Search for $B_c^+$ decays to two charm mesons

A search for decays of $B_c^+$ mesons to two charm mesons is performed for the first time using data corresponding to an integrated luminosity of 3.0 fb$^{-1}$, collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV. The decays considered are $B_c^+\to D^{(*)+}_{(s)} \overline{D}^{(*)0}$ and $B_c^+\to D^{(*)+}_{(s)} D^{(*)0}$, which are normalised to high-yield $B^+\to D^+_{(s)} \overline{D}^0$ decays. No evidence for a signal is found and limits are set on twelve $B_c^+$ decay modes.


Introduction
Flavour transitions between quarks are governed in the Standard Model (SM) of elementary particle physics by the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1,2].Here the transition amplitudes between up-type quarks, q, and down-type quarks, q , are described by the complex numbers V qq , defining the 3 × 3 unitary CKM matrix.Precision measurements of the magnitude and phase of the CKM matrix elements may reveal signs of new physics if observables that could be affected by new particles are found to be inconsistent with SM predictions.
One parameter of particular interest is γ ≡ arg(−V ud V * ub /V cd V * cb ), which can be determined experimentally with negligible theoretical uncertainties from the charge-parity (CP ) asymmetry caused by the interference between b → u and b → c transitions.Presently, the most precise determinations of γ come from measurements of the CP asymmetry in B + → ( ) D 0 K + decays.[3,4].D * 0 , angular distributions provide an alternative method to determine γ [7].Some predicted branching fractions are listed in Table 1.
In the determination of γ, an advantage of D 0 decays over B + → ( ) D 0 K + decays is that the diagram proportional to V cb is colour suppressed, while the diagram proportional to V ub is not, as illustrated in Fig. 1.This results in a large value for the ratio of amplitudes, r decay channels, using data collected by the LHCb experiment and corresponding to an integrated luminosity of 3.0 fb −1 , of which 1.0 fb −1 was recorded at a centre-of-mass energy √ s = 7 TeV and 2.0 fb −1 at √ s = 8 TeV.Charm mesons are reconstructed in the D 0 → K − π + , D 0 → K − π + π − π + , D + → K − π + π + , and D + s → K + K − π + decay modes.For B + c decays that involve one or more excited charm mesons, no attempt is made to reconstruct the low-momentum particles from the decay of excited charm mesons: the distribution of the invariant mass of the partially reconstructed final-state peaks at masses just below the B + c mass.The branching fractions, B, of B + c decays to fully reconstructed states are measured relative to high-yield where f c /f u is the ratio of B + c to B + production cross-sections, N stands for the signal yields, and ε for the total efficiencies.For B + c decays with one excited charm meson, the invariant-mass distributions of D * 0 decays are very similar, and the sum of their branching fractions is measured, weighted by the branching fraction of the excited charged charm meson to a charged charm meson and a low-momentum neutral particle, where TeV [13] and √ s = 8 TeV [14] in the LHCb acceptance.Predictions for B(B + c → J/ψ π + ) range from 6.0 × 10 −4 to 2.9 × 10 −3 [15][16][17], implying a value of f c /f u in the range 0.24%-1.2%.Since B(B + c → J/ψ π + ) is presently not measured, the results in this paper are expressed as the product of f c /f u and the ratio of B + c to B + branching fractions.

