Updated branching fraction measurements of B0(s) → K0Sh+h′ − decays

JHEP11(2017)027 Published for SISSA by Springer Received:July 7, 2017 Revised:September 11, 2017 Accepted:September 29, 2017 Published:November 8, 2017 Updated branching fraction measurements of B0 (s)→K0 Sh+h0− decays The LHCb collaboration E-mail: [email protected] Abstract: The charmless three-body decays B0 (s)→K0 Sh+h0− (where h(0)=π, K) are analysed using a sample of pp collision data recorded by the LHCb experiment, corresponding to an integrated luminosity of 3 fb−1. The branching fractions are measured relative to that of the B0→K0 Sπ+π−decay, and are determined to be: BB0→K0 SK±π∓ B(B0→K0 Sπ+π−)= 0.123 ±0.009 (stat) ±0.015 (syst) , BB0→K0 SK+K− B(B0→K0 Sπ+π−)= 0.549 ±0.018 (stat) ±0.033 (syst) , BB0 s→K0 Sπ+π− B(B0→K0 Sπ+π−)= 0.191 ±0.027 (stat) ±0.031 (syst) ±0.011 (fs/fd), BB0 s→K0 SK±π∓ B(B0→K0 Sπ+π−)= 1.70 ±0.07 (stat) ±0.11 (syst) ±0.10 (fs/fd), BB0 s→K0 SK+K− B(B0→K0 Sπ+π−)∈[0.008 −0.051] at 90% confidence level, where fs/fdrepresents the ratio of hadronisation fractions of the B0 sand B0mesons. Keywords: B physics, Branching fraction, Flavor physics, Hadron-Hadron scattering (experiments) ArXiv ePrint: 1707.01665 Open Access, Copyright CERN, for the benefit of the LHCb Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP11(2017)027 JHEP11(2017)027 Contents 1 Introduction 1 2 Detector and simulation 2 3 Trigger and event selection 3 4 Fit model 6 5 Determination of the efficiencies 8 6 Systematic uncertainties 11 6.1 Fit model 12 6.2 Selection and trigger efficiencies 13 6.3 Particle identification efficiencies 14 7 Results and conclusion 14 A Fit results by category 16 B Breakdown of systematic uncertainties 30 C Dalitz-plot distributions of signal events 31 The LHCb collaboration 37 1 Introduction The measurement of CP-violation observables in the decays B0→K0 Sπ+π−and B0→K0 SK+K−, which are dominated by b→qqs (q=u, d, s) loop transitions, are of great theoretical interest.1In particular, the mixing-induced CP asymmetries in these decays are predicted by the Standard Model (SM) Cabibbo-Kobayashi-Maskawa mechanism [1,2] to be approximately equal to those governed by b→ccs transitions, such as B0→J/ψK0 S. Within the SM the weak phase measurements in b→qqs decays are expected to deviate from the values determined in b→ccs decays but for certain contributions to these decays, such as B0→φK0 Sand B0→ρ0K0 S, this deviation is either expected to be small or can be controlled using flavour symmetries [3–5]. The existence of new particles predicted in several extensions of the SM could introduce additional weak phases that contribute along with the SM mixing phase to the amplitudes of these loop-dominated charmless decays, 1Unless stated otherwise, charge conjugated modes are implicitly included throughout this article. – 1 – JHEP11(2017)027 potentially leading to much greater deviations from the b→ccs values [6–8]. The mixinginduced CP-violating phase can be measured by means of a flavour-tagged time-dependent analysis of the three-body Dalitz plot of these decays [9–12]. The current experimental measurements of this phase in b→qqs decays [13] show a generally good agreement with the results for the weak phase βfrom b→ccs decays for each of the CP eigenstates studied. The experimental uncertainties are, however, currently rather larger than the size of the expected deviations, both in the SM and beyond-the-SM scenarios, and so there is a need for more precise measurements of these quantities. A similar determination of the mixing-induced CP-violating phase in the B0 ssystem is possible with, among others, the B0 s→K0 SK±π∓decays [14]. It is also possible to determine the CKM angle γby combining information from several B→Khh0decays, using either the methods originally proposed in refs. [15,16] and recently developed further in ref. [17], or those proposed in refs. [18–20]. The existing experimental results, which come from the BaBar collaboration [21,22], demonstrate the feasibility of the measurement, albeit with large statistical uncertainties. The decay B0 s→K0 Sπ+π−is dominated by tree-level processes and as such is of particular interest for this effort, with the potential to yield a theoretically clean determination of γ[23]. The measurements of the branching fractions themselves are of great importance in order to confront theoretical predictions. These predictions are based on various approaches to modelling the hadronisation processes, such as QCD factorisation or PQCD, see for example refs. [24–29]. Comparison of the different approaches with the experimental