Measurement of the B0 s → D D branching fractions

Measurement of the B

⁰_s

→ D

^ðÞþs

D

^ðÞ−s

branching fractions

R. Aaijet al.^* (LHCb Collaboration)

(Received 25 February 2016; published 20 May 2016)

The branching fraction of the decayB⁰s→D^ðÞþs D^ðÞ−s is measured usingppcollision data correspond- ing to an integrated luminosity of1.0fb⁻¹, collected using the LHCb detector at a center-of-mass energy of 7 TeV. It is found to beBðB⁰s →D^ðÞþs D^ðÞ−s Þ ¼ ð3.050.100.200.34Þ%, where the uncertainties are statistical, systematic, and due to the normalization channel, respectively. The branching fractions of the individual decays corresponding to the presence of one or two Ds are also measured. The individual branching fractions are found to be BðB⁰s →Ds D^∓sÞ ¼ ð1.350.060.090.15Þ%, BðB⁰s →D^þs D⁻s Þ ¼ ð1.270.080.100.14Þ%. All three results are the most precise determinations to date.

DOI:10.1103/PhysRevD.93.092008

I. INTRODUCTION

Because of B⁰s−B¯⁰s oscillations, the mass and flavor eigenstates of the B⁰_s system do not coincide. The B⁰_s meson mass eigenstates have a relative decay width difference ΔΓ_s=Γ_s, where ΔΓ_s (Γ_s) is the difference (average) of the decay widths between the heavy and light states. The relative decay width difference is one of the key parameters of the B⁰_s system, and its precise determination allows stringent tests of the flavor sector of the standard model.

Under certain theoretical assumptions,B⁰_s→D^ðÞþs D^ðÞ−s

decays were thought to saturate theCP-even contribution to ΔΓ_s, and therefore the branching fraction of B⁰_s→ D^ðÞþs D^ðÞ−s was used as a means of approximatingΔΓ_s=Γ_s [1]. This approximation is now considered to be a poor one [2], as the decay modes containing at least oneDs have a non-negligible CP-odd component, and other three-body B⁰_s decays can contribute to the value ofΔΓ_s at a similar level asB⁰_s→D^ðÞþs D^ðÞ−s decays. A detailed discussion of theoretical predictions of the B⁰s →D^ðÞþs D^ðÞ−s branching fractions, and the predicted contribution of other modes to the value of ΔΓ_s=Γ_s, is given in Ref. [3].

In a more general context, since the branching fraction of B⁰_s →D^ðÞþs D^ðÞ−s decays is one of the dominant contribu- tions to the total inclusiveb→c¯csbranching fraction, its precise measurement is an important ingredient in model- independent searches for physics beyond the standard model in B meson decays [4]. The most recent

measurements are provided by the Belle [5], CDF [6], and D0[7] collaborations who obtain, respectively,

BðB⁰s→D^ðÞþs D^ðÞ−s Þ ¼ ð4.32^þ0.42þ1.04₋₀.39−1.03Þ%;

BðB⁰_s→D^ðÞþs D^ðÞ−s Þ ¼ ð3.380.250.300.56Þ%;

BðB⁰s→D^ðÞþs D^ðÞ−s Þ ¼ ð3.51.01.1Þ%:

The data used in the analysis presented in this paper correspond to an integrated luminosity of 1.0fb⁻¹, col- lected by the LHCb experiment during the 2011 run period.

The branching fraction of the fullB⁰s →D^ðÞþs D^ðÞ−s decay is determined relative to theB⁰→D^þsD⁻decay, which has a similar final state and a precisely measured branching fraction. The charm daughters are reconstructed using the D^þs →K^þK⁻π^þ and D⁻ →K^þπ⁻π⁻ final states.

