Observation of $B^+_c \rightarrow J/\psi D_s^+$ and $B^+_c \rightarrow J/\psi D_s^{*+}$ decays

The decays $B^+_c \rightarrow J/\psi D_s^+$ and $B^+_c \rightarrow J/\psi D_s^{*+}$ are observed for the first time using a dataset, corresponding to an integrated luminosity of 3$fb^{-1}$, collected by the LHCb experiment in proton-proton collisions at centre-of-mass energies of $\sqrt{s}$=7 and 8 TeV. The statistical significance for both signals is in excess of 9 standard deviations. The following ratios of branching fractions are measured to be $BR(B^+_c \rightarrow J/\psi D_s^+)/BR(B^+_c \rightarrow J/\psi \pi+) = 2.90 \pm 0.57 \pm 0.24$, $BR(B^+_c \rightarrow J/\psi D_s^{*+}) / BR (B^+_c \rightarrow J/\psi D_s^+) = 2.37 \pm 0.56 \pm 0.10$, where the first uncertainties are statistical and the second systematic. The mass of the \Bc meson is measured to be $m_{B^+_c} = 6276.28 \pm 1.44 (stat) \pm 0.36(syst) MeV/c^2$, using the $B^+_c \rightarrow J/\psi D_s^+$ decay mode.


Introduction
The B + c meson, the ground state of thebc system, is unique, being the only weakly decaying heavy quarkonium system. Its lifetime [1,2] is almost three times smaller than that of other beauty mesons, pointing to the important role of the charm quark in weak B + c decays. The B + c meson was first observed through its semileptonic decay B + c → J/ψ + ν X [3]. Only three hadronic modes have been observed so far: B + c → J/ψ π + [4], B + c → J/ψ π + π + π − [5] and B + c → ψ(2S)π + [6]. The first observations of the decays B + c → J/ψ D + s and B + c → J/ψ D * + s are reported in this paper. The leading Feynman diagrams of these decays are shown in Fig. 1. The decay B + c → J/ψ D + s is expected to proceed mainly through spectator and colour-suppressed spectator diagrams. In contrast to decays of other beauty hadrons, the weak annihilation topology is not suppressed and can contribute significantly to the decay amplitude.  Assuming that the spectator diagram dominates and that factorization holds, the following approximations can be established where B stands for B + or B 0 and D * denotes D * 0 or D * − . Phase space corrections amount to O(0.5%) for Eq. (1a) and can be as large as 28% for Eq. (1b), depending on the relative orbital momentum. The relative branching ratios estimated in this way, together with more detailed theoretical calculations, are listed in Table 1, where the branching fractions for the B → D * D + s and B → D * π + decays are taken from Ref. [1]. The analysis presented here is based on a data sample, corresponding to an integrated luminosity of 3 fb −1 , collected with the LHCb detector during 2011 and 2012 in pp collisions at centre-of-mass energies of 7 and 8 TeV, respectively. The decay B + c → J/ψ π + is used as a normalization channel for the measurement of the branching fraction B(B + c → J/ψ D + s ). In addition, the low energy release (Q-value) in the B + c → J/ψ D + s mode allows a determination of the B + c mass with small systematic uncertainty.

LHCb detector
The LHCb detector [12] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream. The combined tracking system has momentum resolution ∆p/p that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c, and impact parameter resolution of 20 µm for tracks with high transverse momentum. Charged hadrons are identified using two ring-imaging Cherenkov detectors. Photon, electron and hadron candidates 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 trigger [13] 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. This analysis uses events collected by triggers that select the decay products of the dimuon decay of the J/ψ meson with high efficiency. At the hardware stage either one or two identified muon candidates are required. In the case of single muon triggers the transverse momentum, p T , of the candidate is required to be larger than 1.5 GeV/c. For dimuon candidates a requirement on the product of the p T of the muon candidates is applied, √ p T 1 p T 2 > 1.3 GeV/c. At the subsequent software trigger stage, two muons with invariant mass in the interval 2.97 < m µ + µ − < 3.21 GeV/c 2 and consistent with originating from a common vertex are required.