data will allow further refinement of the theoretical models, which in turn will yield improved predictions of branching fractions and CP asymmetries of these and many other charmless decay modes. In addition, these results can be used to test the level of breaking of the flavour symmetries: isospin, U-spin and SU(3), see for example ref. [30]. Of the decays of neutral Bmesons to K0 Sπ+π−,K0 SK±π∓and K0 SK+K−final states, only the decay B0 s→K0 SK+K−remains to be observed [10,12,31–34]. Most recently, a search for the three B0 sdecays was reported by the LHCb experiment using the 1 fb−1data sample recorded in 2011 [34]. While first observations were made for the B0 s→K0 Sπ+π− and B0 s→K0 SK±π∓modes, no evidence for the decay B0 s→K0 SK+K−was found. In this work, all the aforementioned charmless three-body decays of the B0and B0 smesons are studied using the pp collision data recorded by the LHCb detector, corresponding to an integrated luminosity of 1.0 fb−1at a centre-of-mass energy of 7 TeV in 2011 and 2.0 fb−1at a centre-of-mass energy of 8 TeV in 2012. This sample is three times larger than that used in ref. [34]. The measurements of the time-integrated branching fractions [35] relative to that of B0→K0 Sπ+π−are presented. The notation BB0→K0 SK±π∓is used throughout the document to indicate the sum of the branching fractions BB0→K0 SK+π−and BB0→K0 SK−π+, and similarly for the corresponding B0 sdecays. 2 Detector and simulation The LHCb detector [36,37] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing bor c – 2 – JHEP11(2017)027 quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector (VELO) 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 momentum, p, 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 vertex (PV), the impact parameter (IP), is measured with a resolution of (15 + 29/pT)µm, where pTis the component 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 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. Simulated data samples are used to investigate backgrounds from other b-hadron decays and also to study the detection and reconstruction efficiency of the signal. In the simulation, pp collisions are generated using Pythia [38,39] with a specific LHCb configuration [40]. Decays of hadronic particles are described by EvtGen [41], in which final-state radiation is generated using Photos [42]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [43,44] as described in ref. [45]. 3 Trigger and event selection The online event selection is performed by a trigger [46], which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, in which all charged particles with pT>500 (300) MeV/c are reconstructed for data collected in 2011 (2012). At the hardware trigger stage, events are required to have a muon with high pTor a hadron, photon or electron with high transverse energy in the calorimeters. The software trigger requires a two-, threeor four-track secondary vertex with a significant displacement from all primary pp interaction vertices. At least one charged particle must have transverse momentum pT>1.7 (1.6) GeV/c in the 2011 (2012) data and be inconsistent with originating from a PV. A multivariate algorithm [47] is used for the identification of secondary vertices consistent with the decay of a bhadron. It is required that the software trigger decision must have been caused entirely by tracks from the decay of the signal Bcandidate. To suppress the ‘combinatorial’ background formed by combinations of unrelated tracks, the events satisfying the trigger requirements are filtered in two stages: a preselection based on loose requirements, followed by a multivariate selection. In order to minimise the variation of the selection efficiency over the Dalitz plot, the selection procedure uses only loose requirements on the momenta of the B-meson decay products and relies mainly on topological features such as the flight distance of the Bcandidate. These features depend on whether the Bcandidate or the K0 S,h+,h0− candidates are consistent with having originated from a particular PV. It is therefore necessary to ‘associate’ each candidate with a single PV — that from which it is most consistent with having originated. – 3 – JHEP11(2017)027 The association is defined in terms of the χ2 IP quantity, which is the difference in fit χ2 of the given PV reconstructed with and without the track or tracks from the particle in question. In events that contain more than one PV, each candidate is associated with the PV that has the smallest χ2 IP. Decays of K0 S→π+π−are reconstructed in two different categories: the first