Detector and simulation
The LHCb detector [18,19] 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 siliconstrip vertex detector surrounding the pp interaction region [20], 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 [21] placed downstream of the magnet.The polarity of the dipole magnet is reversed periodically throughout data-taking.
The tracking system provides a measurement of the momentum of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV/c.The minimum distance of a track to a primary pp interaction vertex (PV), the impact parameter (IP), is measured with a resolution of (15 + 29/p T ) µm, where p T is the momentum transverse to the beamline expressed in GeV/c.Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors [22].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 [23].
The online event selection is performed by a trigger [24], 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 muon with high p T or a hadron, photon or electron with high transverse energy in the calorimeters.For hadrons, the transverse energy threshold is about 3.5 GeV.The software trigger requires a two-, three-or four-track secondary vertex with a large sum of the transverse momentum of the tracks and a significant displacement from any PV.At least one track should have p T > 1.7 GeV/c and χ 2 IP with respect to any PV greater than 16, where χ 2 IP is defined as the difference in the vertex-fit χ 2 of a given PV reconstructed with and without the considered particle.A multivariate algorithm [25] is used for the identification of secondary vertices consistent with the decay of a b hadron.
Simulated events are used for the training of the multivariate selection of the B + c signals, for establishing the shape of the invariant-mass distributions of the signals, and for determining the relative efficiency between the B + c signal decays and the B + normalisation modes.In the simulation, pp collisions with B + → D + (s) D 0 decays are generated using Pythia [26] with a specific LHCb configuration [27].For B + c → D + (s) D 0 decays, the Bcvegpy [28] generator is used.The simulated B + c → D + (s) D 0 sample is also used for training and efficiency calculations of the B + c → D + (s) D 0 decay mode.Decays of hadronic particles are described by EvtGen [29], with final-state radiation generated using Photos [30].The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [31] as described in Ref. [32].Known discrepancies in the simulation are corrected using data-driven methods.

Candidate selection
Initially, loose requirements are made to select candidates having both a D + (s) and a D 0 or D 0 meson.The charm-meson candidates are constructed by combining two, three or four tracks that are incompatible with originating from any reconstructed PV.In addition, the tracks must form a high-quality vertex and the scalar sum of their transverse momenta must exceed 1.8 GeV/c.The pion and kaon candidates are also required to satisfy loose particle identification (PID) criteria to reduce the contribution to the selected sample from misidentified particles.Charm-meson candidates must have an invariant mass within ±25 MeV/c 2 of their known value [33].Using the same method as in Ref. [34], threetrack combinations that are compatible with both IP .The reconstructed decay time divided by its uncertainty, t/σ t , of D 0 and D + s mesons with respect to the B + (c) vertex is required to exceed −3, while that of the longer-lived D + meson is required to exceed +3.The tighter decay-time significance criterion on the D + eliminates background from B + → D 0 π + π − π + decays where the negatively charged pion is misidentified as a kaon.
The invariant-mass resolution of B + (c) decays is significantly improved by applying a kinematic fit [35] where the masses of the D 0 and the D + (s) candidates are fixed to their known values [33], all particles from the D + (s) , D 0 , or B + (c) decay are constrained to originate from their decay vertex and the B + (c) is constrained to originate from a PV.To reduce the combinatorial background, while keeping the efficiency for signal as high as possible, a multivariate selection based on a boosted decision tree (BDT) [36,37] is employed.The following variables are used as input for the BDT: the transverse momentum and the ratio of the likelihood between the kaon and pion PID hypotheses of all final-state particles; the fit quality of the B + (c) and both charm-meson vertices; the value of χ  The BDT combines all input variables into a single discriminant.The optimal value of the cut on this discriminant is determined using a procedure based on Ref. [38], maximising ε/( √ N B + 5/2), where N B is the expected background in a ±20 MeV/c 2 window around the B + c mass, and the number 5 is the target significance.Simulated events are used to estimate the signal efficiency ε.
The peak values of both CB components are constrained to be equal and the other shape parameters of the CB functions are obtained from a fit to the simulated events.The peak position of the B + signal is a free parameter in the fit to data, while the peak position of the B + c signal is fixed to the world-average measurement [33].The large B + → D + s D 0 signal from data is well described by this model.Models for decays where one or two low-momentum particles from excited charmmeson decays are missing are implemented as templates, obtained from invariant-mass distributions of simulated data.For decays with one missing low-momentum particle, both D * 0 decays contribute and the template is based on the sum of the two decay modes, weighted by the appropriate branching fractions of the excited charm mesons.For D * 0 decays, it is assumed that both excited charm mesons are produced unpolarised.
The Cabibbo-favoured B + → D 0 K + K − π + decay is a background to the B + → D + s D 0 channel, though its yield is strongly reduced by the charm-meson mass requirement.This background is modelled by a single Gaussian function, with the width determined from a sample of simulated decays and the normalisation determined from the sidebands of the D + s mass peak.The yield of this background is about 40 times smaller than that of the signal, and the shape of the invariant-mass distribution is twice as wide.The combinatorial background is described by the sum of an exponential function and a constant.
An unbinned extended maximum likelihood fit is used to simultaneously describe the invariant-mass distributions of candidates with D 0 0.420 ± 0.005 0.373 ± 0.009 0.441 ± 0.007 0.398 ± 0.010 D * 0 0.372 ± 0.006 0.317 ± 0.010 0.381 ± 0.008 0.337 ± 0.011 D * 0 0.339 ± 0.006 0.278 ± 0.009 0.342 ± 0.007 0.297 ± 0.010 decays, resulting in four independent fits to eight invariant mass distributions.In these fits the background parameters and B + yields are free to vary independently, but the ratio of the B + c yields for the two D 0 decay modes is constrained to the corresponding ratio of B + yields, corrected for the relative efficiencies.The total B + c yield, N tot , is a free parameter in these fits, leading to a B + c yield in each data sample given by the expressions The relative efficiencies that appear in these expressions, calculated for simulated events generated in the rapidity range 2.0 < y(B + (c) ) < 4.5 and with p T (B + (c) ) > 4 GeV/c, are summarised in Table 2.
The results of the fits are shown in Fig. 2, and the corresponding signal yields are listed in Table 3.The small peaks at the B + mass in the D + (s) D 0 final state are due to B + → D + (s) D 0 decays either followed by the doubly Cabibbo-suppressed D 0 → K + π − decay or when both the kaon and pion are misidentified.No significant B + c signals are observed; after taking into account systematic uncertainties, discussed in Sec. 5, none of the signals exceeds a significance of two standard deviations, which is measured as the difference in likelihood when fitting the data with or without signal component in the fit [40].

