First observation of a baryonic $B_c^+$ decay

A baryonic decay of the $B_c^+$ meson, $B_c^+\to J/\psi p\overline{p}\pi^+$, is observed for the first time, with a significance of $7.3$ standard deviations, in $pp$ collision data collected with the LHCb detector and corresponding to an integrated luminosity of $3.0$ fb$^{-1}$ taken at center-of-mass energies of $7$ and $8$ $\mathrm{TeV}$. With the $B_c^+\to J/\psi \pi^+$ decay as normalization channel, the ratio of branching fractions is measured to be \begin{equation*} \frac{\mathcal{B}(B_c^+\to J/\psi p\overline{p}\pi^+)}{\mathcal{B}(B_c^+\to J/\psi \pi^+)} = 0.143^{\,+\,0.039}_{\,-\,0.034}\,(\mathrm{stat})\pm0.013\,(\mathrm{syst}). \end{equation*} The mass of the $B_c^+$ meson is determined as $M(B_c^+)=6274.0\pm1.8\,(\mathrm{stat})\pm0.4\,(\mathrm{syst})\,\mathrm{MeV}/c^2$, using the $B_c^+\to J/\psi p\overline{p}\pi^+$ channel.

p T > 1 GeV/c and χ 2 of the impact parameter (χ 2 IP ) greater than 16 with respect to any primary vertices.The quantity χ 2 IP is the difference between the χ 2 values of a given primary vertex reconstructed with and without the considered track.The second stage of the software trigger selects a muon pair with an invariant mass that is consistent with the known J/ψ mass [28], with the effective decay length significance of the reconstructed J/ψ candidate, S L , greater than 3, where S L is the distance between the J/ψ vertex and the primary vertex divided by its uncertainty.
The offline analysis uses a preselection, followed by a multivariate selection based on a boosted decision tree (BDT) [29,30].In the preselection, the invariant mass of the J/ψ candidate is required to be in the interval [3020,3135] MeV/c 2 .The J/ψ candidates are selected by requiring the χ 2 per degree of freedom, χ 2 /ndf, of the vertex fit to be less than 20.The muons are required to have χ 2 IP > 4 with respect to any reconstructed pp vertex, to suppress the J/ψ candidates produced promptly in pp collisions.The decay B + c → J/ψ π + (B + c → J/ψ ppπ + ) is reconstructed by combining a J/ψ candidate with one (three) charged track(s) under π + (p, p and π + ) mass hypothesis.The requirements χ 2 IP > 4 and p T > 0.1 GeV/c, are applied to these hadron tracks.Particle identification (PID) is performed using dedicated neural networks, which use the information from all the sub-detectors.Well-identified pions are selected by a tight requirement on the value of the PID discriminant P π .A loose requirement is applied to the PID discriminants of protons and anti-protons, P p , P p , followed by the optimization described below.To improve the PID performance, the momenta of protons and anti-protons are required to be greater than 10 GeV/c.The B + c candidate is required to have vertex fit χ 2 /ndf < 6, p T > 2 GeV/c, χ 2 IP < 16 with respect to at least one reconstructed pp collision and decay-time significance larger than 9 with respect to the vertex with the smallest χ 2 IP .To improve the mass and decay-time resolutions, a kinematic fit [31] is applied to the B + c decay, constraining the mass of the J/ψ candidate to the current best world average [28] and the momentum of the B + c candidate to point back to the primary vertex.The BDT is trained with a simulated sample, where B + c candidates are generated with Bcvegpy [32], interfaced to Pythia6 [33], using a specific LHCb configuration [34].Decays of hadronic particles are described by EvtGen [35], in which final-state radiation (FSR) is generated using Photos [36].The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [37] as described in Ref. [38].For the background, candidates in the invariant mass sidebands of the preselected B + c data sample are used.The BDT input variables are p T , χ 2 IP , S L of the B + c candidate, χ 2 /ndf of its vertex fit, the quality of the constrained kinematic fit of the decay chain, and p T , χ 2 IP of the hadrons.For the B + c → J/ψ ppπ + candidates, the selection criteria are fixed by optimizing the BDT discriminant jointly with the product of two proton PID discriminants, P p × P p .The selections on BDT discriminant and the combined PID discriminant are chosen to maximize the figure of merit, aiming for a signal significance of three standard deviations, /(3/2 + √ B) [39], where is the signal efficiency determined using simulated events and B is the number of expected background candidates estimated using sideband events in the data.For the B + c → J/ψ π + decay, the BDT discriminant is selected to maximize the signal significance S/ √ S + B, where S and B are the expected signal and background yields, estimated from simulated events and sideband data, respectively.
Figure 1 shows the invariant mass distributions of the B + c → J/ψ ppπ + and B + , and validated using a variety of known resonances.The uncertainty of the momentum scale calibration is 0.03% [41], which is the difference between momentum scale factors determined using different resonances.This effect is studied by changing the momentum scale by one standard deviation and repeating the analysis, taking the variation of the reconstructed mass as a systematic uncertainty.The amount of material traversed by a charged particle in the tracking system is known with an uncertainty of 10%, and the systematic effect of this uncertainty on the B + c mass measurement is studied by varying the energy loss correction by 10% in the reconstruction [42].Since only charged tracks are reconstructed, the B + c mass is underestimated due to FSR by 0.20 ± 0.03 MeV/c 2 , as determined with a simulated sample.Therefore, the measured mass is corrected by 0.20 MeV/c 2 and 0.03 MeV/c 2 is assigned as a systematic uncertainty.The contribution from the fit model is studied by using alternative fit functions for the signal and background, by using different fit invariant mass ranges or by changing the estimated mass resolution within its uncertainty.The total systematic uncertainty of the mass measurement is 0.42 MeV/c 2 .After the correction for FSR, the mass of the B + c meson is determined to be 6274.0± 1.8 (stat) ± 0.4 (syst) MeV/c 2 .A combination of this result with previous LHCb measurements gives 6274.7 ± 0.9 (stat) ± 0.8 (syst) MeV/c 2 .In the combination of the mass measurements, all systematic uncertainties apart from those due to the mass fit model and FSR are considered fully correlated.
