Determination of the branching fractions of BS0 → DS∓K∓ and B0 → DS−K+

Measurements are presented of the branching fractions of the decays BS0 → DS∓K∓ and B0 → DS−K+ relative to the decays BS0 → DS−π+ and B0 → D−π+, respectively. The data used correspond to an integrated luminosity of 3.0 fb−1 of proton-proton collisions. The ratios of branching fractions are ℬBs0→Ds∓K∓ℬBs0→Ds−π+=0.0752±0.0015±0.0019\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{\mathrm{\mathcal{B}}\left({B}_{\mathrm{s}}^0\to {D}_{\mathrm{s}}^{\mp }{K}^{\mp}\right)}{\mathrm{\mathcal{B}}\left({B}_{\mathrm{s}}^0\to {D}_{\mathrm{s}}^{-}{\pi}^{+}\right)}=0.0752\pm 0.0015\pm 0.0019 $$\end{document} and ℬB0→Ds−K+ℬB0→D−π+=0.0129±0.0005±0.0008,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{\mathrm{\mathcal{B}}\left({B}^0\to {D}_{\mathrm{s}}^{-}{K}^{+}\right)}{\mathrm{\mathcal{B}}\left({B}^0\to {D}^{-}{\pi}^{+}\right)}=0.0129\pm 0.0005\pm 0.0008, $$\end{document} where the uncertainties are statistical and systematic, respectively.


Introduction
This paper presents the measurements of the branching fractions of the decays B 0 s → D ∓ s K ± and B 0 → D − s K + , relative to those of the decays B 0 s → D − s π + and B 0 → D − π + , respectively. The B 0 s → D ∓ s K ± system is of interest as it offers a prime opportunity to measure CP violation in the interference between mixing and decay [1,2]. The B 0 s meson can decay into both charge-conjugate decays, providing sensitivity to the CKM angle γ The CDF and Belle collaborations have pioneered the study of this ratio [6,7], followed by the LHCb collaboration, which measured a ratio about 1.8 standard deviations below the theoretical bound [8], using data corresponding to an integrated luminosity of 336 pb −1 .
The decay B 0 → D − s K + proceeds through the colour-suppressed W -exchange diagram and the branching fraction determination allows the size of the W -exchange amplitude to be estimated, for example in the B 0 s → D ∓ s K ± decay, as used e.g. in ref. [4]. The existing branching fraction measurements by BaBar and Belle, B(B 0 → D − s K + ) = (2.9 ± 0.4 (stat) ± 0.2 (syst)) × 10 −5 [9] and (1.91 ± 0.24 (stat) ± 0.17 (syst)) × 10 −5 [10], respectively, show a difference of about 1.8 standard deviations, and suggest that an enhancement of the branching fraction due to rescattering effects is small [11]. Note that throughout this paper, charge conjugation is implied, and thus that the branching fraction B(B 0 (s) ) corresponds to the average of the branching fraction of the B 0 (s) decay and the B 0 (s) decay. The pp-collision data used in this analysis correspond to an integrated luminosity of 3.0 fb −1 , of which 1.0 fb −1 was collected by LHCb in 2011 at a centre-of-mass energy of √ s = 7 TeV, and the remaining 2.0 fb −1 in 2012 at √ s = 8 TeV. 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 of the magnet. The polarity of the magnet is reversed periodically throughout data-taking. The tracking system provides a measurement of momentum, p, with a relative uncertainty that varies from 0.4% at low momentum to 0.6% at 100 GeV/c. The minimum distance of a track to a primary vertex, the impact parameter, is measured with a resolution of (15 + 29/p T ) µm, where p T is the component of p transverse to the beam, in GeV/c. Different types of charged hadrons are distinguished using information from two ring-imaging detectors.
The trigger 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. The software trigger requires a two-, three-or four-track secondary vertex with a significant displacement from the primary pp interaction vertices (PVs). At least one charged particle must have a transverse momentum p T > 1.7 GeV/c and be inconsistent with originating from the PV. A multivariate algorithm [13] is used for the identification of secondary vertices consistent with the decay of a b hadron.
In  Table 1. Kinematic and PID selection efficiencies for each signal decay, as determined from simulated events and data, respectively. "PID" refers to the selection efficiencies of the PID requirements only, while "Kinematic" refers to the remaining event selection. The kinematic efficiencies represent weighted averages determined from events simulated at √ s = 7 TeV (34%) and √ s = 8 TeV (66%). The binomial uncertainties result from the size of the simulated samples.
LHCb configuration [16]. Decays of hadronic particles are described by EvtGen [17]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [18, 19] as described in ref. [20].