involving K0 Smesons that decay early enough for the resulting pions to be reconstructed in the VELO; and the second containing those K0 Smesons that decay later, such that track segments of the pions cannot be formed in the VELO. These K0 Sreconstruction categories are referred to as long and downstream, respectively. The long category has better mass, momentum and vertex resolution than the downstream category. There are however approximately twice as many K0 Scandidates reconstructed as downstream than as long, simply due to the lifetime of the K0 Smeson and the geometry of the detector. In the following, Bcandidates reconstructed from either a long or downstream K0 Scandidate, in addition to two oppositely charged tracks, are also referred to using these category names. During the 2012 data taking, a significant improvement of the trigger efficiency for long-lived particles, specifically for downstream candidates, was obtained following an update of the software trigger algorithms. To take into account the differences in trigger efficiencies and the different data-taking conditions, the data sample is divided into 2011, 2012a, and 2012b data-taking periods, and each period is divided in two sub-samples according to the K0 Sreconstruction category. The 2012b sample is the largest, corresponding to 1.4 fb−1, and also has the highest trigger efficiency. The two charged pions that form the K0 Scandidates are both required to have momentum p > 2 GeV/c and have χ2 IP with respect to their associated PV greater than 9 (4) for long (downstream) candidates. They are then required to form a vertex with good fit quality (quantified by the fit χ2,χ2 vtx <12) and to have invariant mass within 20 MeV/c2 (30 MeV/c2) of the nominal K0 Smass [48] for long (downstream) candidates. A requirement on the square of the ratio of the separation of the K0 Svertex from its associated PV and the corresponding uncertainty, χ2 VS >80 (50) for long (downstream) candidates, ensures a significant vertex separation. Downstream K0 Scandidates are required in addition to have a momentum p > 6 GeV/c. The Bcandidates are formed from a K0 Scandidate and two oppositely charged tracks (initially reconstructed under the pion mass hypothesis). Each of these two tracks is required to have p < 100 GeV/c, a value beyond which there is little pion-kaon discrimination. The scalar sum of the transverse momenta of the K0 Sand the two h+h0− candidates must be greater than 3.0 GeV/c (4.2 GeV/c), for long (downstream) candidates, and at least two of the three decay products must have pT>0.8 GeV/c. The IP of the B-meson decay product with the largest pTis required to be greater than 0.05 mm relative to the PV associated to the Bcandidate. The Bcandidate decay products are then required to form a vertex that has χ2 vtx <12 and which is separated from any PV by at least 1.7 mm. The difference in χ2 vtx when adding another track must be greater than 4. The Bcandidates must have pT>1.5 GeV/c and invariant mass within the range 4000 < mK0 Sπ+π−<6200 MeV/c2. They are further obliged to be consistent with originating from a PV, quantified by requiring, for long (downstream) candidates, both that χ2 IP <8 (6) and that the cosine of – 4 – JHEP11(2017)027 the angle θDIR between the reconstructed momentum of the Bcandidate and the vector between the associated PV and the decay vertex be greater than 0.9999 (0.999). Finally, the decay vertex of the K0 Scandidate is required to be at least 30 mm downstream, along the beam direction, from that of the Bcandidate. Multivariate discriminants based on a boosted decision tree (BDT) algorithm [49,50] are used to further reduce combinatorial backgrounds. Simulated B0→K0 Sπ+π−events and data from upper mass sidebands, 5425 < mK0 Sπ+π−<6200 MeV/c2, are used as the signal and background training samples, respectively. Contributions from muons and protons are removed from these samples using particle identification (PID) variables. Each of the six samples (resulting from the division by the three data-taking periods and the two K0 S reconstruction categories) is further subdivided into two equally-sized subsamples. Each subsample is then used to train an independent discriminant. In the subsequent analysis the BDT trained on one subsample of a given category is used to select events from the other subsample, in order to avoid bias. The input quantities for the BDTs are: the pT, η,χ2 IP,χ2 VS, cos θDIR and χ2 vtx values of the Bcandidate; the smallest change in the Bcandidate χ2 vtx value when adding another track from the event; the sum of the χ2 IP values of the h+and