The detector acceptance and response are estimated with simulated data. Proton-proton collisions are generated using Pythia 6.4 [14] with the configuration described in Ref. [15]. Particle decays are then simulated by EvtGen [16] in which final state radiation is generated using Photos [17]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [18] as described in Ref. [19].

Event selection
Track quality of charged particles is ensured by requiring that the χ 2 per degree of freedom, χ 2 tr /ndf, is less than 4. Further suppression of fake tracks created by the reconstruction is achieved by a neural network trained to discriminate between these and real particles based on information from track fit and hit pattern in the tracking detectors. A requirement on the output of this neural network, P fake < 0.5 allows to reject half of the fake tracks.
Duplicate particles created by the reconstruction are suppressed by requiring the symmetrized Kullback-Leibler divergence [20], ∆ min KL , calculated with respect to all particles in the event, to be in excess of 5000. In addition, the transverse momentum is required to be greater than 550 (250) MeV/c for each muon (hadron) candidate.
Well identified muons are selected by requiring that the difference in logarithms of the likelihood of the muon hypothesis, as provided by the muon system, with respect to the pion hypothesis, ∆ µ/π ln L [21], is greater than zero. Good quality particle identification by the ring-imaging Cherenkov detectors is ensured by requiring the momentum of the hadron candidates, p, to be between 3.2 GeV/c and 100 GeV/c, and the pseudorapidity to be in the range 2 < η < 5. To select well-identified kaons (pions) the corresponding difference in logarithms of the likelihood of the kaon and pion hypotheses [22] is required to be ∆ K/π ln L > 2(< 0). These criteria are chosen to be tight enough to reduce significantly the background due to misidentification, whilst ensuring good agreement between data and simulation.
To ensure that the hadrons used in the analysis are inconsistent with being directly produced in a pp interaction vertex, the impact parameter χ 2 , defined as the difference between the χ 2 of the reconstructed pp collision vertex formed with and without the considered track, is required to be χ 2 IP > 9. When more than one vertex is reconstructed, that with the smallest value of χ 2 IP is chosen. As in Refs. [23][24][25] the selection of J/ψ → µ + µ − candidates proceeds from pairs of oppositely-charged muons forming a common vertex. The quality of the vertex is ensured by requiring the χ 2 of the vertex fit, χ 2 vx , to be less than 30. The vertex is forced to be well separated from the reconstructed pp interaction vertex by requiring the decay length significance, S flight , defined as the ratio of the projected distance from pp interaction vertex to µ + µ − vertex on direction of µ + µ − pair momentum and its uncertainty, to be greater than 3. Finally, the mass of the dimuon combination is required to be within ±45 MeV/c 2 of the known J/ψ mass [1], which corresponds to a ±3.5σ window, where σ is the measured J/ψ mass resolution.
Candidate D + s mesons are reconstructed in the D + s → (K + K − ) φ π + mode using criteria similar to those in Ref. [26]. A good vertex quality is ensured by requiring χ 2 vx < 25. The mass of the kaon pair is required to be consistent with the decay φ → K + K − , Finally, the mass of the candidate is required to be within ±20 MeV/c 2 of the known D + s mass [1], which corresponds to a ±3.5σ window, where σ is the measured D + s mass resolution, and its transverse momentum to be > 1 GeV/c. Candidate B + c mesons are formed from J/ψ D + s pairs with transverse momentum in excess of 1 GeV/c. The candidates should be consistent with being produced in a pp interaction vertex by requiring χ 2 IP < 9 with respect to reconstructed pp collision vertices. A kinematic fit is applied to the B + c candidates [27]. To improve the mass and lifetime resolution, in this fit, a constraint on the pointing of the candidate to the primary vertex is applied together with mass constraints on the intermediate J/ψ and D + s states. The value of the J/ψ mass is taken from Ref. [1]. For the D + s meson the value of m D + s = 1968.31 ± 0.20 MeV/c 2 is used, that is the average of the values given in Ref. [28] and Ref. [1]. The χ 2 per degree of freedom of this fit, χ 2 fit /ndf, is required to be less than 5. The decay time of the D + s candidate, cτ (D + s ), determined by this fit, is required to satisfy cτ > 75 µm. The corresponding signed significance, S cτ , defined as the ratio of the measured decay time and its uncertainty, is required to be in excess of 3. Finally, the decay time of the B + c candidate, cτ (B + c ), is required to be between 75 µm and 1 mm. The upper edge, in excess of 7 lifetimes of B + c meson, is introduced to remove badly recontructed candidates.
