Measurement of the ratio of branching fractions $\mathcal{B}(B_{c}^{+} \to J/\psi K^{+})/\mathcal{B}(B_{c}^{+} \to J/\psi\pi^{+})$

The ratio of branching fractions $R_{K/\pi} \equiv \mathcal{B}(B_{c}^{+} \to J/\psi K^{+})/\mathcal{B}(B_{c}^{+} \to J/\psi\pi^{+})$ is measured with $pp$ collision data collected by the LHCb experiment at centre-of-mass energies of 7 TeV and 8 TeV, corresponding to an integrated luminosity of 3${\mbox{fb}^{-1}}$. It is found to be $ R_{K/\pi} = 0.079\pm0.007\pm0.003$, where the first uncertainty is statistical and the second is systematic. This measurement is consistent with the previous LHCb result, while the uncertainties are significantly reduced.


Introduction
The B + c meson, the lightest bc bound state, can only decay weakly.Since it contains only heavy quarks, its decays can be analysed using various theoretical approaches, including QCD-based methods [1][2][3] and QCD-inspired phenomenological models [4,5].A measurement of the weak decay properties of B + c mesons can test these approaches and provide insight into the dynamics of the heavy quarks in the B + c meson.The exclusive decay 1 B + c → J/ψ K + is of particular interest since it proceeds via a b → cus transition and thus is CKM-suppressed by a factor |V us /V ud | 2 ∼ 0.05 with respect to B + c → J/ψ π + , where the dominant amplitude is a b → cud transition.In addition to the CKM matrix elements, the ratio of branching fractions R K/π ≡ B(B + c → J/ψ K + )/B(B + c → J/ψ π + ) depends on the form factors of the two decays.Theoretical calculations of R K/π have been carried out using approaches that handle the non-factorisable and non-perturbative contributions in different ways, yielding values in the range from 0.05 to 0.10 [1,[5][6][7][8][9][10][11][12][13][14][15].
The decay B + c → J/ψ K + was first observed by the LHCb collaboration, which reported a measurement of R K/π = 0.069 ± 0.019 ± 0.005 [16].The uncertainty on this value is too large to discriminate between the predictions quoted above.The pp data sample used in Ref. [16], taken at a centre-of-mass energy of 7 TeV and corresponding to an integrated luminosity of 1 fb −1 , is now reanalysed in this paper together with an additional sample taken at a centre-of-mass energy of 8 TeV and corresponding to an integrated luminosity of 2 fb −1 .Owing to improvements in the analysis method as well as the increase in the data sample size, the statistical uncertainty is reduced by a factor of more than two.The systematic uncertainty is also reduced.

Detector and simulation
The LHCb detector [17,18] 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, 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 charged particle momentum, p, 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 vertex (PV), the impact parameter, is measured with a resolution of (15 + 29/p T ) µm, where p T (in GeV/c) is the component of the momentum transverse to the beam direction.Different types of charged hadrons are distinguished using information from two ring-imaging 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 trigger comprises a hardware stage and a software stage.The hardware trigger employed in this analysis uses information from the muon system to select single muons