Event selection
Candidate B 0 (s) mesons are reconstructed by combining a D ± (s) candidate decaying into three light hadrons, with an additional pion or kaon (the "bachelor" particle). Each of the four final-state light hadrons is required to have a good track quality, high momentum and transverse momentum, and a large impact parameter with respect to the primary vertex. The contribution from charmless B 0 (s) decays, such as B 0 s → K + K − π + π − , is suppressed by requiring the D ± (s) candidate to have a significant flight distance from the reconstructed B 0 (s) decay vertex, and by requiring its mass to fall within a small mass window of +22 −24 MeV/c 2 around the D ± (s) mass [21]. To reduce the combinatorial background, a multivariate algorithm is applied. This boosted decision tree (BDT) [22,23] is identical to that used in the analysis of the CP asymmetry in B 0 s → D ∓ s K ± decays [3], and was trained with B 0 s → D − s π + candidates from data, using a weighted data sample based on the sPlot technique [24] as signal and candidates with an invariant mass greater than 5445 MeV/c 2 as background. The variables with the highest discriminating power are found to be the difference between the χ 2 from the vertex fit of the associated PV reconstructed with and without the considered b-hadron candidate, the p T of the final-state particles, and the angle between the b-hadron momentum vector and the vector connecting its production and decay vertices.
Misidentification of particles leads to peaking backgrounds in the signal region, for example B 0 s → D − s π + events reconstructed as B 0 s → D ∓ s K ± candidates. Pions and kaons in these decays are required to satisfy particle identification (PID) requirements, and approximately 60% of the signal is retained while over 99% of the background is rejected. The efficiencies of these requirements are determined by studying kinematically selected D * + → D 0 (→ K − π + )π + and Λ → pπ − decays obtained from data, which provide high-purity PID.
In the B 0 → D − π + selection, loose PID requirements are applied since the branching fraction of the signal process is much larger than those of background decays resulting -3 -JHEP05(2015)019 from misidentification. In the B 0 s → D − s π + and B 0 s → D ∓ s K ± selections, a stricter PID requirement is applied to the D + s decay products, to distinguish D + s and D + mesons. For these decays, a further selection requirement is applied to reduce the background from Λ 0 b → Λ + c π − decays, where one of the D + s daughters is a misidentified proton. This requirement removes any candidate which fulfils two criteria: that there is a large probability for one of the D + s daughters to be a misidentified proton, and that when the D + s decay is reconstructed under the Λ + c hypothesis, its invariant mass falls within 21 MeV/c 2 of the nominal Λ + c mass [21]. This procedure almost fully eliminates this background. The efficiency of the selection is obtained from simulation and is summarised in table 1.

Signal yield determination
An unbinned maximum likelihood fit to the candidate invariant mass distribution is performed for each of the three final states, D − π + , D − s π + , and D ∓ s K ± . The signal shapes are parametrised by a double-sided Crystal Ball shape [25]. This function consists of a central Gaussian part, whose mean and width are free parameters, and power-law tails on both lower and upper sides, to account for energy loss due to final-state radiation and detector resolution effects. The functional form for the combinatorial background, an exponential function with an offset, is obtained from same-charge D ± s π ± combinations in data. All parameters of the combinatorial background are left free in the fit to data.
The physical backgrounds can be split into two categories: misidentified backgrounds, predominantly where one of the final state pions (kaons) is mistaken for a kaon (pion); and partially reconstructed backgrounds, where a neutral pion or a photon is not included in the candidate reconstruction, causing the reconstructed B 0 (s) mass to shift to lower values. Some backgrounds fall into both categories. The number of background components considered varies per final state; the list of background components for each final state can be found in the legend of figures 2 and 3. The invariant mass shapes of these backgrounds are obtained from simulation at √ s = 8 TeV, with the event selection applied. The yield of each background is a parameter in the fit, with most background components Gaussianconstrained around the expected yield normalised to the B 0 → D − π + yield obtained from data. The constraints are assigned an uncertainty of 10%, which reflects the uncertainties from production fractions, branching fractions, and reconstruction efficiencies. The resulting background yields from the fit deviate typically around one standard deviation from the expected values. The results of the fits for the three final states are shown in figures 2 and 3, and in table 2. The three fits are independent, and no parameters are shared among them.
Various consistency checks are performed for each of the fits. The fitted yield of B 0 s → D − s π + events reconstructed in the D ∓ s K ± final state, which is allowed to vary in the fit, is consistent with the expected yield based on the relative branching fraction, particle misidentification probability and reconstruction efficiency. For each of the fits, consistency is also found between the fitted yield for both magnet polarities separately and the fraction of data corresponding to that polarity. This demonstrates that the relative yields are stable as a function of time and magnet polarity. Yield