Throughout the paper, unless stated otherwise, charge- conjugate modes are implied and summed over. The branching fraction ratio is determined as

BðB⁰s→D^ðÞþs D^ðÞ−s Þ BðB⁰→D^þsD⁻Þ ¼fd

fs

·ϵ^B0

ϵ^B0s·BðD⁻→K^þπ⁻π⁻Þ BðD^þ_s →K⁻K^þπ^þÞ·N_B⁰_s

NB⁰

; ð1Þ

wheref_d(f_s) is the fraction ofB¯⁰(B¯⁰_s ) mesons produced in the fragmentation of ab quark,ϵ^B0=ϵ^B0s is the relative efficiency of theB⁰to theB⁰_sselections,BðD⁻→K^þπ⁻π⁻Þ andBðD^þs →K⁻K^þπ^þÞare the branching fractions of the charm daughter decays, andN_B⁰_s=N_B⁰is the relative yield of B⁰_s andB⁰ candidates.

The branching fraction of the exclusive B⁰_s →D^þ_s D⁻_s decay is determined in the same way, along with the branching fraction of B⁰s →Ds D^∓s. The branching frac- tion of theB⁰s→D^þsD⁻s decay has been previously mea- sured by LHCb using the same data as this analysis[8], and

*Full author list given at the end of the article.

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri- bution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

is therefore not determined in this study. However, the selection efficiency and yield in theB⁰s→D^þsD⁻s channel are determined in this analysis, as both are needed for the calculation of the total B⁰s →D^ðÞþs D^ðÞ−s selection efficiency.

II. DETECTOR AND SIMULATION

The LHCb detector [9,10] 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 theppinteraction 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 momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at200GeV=c. The minimum distance of a track to a primary vertex, the impact parameter, is measured with a resolution of ð15þ29=pTÞμm, where pT is the compo- nent of the momentum transverse to the beam, in GeV=c. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors.

Photons, electrons and hadrons are identified by a calo- rimeter system consisting of scintillating-pad and pre- shower 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 event selection is performed in two stages, with an initial online selection followed by a tighter offline selection. The online event selection is performed by a trigger[11], which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which performs a full event reconstruction.

In the simulation, pp collisions are generated using PYTHIA 6 [12] with a specific LHCb configuration [13].

Decays of hadronic particles are described by EVTGEN

[14], in which final-state radiation is generated using PHOTOS [15]. The interaction of the generated particles with the detector, and its response, are implemented using the GEANT4 toolkit [16]as described in Ref. [17].

III. SIGNAL SELECTION

The D^þs meson decays to a D^þs meson and either a photon or a neutral pionð93.50.7Þ%andð5.80.7Þ%

of the time, respectively, nearly saturating the total branch- ing fraction. The remainder of the decays are ignored in this analysis. Neither of the neutral particles is recon- structed in the decay chain, and the individual B⁰s→ Ds D^∓s andB⁰s →D^þs D⁻s decays are identified through the reconstructed invariant mass of theD^þ_sD⁻_s system. The

individual peaks from B⁰s →Ds ð→DsγÞD^∓s and B⁰s → Ds ð→Dsπ⁰ÞD^∓s are not resolved. Therefore the recon- structedD^þ_sD⁻_s mass distribution has three separate peaks, corresponding to decays containing zero, one, or twoD_s particles.

At the hardware trigger stage, events are required to have a muon with highpTor a hadron, photon or electron with high transverse energy in the calorimeters. For hadrons, the transverse energy threshold is 3.5 GeV. CandidateB⁰s and B⁰ mesons are used in the analysis if at least one of the associated tracks is selected by the hardware trigger, or if the event is triggered independently of the particles in the signal decay. The software trigger considers all charged particles withpT>500MeV=cand constructs two-, three-, or four-track secondary vertices which require a significant displacement from the primaryppinteraction vertices. At least one charged particle must have a transverse momen- tumpT>1.7GeV=cand be inconsistent with originating from a primary vertex. A multivariate algorithm [18] is used for the identification of secondary vertices consistent with the decay of abhadron. The selection to this point is hereafter referred to as the initial selection.