h−candidates; the χ2 IP,χ2 VS and χ2 vtx values of the K0 Scandidate; and the pTasymmetry pTasym ≡pTB−pTcone pTB+pTcone ,(3.1) where pTcone is the transverse component of the sum of all particle momenta inside a cone around the B-candidate direction, of radius R≡pδη2+δφ2= 1.5, where δη and δφ are the difference in pseudorapidity and azimuthal angle (in radians) around the beam direction, between the momentum vector of the track under consideration and that of the Bcandidate. The selection requirement placed on the output of the BDTs is independently optimised for each data sample. For all signal decay modes that have previously been observed, the following figure of merit is used Q1≡Nsig pNsig +Nbg ,(3.2) where Nsig (Nbg) represents the number of expected signal (combinatorial background) events for a given selection. The value of Nsig is estimated based on the known branching fractions and efficiencies, while Nbg is calculated by fitting the sideband above the signal region and extrapolating into the signal region, defined as the invariant-mass window of five times the typical resolution around the B0and the B0 smasses. For the yet unobserved B0 s→K0 SK+K−mode, an alternative figure of merit [51] is used Q2≡εsig 1 + pNbg ,(3.3) where the signal efficiency (εsig) is estimated from the signal simulation. The optimisation is performed separately for each of the six categories. As each final state contains both B0 and B0 ssignals, one of which is favoured and the other suppressed, this procedure results in applying two differently optimised selections on each final state. – 5 – JHEP11(2017)027 Particle identification requirements are subsequently applied in order to reduce backgrounds from decays such as Λ0 b→K0 Spπ−and B0 (s)→J/ψ (→µ+µ−)K0 Swhere, respectively, the proton and muons are misidentified as pions or kaons. PID information is also used to assign each candidate exclusively to one out of four possible final states: K0 Sπ+π−, K0 SK+π−,K0 Sπ+K−, and K0 SK+K−. The PID requirements are optimised to reduce the cross-feed between the different signal decay modes using the same figures of merit introduced for the BDT optimisation. Fully reconstructed B-meson decays into two-body Dh or (cc)K0 Scombinations, where (cc) indicates a charmonium resonance, may result in a K0 Sh±h0∓ final state that satisfies the selection criteria and has the same B-candidate invariant mass distribution as the signal candidates. The decays of Λ0 bbaryons to Λ+ chwith Λ+ c→pK0 Salso peak under the signal when the proton is misidentified. Therefore, the following Dand Λ+ c decays are explicitly reconstructed under the relevant particle hypotheses and vetoed in all the spectra: D0→K−π+,D+→K0 SK+,D+→K0 Sπ+,D+ s→K0 SK+,D+ s→K0 Sπ+, and Λ+ c→pK0 S. Additional vetoes on charmonium resonances, J/ψ →π+π−, K+K−and χc0→π+π−, K+K−, are applied to remove the small number of fully reconstructed and well identified peaking B0 (s)→(J/ψ , χc0)K0 Sdecays. The vetoed region for each reconstructed charm (charmonium) state is an invariant-mass window of 30 (48) MeV/c2around the world average mass value of that state [48]. This range reflects the typical mass resolution obtained at LHCb. The fraction of selected events containing more than one Bcandidate is at the percent level. The candidate to be retained in each event is chosen randomly, but reproducibly. 4 Fit model The signal yields corresponding to each of the BDT optimisations are determined by means of a simultaneous unbinned extended maximum likelihood fit to the B-candidate invariant mass distributions of all final states in the six categories. Four types of components contribute to each invariant mass distribution: signal decays, backgrounds resulting from cross-feeds, partially reconstructed decays, and random combinations of unrelated tracks. Signal B0 (s)→K0 Sh±h0∓ decays with correct identification of the final-state particles are modelled with the sum of two Crystal Ball (CB) functions [52] that share common values for the peak position and width but have independent power law tails on opposite sides of the peak. The B0and B0 smasses (peak positions of the CB functions) are free parameters in the fit and are allowed to take different values in the different data-taking periods in order to allow for small differences in momentum calibration. Seven parameters related to the widths of the CB functions are also free parameters of the fit: the width of the downstream B0→K0 Sπ+π−signal in each of the three data-taking periods; the ratio of the widths of the B0 sand B0decay modes; the relative widths of K0 SK±π∓and K0 SK+K−to