Systematic uncertainties
The systematic uncertainties on the B + c yields are listed in Table 4 and described below.The signal shape parameters for the fully reconstructed modes are varied according to Gaussian distributions that take into account the covariance matrix of the fit to the simulated events, and evaluating the change in yield and its uncertainty for 1000 variations.An additional uncertainty is attributed to the signal model by changing its description from a sum of two CB functions to a sum of two Gaussian functions.The assumed peak position of the D 0 signal may differ from the true value.
This is taken into account by varying the B + c peak position by its uncertainty, taken as the squared sum of uncertainty on the world-average B + c mass (0.8 MeV/c 2 ) and the contribution from the LHCb momentum-scale uncertainty (0.8 MeV/c 2 ) [41].The signal shape of the decays with one missing low-momentum particle is based on the assumption ).Since the B + c branching fractions are unknown, the signal composition is varied using D * 0 only and the largest difference is taken as the systematic uncertainty.As the polarisation of excited charm mesons in D * 0 decays is unknown, the signal shapes are varied between fully longitudinal and fully transverse polarisations, and the largest yield difference with the unpolarised decay model is taken as the uncertainty.To evaluate the uncertainty in the choice of the shape of the combinatorial background, an alternative fit is applied using an exponential function to model the background.To evaluate eventual biases of the B + c yields in the fit, pseudoexperiments are generated where the candidates in the signal window are replaced by the expected distribution using only background.The yields are corrected for this bias and the attributed uncertainty is the squared sum of the bias and its statistical uncertainty.
Systematic uncertainties that affect the normalisation are listed in Table 5 and are described below.The limited size of the simulated signal samples affects the normalisation as well as the statistical uncertainties of the B + yields.The systematic uncertainties of the B + yields are evaluated by varying the signal shape according to the covariance matrix of the fit to simulated data and by changing the signal model to the sum of two Gaussian functions.The B + yield is also affected by uncertainties on the background, which are evaluated by changing the background shape to an exponential function and by varying the single-charm background by 100% of its yield.The impact on the efficiency ratio of the uncertainty on the B + c lifetime is evaluated by changing its lifetime by one standard deviation.Imperfections in the rescaling of the PID variables [22] are quantified by considering the efficiency ratio with and without PID corrections and assigning the difference as a systematic uncertainty.The D 0 → K − π + π − π + decay has a complicated substructure, but was simulated according to a phase-space model.The systematic uncertainty is taken as the quadratic sum of the differences in efficiency ratio when the simulated events are weighted to reproduce the π + π − , K − π + , K − π + π − and π + π − π + invariant-mass distributions observed in data.The difference in efficiency when applying the model variations for B + c decays with one or two excited charm mesons in the final state is Table 4: Systematic uncertainties on the B + c yields, for the combined fit to both the D 0 → K − π + and the D 0 → K − π + π − π + decay channels.The total systematic uncertainty is calculated as the quadratic sum of the individual components.taken into account as a systematic uncertainty.The determinations of the B + c → D * + ( ) D * 0 branching fraction ratios are corrected for B(D * + → D + π 0 , γ) = (32.3± 0.5)% [33], as is indicated in Eq. 3, and the corresponding uncertainty is assigned as a systematic uncertainty.