SignalB⁰sand normalizationB⁰→D^þsD⁻candidates are required to satisfy a number of additional conditions in order to be included in the final samples. Kaons and pions are required to be identified by the particle identification (PID) system. All D^þ_s and D⁻ candidates must have an invariant mass within 30MeV=c² of their known values [19]. Signal B⁰s candidates are required to have a reconstructed mass in the range 4750–5800MeV=c², whereas B⁰ candidates must have a mass in the range 5050–5500MeV=c². After these requirements are applied there are still contributions from other b -hadron decays into final states with two charm particles. The decays Λ⁰_b→Λ^þcð→pK⁻π^þÞD⁻s, where thepis misidentified as a K^þ, and B⁰→D^þsD⁻ð→K^þπ⁻π⁻Þ, where a π⁻ is mis- identified as aK⁻, result in background contamination in the signal channel, while the decayB⁰s →D^þsD⁻s contrib- utes to the background in the normalization channel if the K^þ inD^þ_s →K^þK⁻π^þ is misidentified as aπ^þ. As these backgrounds accumulate in reconstructed mass close to the signal peaks, candidates consistent with any one of these background decay hypotheses are rejected in the selection by applying a veto based on the invariant mass of the candidate under the alternative particle type hypotheses.

Candidate D^þ_s mesons are vetoed if they have a reconstructed mass in the range 2271–2301MeV=c² when the K^þ candidate is assumed to be a proton, or a mass in the range 1835–1905MeV=c² when the K^þ candidate is assigned theπ^þ mass. CandidateD⁻ mesons are vetoed if they have a reconstructed mass in the range 1950–1990MeV=c² when aπ⁻ candidate is assigned the kaon mass. In a simulated sample ofB⁰→D^þ_sD⁻ decays, 17.7% of the events meet all of the B⁰_s →D^ðÞþs D^ðÞ−s

R. AAIJet al. PHYSICAL REVIEW D 092008 (2016)

selection criteria before the D veto is applied. After the veto, only 0.05% of the simulatedB⁰→D^þsD⁻sample still pass the full B⁰s →D^ðÞþs D^ðÞ−s selection. The decayB⁰→ D^þsD⁻s and three-bodyB →D^þ_ðsÞD⁻_ðsÞh decays, whereh is either a kaon or pion, are examined as other potential background sources, but are all disregarded because of either a small selection efficiency or small branching fraction relative to the signal channels.

In order to further improve the purity of the signal and normalization samples, a boosted decision tree (BDT) classifier is used to distinguish real B⁰_ðsÞ decays from combinatorial background[20]. The BDT is trained using the AdaBoost algorithm [21] to distinguish simulated B⁰_s signal decays from background candidates obtained from mass sidebands in the data. Background candidates must contain a B⁰s candidate with a mass greater than 5600MeV=c² and two D_s candidates with masses less than1930MeV=c²or greater than2010MeV=c². The set of 14 variables used as input to the BDT exploits the topology of theB⁰s decay chain and includes the transverse momentum of the B⁰_s candidate and of the two D_s daughters, as well as the product of the absolute transverse momenta of the pions and kaons produced in the decay of eachDs. The decay times of the twoDs candidates with respect to the primary vertex and variables related to the consistency of theB⁰s and of the twoDs to come from the primary vertex are also used. The optimal BDT requirement

is chosen to maximize the value ofNs= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi NsþNb

p , where

Nsis the total number of signal candidates matching any of the three exclusive decays inB⁰s →D^ðÞþs D^ðÞ−s and Nb is the total number of combinatorial background events as taken from the fit. The same BDT classifier and selection criteria are also applied to the normalization sample.

The efficiencies of the selection criteria in both the signal and normalization channels are listed in Table I. The efficiencies of the background vetoes, trigger, reconstruction, and BDT selection are determined using simulated signal samples. The efficiencies of identifyingK^þ andπ^þ mesons are determined using a calibration data sample of D^þ→D⁰ð→K⁻π^þÞπ^þ decays, with kinematic quantities reweighted to match those of the signal candidates. The efficiency of the PID selection is found to beð82.40.2Þ%

for signalB⁰_sdecays andð84.20.1Þ%forB⁰decays. The efficiency of the fullB⁰_s →D^ðÞþs D^ðÞ−s decay is determined by calculating a weighted average of the individual signal channels, with weights given by the relative yields in data.

The relative efficiencies of the B⁰ decay to the three individual channels and the full decay are given in TableII.