The mass distribution of the selected B + c → J/ψ D + s candidates is shown in Fig. 2. The peak close to the known mass of the B + c meson [1,29] with a width compatible with the expected mass resolution is interpreted as being due to the B + c → J/ψ D + s decay. The wide structure between 5.9 and 6.2 GeV/c 2 is attributed to the decay B + c → J/ψ D * + s , followed by D * + s → D + s γ or D * + s → D + s π 0 decays, where the neutral particles are not detected. The process B + c → J/ψ D * + s being the decay of a pseudoscalar particle into two vector particles is described by three helicity amplitudes: A ++ , A 00 and A −− , where indices correspond to the helicities of the J/ψ and D * + s mesons. Simulation studies show that the J/ψ D + s mass distributions are the same for the A ++ and A −− amplitudes. Thus, the J/ψ D + s mass spectrum is described by a model consisting of the following components: an exponential shape to describe the combinatorial background, a Gaussian shape to describe the B + c → J/ψ D + s signal and two helicity components to describe the B + c → J/ψ D * + s contributions corresponding to the A ±± and A 00 amplitudes. The shape of these components is determined using the simulation where the branching fractions for D * + s → D + s γ and D * + s → D + s π 0 decays are taken from Ref. [1]. To estimate the signal yields, an extended unbinned maximum likelihood fit to the mass distribution is performed. The correctness of the fit procedure together with the reliability of the estimated uncertainties has been extensively checked using simulation. The fit has seven free parameters: the mass of the B + c meson, m B + c , the signal resolution, σ B + c , the relative amount of the A ±± helicity amplitudes of total B + c → J/ψ D * +   Table 2. The fit result is also shown in Fig. 2.
To check the result, the fit has been performed with different models for the signal: a double-sided Crystal Ball function [30,31], and a modified Novosibirsk function [32]. For these tests the tail and asymmetry parameters are fixed using the simulation values, while the parameters representing the peak position and resolution are left free to vary. As alternative models for the background, the product of an exponential function and a fourth-order polynomial function are used. The fit parameters obtained are stable with respect to the choice of the fit model and the fit range interval.
The statistical significance for the B + c → J/ψ D + s signal is estimated from the change in Table 2: Signal parameters of the unbinned extended maximum likelihood fit to the J/ψ D + s mass distribution.

Parameter
Value the likelihood function S σ = 2 ln L B+S L B , where L B is the likelihood of a background-only hypothesis and L B+S is the likelihood of a background-plus-signal hypothesis. The significance has been estimated separately for the B + c → J/ψ D + s and B + c → J/ψ D * + s signals. To exclude the look-elsewhere effect [33], the mass and resolution of the peak are fixed to the values obtained with the simulation. The minimal significance found varying the fit model as described above is taken as the signal significance. The statistical significance for both the B + c → J/ψ D + s and B + c → J/ψ D * + s signals estimated in this way is in excess of 9 standard deviations.