Signal yields and efficiency correction
The measurement is made by evaluating where N (B + c → J/ψ K + ) and N (B + c → J/ψ π + ) are the signal yields, and (B + c → J/ψ K + ) and (B + c → J/ψ π + ) are the total efficiencies estimated with simulation and control samples of data.
The signal yields N (B + c → J/ψ K + ) and N (B + c → J/ψ π + ) are obtained from a simultaneous unbinned maximum likelihood fit to the distribution of B + c candidate masses in the range 6000 to 6600 MeV/c 2 .These candidates include the part of the background training sample that passes the full selection; the effect of doing so has been investigated and found not to lead to any systematic bias.The fit model includes components due to signal, combinatorial background and misidentified decays (B + c → J/ψ π + misidentified as B + c → J/ψ K + , or vice versa).
A partially reconstructed background component is included for B + c → J/ψ π + .This background is mainly due to B + c → J/ψ ρ + decays followed by ρ + → π + π 0 .The data show no clear indication of partially reconstructed background for B + c → J/ψ K + .A systematic uncertainty is assigned due to the non-inclusion of this background component.
The signal mass distribution of B + c → J/ψ h + is described by the sum of two doublesided Crystal Ball (F DSCB ) functions consisting of a Gaussian core and power law tails on both sides, where M B + c is the invariant mass of the µ + µ − h + combination with the mass of the µ + µ − pair constrained to the known J/ψ mass.In the simultaneous fit, the Gaussian mean and the core mass resolution σ 1 of F DSCB 1 are allowed to vary, and set to be the same for both the B + c → J/ψ π + and the B + c → J/ψ K + decays.The tail parameters, the fraction α and Since the running conditions changed between 7 TeV and 8 TeV, the systematic uncertainties on R K/π are determined separately for the two samples.Table 1 summarises the relative systematic uncertainties associated with the mass fit and efficiency estimates that affect the ratio of branching fractions.The sources of these uncertainties are discussed below.
Each of the systematic uncertainties associated with the mass fit is studied by generating an ensemble of pseudoexperiments according to the nominal model described above and fitting them with an alternative model.The difference in the mean values of R K/π obtained is taken as the systematic uncertainty.
Changing the signal model from the sum of two DSCB functions to a single DSCB function leads to relative systematic uncertainties of 0.5% and 0.8% for the 7 TeV and 8 TeV data, respectively.Using a third-order polynomial in place of an exponential function for    the combinatorial background changes the mean values of R K/π by 1.1% and 0.5% for the two samples.
In the nominal fit, the partially reconstructed background is neglected for B + c → J/ψ K + decays for reasons of fit stability.The associated systematic uncertainties are estimated by including such a component in the same way as was done for B + c → J/ψ π + decays, and are found to be 3.3% and 3.2% for the 7 and 8 TeV data, respectively.Using the sum of two DSCB functions instead of a single DSCB function for the misidentification background events changes the mean values of R K/π by 0.2% and 0.0% for the two samples.
The selection and trigger efficiencies are calculated with simulated samples.Systematic effects on the efficiency evaluation due to differences between data and simulation in the distributions of variables such as muon momentum and B + c decay time are investigated.Such effects are found to cancel in the efficiency ratio and thus have negligible impact on R K/π .
The kaon and pion identification efficiencies are measured as functions of momentum and pseudorapidity with a control sample of D * + → D 0 π + , D 0 → K − π + decays, and represented by two-dimensional histograms.When the histogram binning is varied, the largest changes in the efficiency ratio seen are 0.2% and 0.1% for the 7 TeV and 8 TeV samples, and these values are assigned as the corresponding relative systematic uncertainties.
The simulation accounts for the different interaction cross-sections of pions and kaons with matter.However, if the amount of material in the detector is not modelled correctly, this would alter the efficiency ratio.A systematic uncertainty of 0.3% associated with this effect is assigned for both 7 TeV and 8 TeV samples.Adding all of the above contributions in quadrature, the total relative systematic uncertainties on R K/π are 3.5% and 3.4% for the 7 TeV and 8 TeV results.

Results and summary
Using the yield and efficiency ratios, the ratio of branching fractions of B + c → J/ψ K + and B + c → J/ψ π + is evaluated as R K/π = 0.089 ± 0.013 ± 0.003 for the 7 TeV data sample and R K/π = 0.075 ± 0.008 ± 0.003 for the 8 TeV sample, where the first uncertainties are statistical and the second are systematic.
The two results are combined by evaluating their weighted average.The systematic uncertainties of both measurements are dominated by the contribution from the noninclusion of the partially reconstructed background for B + c → J/ψ K + decays, and so are assumed to be fully correlated, while their statistical uncertainties are independent.The combined measurement for the 7 TeV and 8 TeV data sample is R K/π = 0.079 ± 0.007 ± 0.003 .This is consistent with the previous LHCb measurement R K/π = 0.069 ± 0.019 ± 0.005 [16], which was based on the 7 TeV data alone.The uncertainties are significantly reduced due to both the increased sample size and the improved event selection.The result supersedes the previous measurement [16] and agrees with the theoretical predictions in Refs.[1, 5-7, 10, 12-15], but disfavours that based on QCD sum rules [11].

Figure 1 :
Figure 1: Fits to the reconstructed B + c → J/ψ K + (left) and B + c → J/ψ π + (right) mass distributions using 7 TeV (top) and 8 TeV (bottom) data samples.The contributions from the signal, the misidentification background, the combinatorial background and the partially reconstructed background are indicated in the figures.

Table 1 :
Summary of the relative systematic uncertainties on R K/π .
Università di Milano Bicocca, Milano, Italy j Università di Roma Tor Vergata, Roma, Italy k Università di Roma La Sapienza, Roma, Italy l AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland m LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain n Hanoi University of Science, Hanoi, Viet Nam o Università di Padova, Padova, Italy p Università di Pisa, Pisa, Italy q Università degli Studi di Milano, Milano, Italy r Università di Urbino, Urbino, Italy s Università della Basilicata, Potenza, Italy t Scuola Normale Superiore, Pisa, Italy u Università di Modena e Reggio Emilia, Modena, Italy v Iligan Institute of Technology (IIT), Iligan, Philippines i