IV. SIGNAL AND BACKGROUND SHAPES The B⁰_s and B⁰ yields in the signal channels and the normalization mode are extracted by performing a three- dimensional extended unbinned maximum likelihood fit to the mass distributions of theB⁰_ðsÞmeson and the two charm daughters.

In order to determine the yields for the individual signal peaks, theB⁰scandidate mass distribution in each channel is modeled using simulated signal events. TheB⁰s →D^þsD⁻s

peak is parametrized as the sum of a Crystal Ball function [22] and a Gaussian function. The tail parameters of the Crystal Ball function, the ratio of the width of its Gaussian core to the width of the Gaussian function, and the relative weight of each function in the full distribution, are taken TABLE I. Efficiencies of the various selection criteria for the three individual channels ofB⁰s →D^ðÞþs D^ðÞ−s , and forB⁰→D^þsD⁻. Each efficiency is presented relative to the previous cut and measured using simulated events, except for the PID efficiency which is obtained from data. TheD^þs veto was only applied to the normalization mode, B⁰→D^þsD⁻.

Selection efficiency (%)

Selection B⁰s →D^þsD⁻s B⁰s →Ds D^∓s B⁰s →D^þs D⁻s B⁰→D^þsD⁻ Reconstruction 0.11840.0003 0.11270.0005 0.10610.0005 0.10710.0002 Initial selection 1.3620.008 1.2500.010 1.1000.010 1.4160.009

Mass requirements 89.40.6 87.81.0 88.31.0 88.50.6

BDT 97.90.7 96.61.1 96.71.1 97.60.7

D^þveto 48.70.5 50.30.8 48.90.8 68.70.6

D^þs veto — — — 64.80.7

Λ^þc veto 96.31.0 96.31.6 95.91.6 98.20.8

Trig. requirement 96.60.7 96.71.1 96.61.1 96.80.7

PID requirements 82.40.2 82.40.2 82.40.2 84.20.1

Total 0.05270.0067 0.04600.0095 0.03720.0081 0.04670.0060

TABLE II. Efficiency of the normalization channel B⁰→ D^þsD⁻relative to the signal decays.

Channel ϵ^B0=ϵ^B0s

B⁰s →D^þsD⁻s 0.890.02 B⁰s →Ds D^∓s 1.020.03 B⁰s →D^þs D⁻s 1.260.03 B⁰s →D^ðÞþs D^ðÞ−s 1.060.02

from simulation. The mean and width of the Gaussian core are allowed to float. The two Ds distributions are also parametrized using this model, with all shape parameters fixed to the values found in simulation.

Because of the kinematic differences between theD^þs → D^þsγ and D^þs →D^þsπ⁰ decays, the peak of the B⁰s→ Ds D^∓s mass distribution is parametrized by a superposition of two Gaussian functions. The individual mean values, the ratio of the widths, and the fraction of each Gaussian function in the full distribution are fixed to values taken from simulation. The peak corresponding toB⁰s →D^þs D⁻s

decays is modeled using a single Gaussian function, with the mean fixed to the value found from simulated events.

There is also a component in the fit to describe the presence of background decays of the formB⁰s→D^þ_sJD⁻s, where the D^þ_sJcan be either aD_s1ð2460Þ^þor aD_s0ð2317Þ^þmeson that decays to a D^þs along with some combination of photons and neutral or charged pions. As some decay products are missed, this background is present only at the low mass region of the signal distribution. The shape of the distribution is determined by fitting toB⁰s→Ds1ð2460Þ^þD⁻s simulated events, as the contribution from D_s1ð2460Þ^þ is currently the best understood among theD^þ_sJdecays. It is found to be well modeled by an Argus function[23], all shape parameters for which are fixed to the values found in simulation.

The combinatorial background shape in theB⁰scandidate mass distribution is parametrized by a second-order poly- nomial, and the model is validated with candidates passing a wrong-sign version of the selection. The wrong-sign selection is identical to the signal selection but instead looks for events containing two D^þ_s mesons. The param- eters of the combinatorial background distribution are allowed to float in the full fit to data, and are found to be compatible with the values obtained from the fit to the wrong-sign sample. The combinatorial background shape in the Ds distribution is determined using events taken from the high-mass sideband region of theB⁰s distribution, and is found to be consistent with a first-order polynomial.