The low Q-value for the B + c → J/ψ D + s decay mode allows the B + c mass to be precisely measured. This makes use of the D + s mass value, evaluated in Sect. 3, taking correctly into account the correlations between the measurements. The calibration of the momentum scale for the dataset used here is detailed in Refs. [28,34]. It is based upon large calibration samples of B + → J/ψ K + and J/ψ → µ + µ − decays and leads to an accuracy in the momentum scale of 3 × 10 −4 . This translates into an uncertainty of 0.30 MeV/c 2 on the B + c meson mass. A further uncertainty of 0.11 MeV/c 2 arises from the knowledge of the detector material distribution [28,29,34,35]  5 Normalization to the B + c → J/ψ π + decay mode A large sample of B + c → J/ψ π + decays serves as a normalization channel to measure the ratio of branching fractions for the B + c → J/ψ D + s and B + c → J/ψ π + modes. Selection of B + c → J/ψ π + events is performed in a manner similar to that described in Sect. 3 for the signal channel. To further reduce the combinatorial background, the transverse momentum of the pion for the B + c → J/ψ π + mode is required to be in excess of 1 GeV/c. The mass distribution of the selected B + c → J/ψ π + candidates is shown in Fig. 3.  To determine the yield, an extended unbinned maximum likelihood fit to the mass distribution is performed. The signal is modelled by a double-sided Crystal Ball function and the background with an exponential function. The fit gives a yield of 3009 ± 79 events. As cross-checks, a modified Novosibirsk function and a Gaussian function for the signal component and a product of exponential and polynomial functions for the background are used. The difference is treated as systematic uncertainty.
The ratio of the total efficiencies (including acceptance, reconstruction, selection and trigger) for the B + c → J/ψ D + s and B + c → J/ψ π + modes is determined with simulated data to be 0.148 ± 0.001, where the uncertainty is statistical only. As only events explicitly selected by the J/ψ triggers are used, the ratio of the trigger efficiencies for the B + c → J/ψ D + s and B + c → J/ψ π + modes is close to unity.

Systematic uncertainties
Uncertainties on the ratio R D + s /π + related to differences between the data and simulation efficiency for the selection requirements are studied using the abundant B + c → J/ψ π + channel. As an example, Fig. 4 compares the distributions of χ 2 fit (B + c ) and χ 2 IP (B + c ) for data and simulated B + c → J/ψ π + events. For background subtraction the sPlot techinque [36] has been used. It can be seen that the agreement between data and simulation is good. In addition, a large sample of selected B + → J/ψ (K + K − ) φ K + events has been used to quantify differences between data and simulation. Based on the deviation, a systematic uncertainty of 1% is assigned.
The agreement of the absolute trigger efficiency between data and simulation has been validated to a precision of 4% using the technique described in Refs. [13,31,37] with a large sample of B + → J/ψ (K + K − ) φ K + events. A further cancellation of uncertainties occurs in the ratio of branching fractions resulting in a systematic uncertainty of 1.1%.
The systematic uncertainties related to the fit model, in particular to the signal shape, mass and resolution for the B + c → J/ψ D + s mode and the fit interval have been discussed in Sects. 4 and 5. The main part comes from the normalization channel B + c → J/ψ π + . Other systematic uncertainties arise from differences in the efficiency of charged particle reconstruction between data and simulation. The largest of these arises from the knowledge of the hadronic interaction probability in the detector, which has an uncertainty of 2% per track [37]. A further uncertainty related to the reconstruction of two additional kaons in the B + c → J/ψ D + s mode with respect to the B + c → J/ψ π + mode is estimated to be 2 × 0.6% [38]. Further uncertainties are related to the track quality selection requirements χ 2 tr < 4 and P fake < 0.5. These are estimated from a comparison of data and simulation in the B + c → J/ψ π + decay mode to be 0.4% per final state track. The uncertainty associated with the kaon identification criteria is studied using the combined B + c → J/ψ D + s and B + c → J/ψ D * + s signals. The efficiency to identify a kaon pair with a selection on ∆ K/π ln L has been compared for data and simulation for various selection requirements. The comparison shows a (−1.8 ± 2.9)% difference between data and simulation in the efficiency to identify a kaon pair with 2 ≤ min ∆ K/π log L. This estimate has been confirmed using a kinematically similar sample of reconstructed B + → J/ψ (K + K − ) φ K + events. An uncertainty of 3% is assigned. The limited knowledge of the B + c lifetime leads to an additional systematic uncertainty due to the different decay time acceptance between the B + c → J/ψ D + s and B + c → J/ψ π + decay modes. To estimate this effect, the decay time distributions for simulated events are reweighted to change the B + c lifetime by one standard deviation from the known value [1], as well as the value recently measured by the CDF collaboration [2], and the efficiencies are recomputed. An uncertainty of 1% is assigned.