In the branching fraction measurement of the decay B + c → J/ψ ppπ + , to account for any difference between data and simulation, the PID efficiency is calibrated using control data samples.To allow easy calibration of the PID efficiency, the selection on the individual PID discriminants, P p and P p , is applied instead of their product.The same cut value is applied to the two PID variables, and this cut value is optimized simultaneously with the BDT discriminant, maximizing the same figure of merit.With the new selection criteria, used to determine the branching fraction, the signal yield of the B + c → J/ψ ppπ + decay is 19.3 + 5.3 − 4.6 (stat).The ratio of yields between the B + c → J/ψ ppπ + and B + c → J/ψ π + modes is determined to be r N = 0.0068 + 0.0019 − 0.0016 (stat).The ratio of branching fractions is calculated as where r ≡ (B + c → J/ψ ppπ + )/ (B + c → J/ψ π + ) is the ratio of the total efficiencies.The geometrical acceptance, reconstruction, selection and trigger efficiencies are determined from simulated samples for both channels.The central value of the B + c lifetime measured by LHCb, 509 ± 8 (stat) ± 12 (syst) fs [12], is used in the simulation.The PID efficiency for each track is measured in data in bins of momentum, p, pseudorapidity, η of the track and track multiplicity of the event, n trk .The PID efficiency for pions is determined with π + from D * -tagged D 0 → K − π + decays.Similarly, the PID efficiency for protons is determined using protons from Λ + c → pK − π + decays.These efficiencies are assigned to the simulated candidate according to p and η of the final state hadron tracks, and n trk of the event.The distribution of n trk in simulation is reweighted to match that in data.The overall ratio of efficiencies, r , is found to be (4.76 ± 0.06)%, where the uncertainty is statistical.
The systematic uncertainties for the branching fraction measurement are summarized in Table 2.For the signal yields, the systematic uncertainty is obtained by varying the invariant mass fit functions of the two modes.The effect of geometrical acceptance is evaluated by comparing the efficiencies obtained from samples simulated with different data taking conditions.The systematic uncertainty due to the trigger requirement is studied by comparing the trigger efficiency in data and simulated samples, using a large J/ψ sample [7,43].The impact of the uncertainty of the B + c lifetime is evaluated from the variation of the relative efficiency when the B + c lifetime is changed by one standard deviation of the LHCb measurement [12].The systematic uncertainty associated with the reconstruction efficiency of the two additional hadron tracks, p and p, in the B + c → J/ψ ppπ + mode compared to the B + c → J/ψ π + mode, is also studied.Different assumptions for the pion PID efficiency in the kinematic regions where no calibration efficiency is available introduce a systematic uncertainty.For the protons, the systematic uncertainty from PID selection takes into account the uncertainties in the single-track efficiencies, the binning scheme in (p, η, n trk ) intervals and the uncertainty of the track multiplicity distribution.Another systematic uncertainty is related to the unknown decay model of the mode B + c → J/ψ ppπ + .The simulated sample is generated according to a uniform phase-space decay model.Figure 2 shows the one-dimensional invariant mass distributions of M (pp) and M (pπ + ) for data, with background subtracted using the sPlot method [44].Figure 2 also shows the distributions for simulated events, which agree with those in data within the large statistical uncertainties.The efficiency calculated using the observed distribution in data relative to the efficiency determined using the simulated decay model is 0.949 ± 0.067, where the uncertainty is statistical.Since the value is consistent with unity within the uncertainty, no correction to the efficiency is made and a systematic uncertainty of 6.7% is assigned.The total systematic uncertainty associated with the relative branching fraction measurement is 8.9%.
As a result the ratio of branching fractions is measured to be which is consistent with the expectation from the spectator decay model assuming factorization [45], B(B 0 →D * − π + ) = 0.17 ± 0.02.The branching fractions for B 0 → D * − ppπ + and B 0 → D * − π + decays are taken from Ref. [28].
In conclusion, the decay B + c → J/ψ ppπ + is observed with a significance of 7.3 standard deviations, using a data sample corresponding to an integrated luminosity of 3.0 fb −1 collected by the LHCb experiment.Thi is the first observation of a baryonic decay of the B + c meson.The branching fraction of this decay relative to that of the B + c → J/ψ π + decay is measured.The mass of the B + c meson is measured to be 6274.0± 1.8 (stat) ± 0.4 (syst) MeV/c 2 .In combination with previous results by LHCb [7,11], the B + c mass is determined to be 6274.7 ± 0.9 (stat) ± 0.8 (syst) MeV/c 2 .

Table 1 :
Systematic uncertainties for the B + c mass measurement.

Table 2 :
Systematic uncertainties (in percent) for the relative branching fraction measurement.