The impact of adding a small Gaussian contribution to account for the presence of real D_s mesons in the combinatorial background was found to be minimal, with the observed deviations from the nominal signal yields being smaller than the statistical uncertainty in each case.

The B⁰ distribution is modeled using the same para- metrization as for the full B⁰_s distribution, with one exception. The peak where either the D^þs or D⁻ comes from the decay of an excited state is modeled by a superposition of three Gaussian functions, rather than the two-Gaussian model used in the B⁰_s case, to account for the difference in distributions fromD^þs andD⁻decays, as the D⁻ decay contains a π⁰ in the final state more frequently than D^þ_s decays. There is also a small con- tribution from the decay B⁰s →D⁻sD^þ, which is modeled with the same distribution as for the signalB⁰s candidates.

V. FIT RESULTS

The fit to the signal data samples is shown in Fig. 1, where the triple peaked structure of the full decay is clearly visible. The yields for the individual signal channels and the two backgrounds are given in TableIII. The totalB⁰s → D^ðÞþs D^ðÞ−s yield is the sum of the individual signal channel yields, with the uncertainty calculated using the correlation coefficients between the individual yields, and is found to be 223063. The full fit to the data sample for the normalization mode is shown in Fig.2, and the yields are given in Table IV. Almost all B⁰→Ds D^∓ decays are reconstructed with a mass lower than the 5050MeV=c² mass cut imposed on the B⁰ candidates. There is thus a relatively small yield from this channel. Only the main B⁰→D^þsD⁻ peak is used for normalization purposes.

VI. SYSTEMATIC UNCERTAINTIES

A number of systematic uncertainties affect the measure- ments of the ratios of branching fractions; the sources and magnitudes of these uncertainties are summarized in TableV. The dominant source of uncertainty for two of the three branching fractions comes from thebfragmentation fraction ratio,fs=fd¼0.2590.015[24]. Part of the uncertainty on this ratio is due to the ratio of the charm branching fractions BðD^þ_s →K^þK⁻π^þÞ=BðD⁻→K^þπ⁻π⁻Þ ¼0.5940.020

2] Mass [MeV/c

-

Ds +

Ds

5000 5500

2Candidates /25 MeV/c

0 50 100 150 200

250 LHCb

-

Ds +

Ds

→

0

Bs -

Ds

*+

Ds

→

0

Bs

*-

Ds

*+

Ds

→

0

Bs

Background

-

Ds +

DsJ

→

0

Bs

Comb. Background Data

Fit

FIG. 1. Invariant mass distribution of the B⁰s →D^ðÞþs D^ðÞ−s

candidates. Also shown is the fit function and the individual components of the fit model.

TABLE III. The yields extracted from the fit to the B⁰s → D^ðÞþs D^ðÞ−s candidate sample.

Decay Mode Yield

B⁰s →D^þsD⁻s 41223 B⁰s →Ds D^∓s 103239 B⁰s →Ds D^∓s 78648 Combinatorial background 134247 B⁰s →Dsð2460ÞD^∓s 43242

R. AAIJet al. PHYSICAL REVIEW D 092008 (2016)

[24], the inverse of which is used in the measurements presented in this paper, as shown in Eq.(1). With the two values from Ref.[24], the part of the uncertainty onfs=fd

due to the charm branching fractions cancels, leading to a total uncertainty for the product f_d=f_s×BðD⁻→ K^þπ⁻π⁻Þ=BðD^þs →K^þK⁻π^þÞof 4.7%.