Possible uncertainties related to the stability of the data taking conditions are tested by studying the ratio of the yields of B + → J/ψ K + π + π − and B + → J/ψ K + decays for different data taking periods and dipole magnet polarities. This results in a further 2.5% uncertainty.
The largest systematic uncertainty is due to the knowledge of the branching fraction of the D + s → (K − K + ) φ π + decay, with a kaon pair mass within ±20 MeV/c 2 of the known φ meson mass. The value of (2.24 ± 0.11 ± 0.06)% from Ref. [39] is used in the analysis. The systematic uncertainties on R D + s /π + are summarized in Table 3. The ratio R D * + s /D + s is estimated as where the ratio of yields is given in Table 2. The uncertainty associated with the assumption that the efficiencies for the B + c → J/ψ D + s and B + c → J/ψ D * + s modes are equal, is evaluated by studying the dependence of the relative yields for these modes for loose (or no) requirements on the χ 2 IP (B + c ), χ 2 fit (B + c ) and cτ (B + c ) variables. For this selection the measured ratio of B + c → J/ψ D * + s to B + c → J/ψ D + s events changes to 2.27 ± 0.59. An uncertainty of 4% is assigned to the R D * + s /D + s ratio. The uncertainty on the fraction of the A ±± amplitude, f ±± , has been studied with different fit models for the parameterization of the combinatorial background, as well as different mass resolution models. This is negligible in comparison to the statistical uncertainty.

Results and summary
The decays B + c → J/ψ D + s and B + c → J/ψ D * + s have been observed for the first time with statistical significances in excess of 9 standard deviations. The ratio of branching fractions for B + c → J/ψ D + s and B + c → J/ψ π + is calculated as where the value of B D + s = B D + s → (K − K + ) φ π + [39] with the mass of the kaon pair within ±20 MeV/c 2 of the known value of the φ mass is used, together with the ratio of efficiencies, and the signal yields given in Sects. 4 and 5. This results in B (B + c → J/ψ D + s ) B (B + c → J/ψ π + ) = 2.90 ± 0.57 (stat) ± 0.24 (syst).
The value obtained is in agreement with the naïve expectations given in Eq. (1a) from B 0 decays, and the values from Refs. [8][9][10] but larger than predictions from Refs. [7,11] and factorization expectations from B + decays. The ratio of branching fractions for the B + c → J/ψ D * + s and B + c → J/ψ D + s decays is measured to be B (B + c → J/ψ D * + s ) B (B + c → J/ψ D + s ) = 2.37 ± 0.56 (stat) ± 0.10 (syst).
This result is in agreement with the naïve factorization hypothesis (Eq. (1b)) and with the predictions of Refs. [8,9]. The fraction of the A ±± amplitude in the B + c → J/ψ D * + s decay is measured to be Γ ±± (B + c → J/ψ D * + s ) Γ tot (B + c → J/ψ D * + s ) = (52 ± 20)%, in agreement with a simple estimate of 2 3 , the measurements [40,41] and factorization predictions [42] for B 0 → D * − D * + s decays, and expectations for B + c → J/ψ + ν decays from Refs. [43,44]. The B + c mass measurement is in good agreement with the previous result obtained by LHCb in the B + c → J/ψ π + mode [29] and has smaller systematic uncertainty.