ratios for these processes are Br(Z 0 → J/ψqq) = 1.9 × 10 −4 and Br(Z 0 → J/ψcc) = 0.8 × 10 −4 . These Monte Carlo sets are equivalent to 40 and 100 times the size of the data sample, respectively.
The resulting invariant mass distributions for the B c candidates in the three modes are shown in figure 5. From these distributions we estimate the background level (see table 1) by counting the number of candidates in the signal region and normalising to the number of events expected in the data sample. The contribution to the background from B → J/ψX events is normalised using the measured rate Br(Z 0 → J/ψX) = (3.9 ± 0.2 ± 0.3) × 10 −3 [5]. The contribution from prompt J/ψ is normalised using the measured rate of prompt J/ψ production Br(Z 0 → prompt J/ψX) = (1.9 ± 0.7 ± 0.7) × 10 −4 , with the two components of the prompt J/ψ signal each assigned a fraction of the total branching rate according to the ratio of their theoretical production rates. The measured rate of prompt J/ψ production is in agreement with the theoretical rates. The uncertainty in the normalisation factors is used as a systematic error for each background estimate.

Background
Decay Mode 0.22 ± 0.09 ± 0.02 1.01 ± 0.19 ± 0.09 0.61 ± 0.15 ± 0.06 J/ψ(c quark frag.) 0.24 ± 0.05 ± 0.13 0.07 ± 0.03 ± 0.04 0.13 ± 0.04 ± 0.07 J/ψ(gluon frag.) 0.17 ± 0.06 ± 0.09 0.02 ± 0.02 ± 0.01 0.07 ± 0.04 ± 0.04 Total 0.63 ± 0.12 ± 0.16 1.10 ± 0.19 ± 0.10 0.82 ± 0.16 ± 0.10 Table 1: Background estimates from samples of 80,000 B → J/ψX enriched events, 4000 prompt J/ψ from the gluon fragmentation process, Z 0 → J/ψqq, and 4000 prompt J/ψ from the c quark fragmentation process, Z 0 → J/ψcc. The first error is statistical and the second is systematic. Figure 6 shows the invariant mass distributions of the J/ψπ + , J/ψa + 1 , and J/ψℓ + ν candidates in the data sample. The shapes and overall levels of the distributions below the signal regions are consistent with the distributions obtained from the simulated background samples. In the mode J/ψπ + we find two events in the signal range 6.0 to 6.5 GeV/c 2 . The invariant masses of the two B c candidates are (6.29 ± 0.17) GeV/c 2 and (6.33 ± 0.063) GeV/c 2 . The errors are calculated from the errors on the track parameters. The reconstructed decay times of the two candidates are τ = (−0.06 ± 0.19) ps and τ = (0.09 ± 0.10) ps, respectively. The estimated background in this mode is (0.63 ± 0.20) events. The probability for a background of 0.63 events to fluctuate to 2 or more is 13.2%. In the mode J/ψℓ + ν we find one event in the signal region. The mass of the candidate J/ψℓ + combination is 5.76 GeV/c 2 . The momentum is 15.4 GeV/c. The reconstructed decay length is (0.14 ± 0.14) cm. The estimated background in this mode is (0.82 ± 0.19) events. In the signal region above the mass of the candidate event, 5.76 to 6.5 GeV/c 2 , the probability to observe one or more events from background is 8.9%, while the efficiency is reduced to (0.6 ± 0.2)%. There are no candidate events in the J/ψa +    Table 2: Summary of systematic errors on the product branching ratio upper limits.

Results and Upper Bounds on the Production Rates
where N (Z 0 ) is the total number of hadronic Z 0 events in the data sample; ǫ had is the hadronic event selection efficiency, 0.981 ± 0.005; ǫ is the reconstruction efficiency for each mode; and Br(J/ψ → ℓ + ℓ − ) is the branching ratio for the leptonic decays of J/ψ, J/ψ → e + e − and J/ψ → µ + µ − , 0.1203 ± 0.0028 [25].
If we interpret the two candidate events in the B + c → J/ψπ + mode as signal we find a branching ratio of, Br(Z 0 → B + c X) Br(Z 0 → qq) × Br(B + c → J/ψπ + ) = (3.8 +5.0 −2.4 ± 0.5) × 10 −5 , where the first error is statistical and the second systematic.

Conclusion
We have performed a search for B c meson decays in data collected with the OPAL detector at LEP. Two candidate B c → J/ψπ + decays are observed in a mass window around the theoretical prediction of the B c mass, compared with an estimated background of (0.63 ± 0.20) events in this mode. The weighted average mass of the two candidates is (6.32 ± 0.06) GeV/c 2 , which is consistent with the predicted mass of the B c meson. One candidate is observed in the mode B + c → J/ψℓ + ν, with a J/ψℓ + mass of 5.76 GeV/c 2 . The estimated background in this mode is (0.82 ± 0.19) events. We have also searched for the decay B + c → J/ψa + 1 , but no candidate events were observed. The estimated background in this mode is (1.10±0.22) events. Upper limits at the 90% confidence level are calculated for the production rates of these processes, × Br(B + c → J/ψπ + ) < 1.06 × 10 −4 , Br(Z 0 → B + c X) Br(Z 0 → qq) × Br(B + c → J/ψℓ + ν) < 6.96 × 10 −5 .
The branching ratio limits for the B + c → J/ψπ + and B + c → J/ψℓ + ν mode are comparable with the limits reported by the ALEPH, DELPHI and CDF collaborations [27][28] [29].