The fit model used for the yield extraction is validated using pseudoexperiments and is found to be unbiased. The uncertainty due to the imperfect knowledge of the shape of the full mass distribution is investigated by measuring the yields using alternative models for each of the peaks. The D^þsD⁻s peak is modeled with an Apollonios function[25]or

a Cruijff function[26], theDs D^∓s peak is modeled using a single Gaussian function, and theD^þs D⁻s peak is modeled using a combination of two Gaussian functions. TheB⁰→ D^ðÞs D^ðÞ∓ fit model uncertainty is assessed by modeling the B⁰→D⁻_sD^þ peak with both an Apollonios function and a Cruijff function. In all cases, the systematic uncer- tainty is taken to be the RMS deviation of the sets of yields with respect to the nominal yields found using the standard fits. TheB⁰→D⁻_sD^þ uncertainty is added in quadrature to the signal channel uncertainties, leading to a systematic uncertainty of 3.4% for the D_s D^∓s branching fraction ratio, 2.2% for theD^þs D⁻s branching fraction ratio, and 2.2% for the total B⁰_s→D^ðÞþs D^ðÞ−s branching fraction ratio.

The uncertainty on the combinatorial background yield is determined by considering the differences when instead fitting this background with an exponential function, and is of the order of 1.5% for all of the branching fraction ratios.

The dominant uncertainty for the B⁰_s →D^þ_s D⁻_s decay channel results from the lack of knowledge of the B⁰_s → D^þ_sJD⁻s background decays. The shape of this background overlaps mostly with theB⁰s →D^þs D⁻s signal decays, and therefore the systematic uncertainty due to this background shape is much larger for this channel (5.0%) than for the other two exclusive branching fractions (0.2%–0.4%). The uncertainty is measured by repeating the fit with the cutoff point of the Argus function varied from5050MeV=c² to 5200MeV=c², where the upper limit is chosen in order to account for the presence of decays containingD_s0ð2317Þ^þ mesons. The changes to the yields from the values found in the nominal fit are calculated in each case. The systematic uncertainty in each channel is then assigned as the RMS of the full set of deviations. The uncertainty on the overall branching fraction ratio is also determined in this way, and is found to be 1.9%.

The uncertainties on the overall efficiencies due to the limited size of the simulated samples are calculated individually for each channel. For the total measurement, BðB⁰_s→D^ðÞþs D^ðÞ−s Þ, a weighted average of the individual uncertainties is used, with weights proportional to the final

2] Mass [MeV/c D-

+

Ds

5100 5200 5300 5400 5500

2Candidates /6 MeV/c

0 100 200 300 400 500 600

D- +

Ds

→ B0

+

Ds

/D-*

D- +*

Ds

→ B0

D-*

+*

Ds

→ B0

D- +

Ds

→

0

Bs

Comb. Background Data

Fit

LHCb

FIG. 2. Invariant mass distribution of the B⁰→D^ðÞs D^ðÞ∓

candidates. Also shown is the fit function and the individual components of the fit model.

TABLE IV. The yields extracted from the fit to the B⁰→ D^ðÞs D^ðÞ∓ candidate sample.

Decay Mode Yield

B⁰→D^þsD⁻ 363664 B⁰→D^þs D⁻=D⁻D^þs 3579110 B⁰→D^þs D⁻ 16686 B⁰s→DsD^∓ 8513

Combinatorial background 154256

TABLE V. Systematic uncertainties, in % of the relevant branching fraction ratio, for the B⁰s→D^ðÞþs D^ðÞ−s

branching fraction ratios.

Source B⁰s →Ds D^∓s B⁰s →D^þs D⁻s B⁰s→D^ðÞþs D^ðÞ−s

fd=fs×_BðD^BðDþ^{−→Kþπ−π−Þ}

s→K^þK⁻π^þÞ 4.7 4.7 4.7

Fit model 3.4 2.2 2.2

Comb. background 1.2 1.9 1.5

D^þsJ background 0.4 5.0 1.9

Simulation statistics 1.9 2.1 1.9

PID efficiency 1.4 1.8 1.5

Trigger efficiency 1.5 1.5 1.5

Total 6.6 8.1 6.4

yield values obtained from data. These uncertainties on the efficiencies are then propagated to the branching fraction ratios.