K0 Sπ+π−; and the ratio of the widths in the long and downstream categories. The dependence of the width on each of these divisions is assumed to factorise; for example the width σof the long B0 s→K0 SK+K−signal in the 2011 data-taking period is related to – 6 – JHEP11(2017)027 that of the downstream B0→K0 Sπ+π−signal in the same data-taking period by σ2011 long B0 s→K0 SK+K−=σ2011 downstream B0 →K0 Sπ+π−×rB0 s/B0×rK0 SK+K−/K0 Sπ+π−×rlong/downstream ,(4.1) where rx/y indicates the ratio of the widths of categories xand y. These assumptions are made necessary by the otherwise poor determination of the width of the suppressed mode in each spectrum. The other parameters of the CB components are obtained by a simultaneous fit to simulated samples. Cross-feed contributions from misidentified signal decays are modelled empirically by the sum of two CB functions using simulated events. Only contributions from the decays B0→K0 Sπ+π−and B0→K0 SK+K−reconstructed and selected as K0 SK±π∓, or the decays B0 s→K0 SK±π∓and B0→K0 SK±π∓reconstructed and selected as either K0 SK+K−or K0 Sπ+π−are considered. Other potential misidentified decays are neglected, as their contributions have been checked to be below one event. The relative yield of each misidentified decay is constrained with respect to the yield of the corresponding correctly identified decay. The constraints are implemented using Gaussian prior probability distributions included in the likelihood. The mean values are obtained from the ratio of selection efficiencies and the widths include uncertainties originating from the finite size of the simulated event samples and the systematic uncertainties related to the determination of the PID efficiencies. Backgrounds from partially reconstructed decays such as B0 s→K∗0(→K0 Sπ0)K∗0(K−π+), where the neutral pion is not reconstructed, are also modelled. Four categories are included in each of the final state spectra, where the background results from either charmed or charmless decays of B0,+or B0 smesons. These decays are modelled by means of generalised ARGUS functions [53] convolved with a Gaussian resolution function. Their parameters are determined from simulated samples of the expected dominant decays in each category. Radiative decays and those from B0→η0K0 Sare considered separately and included only in the K0 Sπ+π−final state. The normalisation of all such contributions is constrained with respect to the signal in the relevant final state using Gaussian prior probability distributions based on the ratio of efficiencies and the ratio of branching fractions from world averages [48]. The relative uncertainties on these ratios vary between 20% and 100%. The combinatorial background is modelled by a linear function. The variations of the slope parameter between data-taking periods, K0 Sreconstruction categories and the different final states are assumed to factorise (in an analogous way to the widths of the signal distributions), leaving six free parameters. This assumption, as well as the choice of the linear model, are considered as sources of systematic uncertainties. The fit results for each BDT optimisation, combining all data-taking periods, are displayed in figures 1and 2. The separate plots for the individual data-taking periods are shown in figures 3–14 in appendix A. Table 1shows the signal yields for each mode summed over all data-taking periods and K0 Sreconstruction categories, along with a weighted sum of efficiencies. The fitted yields of each decay mode for each of the three data-taking periods and two K0 Sreconstruction categories are given in appendix A. Statistical correlations between the signal yields are below 10% in all cases and are neglected. For the suppressed modes, the combinatorial background is negligible in the high invariant-mass region for the K0 Sπ+π−and K0 SK+K−final states, leading to a small systematic uncertainty related – 7 – JHEP11(2017)027 downstream long Decay Yield Efficiency (%) Yield Efficiency (%) B0→K0 Sπ+π−2766 ±66 0.0447 ±0.0039 1411 ±45 0.0168 ±0.0015 B0→K0 SK±π∓261 ±24 0.0340 ±0.0031 160 ±17 0.0120 ±0.0012 B0→K0 SK+K−1133 ±39 0.0300 ±0.0035 685 ±29 0.0142 ±0.0017 B0 s→K0 Sπ+π−146 ±19 0.0359 ±0.0030 74 ±11 0.0127 ±0.0011 B0 s→K0 SK±π∓1100 ±41 0.0387 ±0.0035 568 ±28 0.0146 ±0.0013 B0 s→K0 SK+K−12 ±6 0.0282 ±0.0023 7 ±4 0.0094 ±0.0013 Table 1. Signal yields obtained from the simultaneous fit to the data. The yields are the sum of those obtained in the three data-taking periods when fitting the data sample selected using the BDT optimisation chosen for the given decay mode. The uncertainties are statistical