Results and conclusion
To determine the branching fraction ratios, fits to data are performed where the free parameters are not the individual yields, but correspond to the left-hand-side terms of Eqs.1-3.In these fits, the systematic uncertainties are taken into account as Gaussian constraints.
The measured branching fraction ratios for the fully reconstructed B + c decays are listed below.Quoted in brackets are the corresponding upper limits calculated at 90% (95%) 1.5 Total 3.9 4.4 4.9 6.9 confidence level with the asymptotic CL s method [42], For B + c decays with one excited charm meson, the results are For B + c decays with two excited charm mesons, the measurements give The presented limits are consistent with the theoretical expectations: assuming a value of f c /f u = 1.2%, the branching fraction ratio limits give B(B + c → D + D 0 ) < 6.0 (7.0)×10 −4 at 90% (95%) confidence level, well above the values shown in Table 1.[
and as a D + candidate otherwise.The two charm mesons are combined into a B + (c) candidate, which is retained if its invariant mass is in the range 4.8 − 7.0 GeV/c 2 .The D + (s) ( ) D 0 pair must form a good-quality vertex with transverse momentum exceeding 4.0 GeV/c.The resulting trajectory of the B + (c) candidate must be consistent with originating from the associated PV, where the associated PV is the PV with which the B + (c) candidate has the smallest χ 2

Four
distinct classifiers are constructed: the BDT training is performed separately for the D + s ( ) D 0 and D + ( ) D 0 final states and for the D 0 → K − π + and D 0 → K − π + π − π + decay channels.For a given D 0 final state, the same classifier is used for both B + c → D + (s) D 0 and B + c → D + (s) D 0 decays.For signal, the BDT is trained using simulated B + c events, while for background data in the range 5350 < m(D + (s) ( ) D 0 ) < 6200 MeV/c 2 are used.Studies indicate that the combinatorial background is dominated by non-charm and single-charm candidates, while combinations of two real charm mesons contribute less than 5%.To increase the size of the background sample for the BDT training, the charm mass windows are increased from ±25 MeV/c 2 to ±75 MeV/c 2 .

4
Data fit After the selection, a model of the invariant-mass distribution of B + (c) → D + (s) ( ) D 0 candidates is fitted to the data.The model is composed of six components: the signals for fully reconstructed B + and B + c decays; the signal for B + c decays with one excited charm meson in the final state; the signal for B + c decays with two excited charm mesons in the final state; the background from B + → D 0 K + K − π + decays; and the combinatorial background.Fully reconstructed B + and B + c signals are described by the sum of two Crystal Ball (CB) [39] functions, with power-law tails proportional to [m(D + (s) ( )

Figure 2 :
Figure 2: Fits to the (top row) D + s D 0 , (second row) D + s D 0 , (third row) D + D 0 and (bottom row) D + D 0 final states.For the left plots, the D 0 meson is reconstructed in the K − π + final state, while the right column corresponds to the D 0 → K − π + π − π + mode.

Table 2 :
Ratio ε B + c /ε B + of total efficiencies of B +c decays relative to the corresponding fully reconstructed B + decays.The quoted uncertainties are statistical only.

Table 3 :
Signal yields from the fits of B → D + D 0 decays.Samples with D 0 → K − π + and D 0 → K − π + π − π + are fitted simultaneously.The uncertainties are statistical only.

Table 5 :
Systematic uncertainties, in %, on the normalisation of the B + c branching fraction determination.The total systematic uncertainty is calculated as the quadratic sum of the individual components.