There is a systematic uncertainty arising from the calculation of the efficiencies of the PID cuts. The calibration of the data samples is performed in bins of momentum and pseudorapidity, which results in an uncer- tainty on the calculated efficiencies owing to the finite size of the D^þ→D⁰π^þ calibration samples and the binning scheme used. The uncertainty resulting from the calibration sample size and binning scheme is determined by redoing the calibration using different binning schemes. Another systematic uncertainty is due to the presence of a small combinatorial background component in the samples that are used to determine the PID efficiencies. The systematic uncertainty due to this contamination is estimated by comparing the efficiencies found in data to those found when calibrating simulated signal events. The total uncer- tainties due to the PID efficiency calculation for the three branching fraction ratios presented in this paper are shown in Table V. The value for B⁰s →D^ðÞþs D^ðÞ−s is again the weighted average of the contributing channels, with the uncertainty for theD^þsD⁻s contribution being 1.1%.

The uncertainty of 1.5% from the trigger response is assessed by considering variations in the response between data and simulation. The individual uncertainties are combined in quadrature to give the total relative systematic uncertainties for each measurement given in Table V.

VII. SUMMARY AND DISCUSSION

Inserting the measured yields and relative efficiencies into Eq. (1), along with the f_s=f_d and BðD⁻→ K^þπ⁻π⁻Þ=BðD^þs →K^þK⁻π^þÞ values taken from [24], gives

BðB⁰s →D^ðÞþs D^ðÞ−s Þ

BðB⁰→D^þsD⁻Þ ¼4.240.14ðstatÞ 0.27ðsystÞ;

BðB⁰_s→D_s D^∓sÞ

BðB⁰→D^þ_sD⁻Þ ¼1.880.08ðstatÞ 0.12ðsystÞ;

BðB⁰_s →D^þs D⁻s Þ

BðB⁰→D^þsD⁻Þ ¼1.760.11ðstatÞ 0.14ðsystÞ:

Using the current world average measurement of the B⁰→D^þsD⁻ branching fraction ofð7.20.8Þ×10⁻³[19], gives

BðB⁰s →D^ðÞþs D^ðÞ−s Þ ¼ ð3.050.100.200.34Þ%;

BðB⁰_s→Ds D^∓sÞ ¼ ð1.350.060.090.15Þ%;

BðB⁰_s →D^þ_s D⁻_s Þ ¼ ð1.270.080.100.14Þ%;

where the uncertainties are statistical, systematic, and due to the branching fraction of the normalization channel, respectively.

Figure3shows the LHCb measurement of the totalB⁰s → D^ðÞþs D^ðÞ−s branching fraction, along with the previous measurements by Belle [5], CDF [6], and D0 [7], the average of these previous measurements as calculated by HFAG [27], and the theoretical value from Ref. [3].

The theoretical prediction is for a decay timet¼0, while the measurements integrate over theB⁰smeson lifetime; the correction factor for mixing is known[28], but has not been applied. The LHCb result is consistent with all previous measurements and calculations, and is the most precise determination to date. In addition, the LHCb measurements of the individualB⁰s →Ds D^∓s andB⁰s→D^þs D⁻s branch- ing fractions are consistent with, and more precise than, all previous measurements.

Using this measurement of the branching fraction of B⁰_s→D^ðÞþs D^ðÞ−s decays to calculate ΔΓ_s=Γ_s as detailed in Ref. [1] gives a value approximately half as large as the most recent HFAG determination [27], suggesting that indeed B⁰_s →D^ðÞþs D^ðÞ−s decays do not saturate the CP-even modes [2]. The measurements presented in this analysis will be useful in improving the understanding of hadronization effects inB⁰_s decays via theb→c¯csquark transition, and in determining a precise value of the inclusive branching fraction of theseb→c¯cs decays.

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: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy);

FOM and NWO (The Netherlands); MNiSW and NCN

) [%]

s

D(*)- s

D(*)+

s→ B(B0

2 4 6 8

Theory HFAG Av.

D0 CDF Belle

-1) LHCb (1fb

FIG. 3. The B⁰s →D^ðÞþs D^ðÞ−s branching fraction measure- ments by Belle, CDF, and D0, the current world average, the theoretical prediction from Ref.[3], and the new LHCb result.

R. AAIJet al. PHYSICAL REVIEW D 092008 (2016)

(Poland); MEN/IFA (Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities

behind the multiple open source software packages on which we depend. Individual groups or members have received support from AvH Foundation (Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union), Conseil Général de Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), The Royal Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust (United Kingdom).

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