Systematic uncertainties
Systematic uncertainties arise from the fit model and the candidate selection, and are summarised in table 3. The systematic uncertainty from the fit model is determined by applying variations to the fit model and comparing the yield to the nominal result, taking the difference as a systematic uncertainty. These variations include a different combinatorial shape, fixing the signal shape tail parameters to values obtained from simulation, and using background shapes determined from simulation matching the LHCb conditions during 2011 ( √ s = 7 TeV). In the D − π + analysis, the fit range is reduced to start at 5100 MeV/c 2 . In the D ∓ s K ± analysis, the as yet unobserved decay Λ 0 b → D − s p is omitted from the fit. The uncertainty on the candidate selection is separated into three parts: the uncertainty due to the kinematic selection, that due to the PID requirements on the final state pions and kaons, and that due to the hardware trigger efficiency. The first of these uncertainties is determined from the selection efficiency difference between magnet polarities in simulation, and by estimating the uncertainty on the BDT selection efficiency due to differences between data and simulation. This is calculated by reweighting simulated events to match the data more closely, and calculating the difference in BDT efficiency between those and the unweighted samples. The uncertainty on the PID efficiency and misidentification rate is estimated by comparing the PID performance measured using a simulated D * calibration sample with that observed in simulated signal events. The systematic uncertainty from the hardware trigger efficiency arises from measured differences between the pion and kaon trigger efficiencies which are not reproduced in the simulation. The uncertainty is scaled with the fraction of events where a pion or a kaon from the reconstructed decay was responsible for triggering.  Table 3. Systematic uncertainties on the ratios of branching fractions, in %, obtained as described in the text. The total uncertainty is obtained by adding the separate contributions in quadrature.
A further systematic uncertainty is added to account for possible charmless B 0 decays peaking under the B 0 → D − s K + signal. Some of the uncertainties cancel in the ratios of branching fractions, leading to lower overall systematic uncertainties than those determined individually for each decay channel. The total systematic uncertainty for each ratio of branching fractions is the quadratic sum of the individual systematic uncertainties.

Determination of branching fractions
The ratios of branching fractions are evaluated using the expression where ε X , f X and N X are the selection efficiency, the hadronisation fraction, and the fitted yield of decay X, respectively, and B D ± (s) is the branching fraction of D ± (s) decays, as appropriate. The following values are used as input [21]: As a cross-check, a value B(B 0 s → D − s π + ) = (2.95 ± 0.01 (stat)) × 10 −3 was obtained from the measured B 0 s → D − s π + and B 0 → D − π + yields using eq. (5.1). This measurement is compatible with the world-average value, and the central value is unchanged with respect to the previous result published by LHCb [8].
The branching fractions of B 0 s → D ∓ s K ± and B 0 → D − s K + presented here are more precise than the current world-average values. The result for is compatible with theoretical expectations [4] and with the previous result from LHCb. As expected [5], the branching fraction of the decay B 0 → D − s K + , dominated by the W -exchange topology, is suppressed compared to the decay B 0 → D − π + , which predominantly proceeds through the colour-allowed tree topology. The measured value of B(B 0 → D − s K + ) is in good agreement with existing measurements from the BaBar collaboration [9], and is larger than the result published by the Belle collaboration [10] with a significance of more than three standard deviations.

Acknowledgments
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.