only. The average selection efficiencies, described in section 5, are also shown for each decay mode together with the corresponding total uncertainty due to the limited simulation sample size and systematic effects in their determination. to the assumptions used to fit this component. In order to determine the significance of the B0 s→K0 SK+K−signal, likelihood profiles are constructed for the B0 s→K0 SK+K− yield in each fit category, taking into account systematic uncertainties. The profiles are constructed from fits where the shape parameters of the B0 s→K0 SK+K−signal are fixed to the values obtained from the nominal fit, which allows the change in the fit likelihood to be interpreted using Wilks’ theorem [54]. Combining these profiles yields a significance of 2.5σ. 5 Determination of the efficiencies The measurements of the branching fractions of the B0 (s)→K0 Sh±h0∓ decays relative to the well established B0→K0 Sπ+π−decay mode proceed according to B(B0 (s)→K0 Sh±h0∓) B(B0→K0 Sπ+π−)= εsel B0 →K0 Sπ+π− εsel B0 (s) →K0 Sh±h0∓ NB0 (s) →K0 Sh±h0∓ NB0 →K0 Sπ+π− fd fd,s ,(5.1) where εsel is the selection efficiency (which includes geometrical acceptance, reconstruction, selection, trigger and particle identification components), Nis the fitted signal yield, and fdand fsare the hadronisation fractions of a bquark into a B0and B0 smeson, respectively. The ratio fs/fdhas been precisely determined by the LHCb experiment from hadronic and semileptonic measurements to be fs/fd= 0.259±0.015 [55,56]. Since the CP content of the three B0 sdecays is currently unknown, the calculation of the corresponding efficiencies assumes an effective lifetime of 1/Γs, where Γsis the average width of the two CP-eigenstates of the B0 smeson. The effect of varying the decay width by ±∆Γs/2, where ∆Γsis the width difference between the two B0 sCP-eigenstates, results in relative changes to the average efficiency of ∓4%. – 8 – JHEP11(2017)027 Using the world average value omitting the previous LHCb result, B(B0→K0π+π−) = (4.96 ±0.20) ×10−5[13,48], the measured time-integrated branching fractions are B(B0→( ) K0K±π∓) = (6.1±0.5±0.7±0.3) ×10−6, B(B0→K0K+K−) = (27.2±0.9±1.6±1.1) ×10−6, B(B0 s→K0π+π−) = (9.5±1.3±1.5±0.4) ×10−6, B(B0 s→( ) K0K±π∓) = (84.3±3.5±7.4±3.4) ×10−6, B(B0 s→K0K+K−)∈[0.4−2.5] ×10−6at 90% C.L. , where the first uncertainty is statistical, the second systematic and the last due to the uncertainty on B(B0→K0π+π−). These results are in agreement with the available predictions for these channels [24–27]. The first Dalitz-plot analyses by the LHCb experiment of the dominant decays (B0→ K0 Sπ+π−,B0 s→K0 SK±π∓, and B0→K0 SK+K−) are the next step of the physics programme introduced in this work. These studies will follow and benefit from the selection methods developed for this analysis. 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); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (U.S.A.). 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 (U.S.A.). 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 Sk lodowska-Curie Actions and ERC (European Union), Conseil G´en´eral de Haute-Savoie, Labex ENIGMASS and OCEVU, R´egion Auvergne (France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust (United Kingdom). – 15 – JHEP11(2017)027 A Fit results by category Signal yields and efficiencies for the different decays, data-taking periods and K0 Sreconstruction categories are shown for each of the two BDT optimisation points in tables 3–5. Fit results for the different data-taking periods and K0 Sreconstruction categories are shown for each of the two BDT optimisation points in figures 3–14. downstream long Decay Yield Efficiency (%) Yield Efficiency (%) B0→K0 Sπ+π−803 ±36 0.0488 ±0.0093 471 ±27 0.0188 ±0.0036 B0→K0 SK+K−281 ±19 0.0292 ±0.0063 222 ±17 0.0157 ±0.0034 B0 s→K0 SK±π∓333 ±23 0.0361 ±0.0064 207 ±16 0.0148 ±0.0025 B0→K0 SK±π∓76 ±13 0.0322 ±0.0063 50 ±9 0.0174 ±0.0034 B0 s→K0 Sπ+π−43 ±10 0.0316 ±0.0051 21 ±8 0.0160 ±0.0025 B0 s→K0 SK+K−5±3 0.0244 ±0.0052 4 ±3 0.0129 ±0.0029 Table 3. Signal yields obtained for the 2011 category from the simultaneous fit to the data. The yields shown are those obtained when fitting the data sample selected using the BDT optimisation chosen for the given decay mode. The uncertainties are statistical only. The average selection efficiencies, described in section 5, are also shown for each decay mode together with the corresponding total uncertainty due to the limited simulation sample size and systematic effects in their determination. downstream long Decay Yield Efficiency (%) Yield Efficiency (%) B0→K0 Sπ+π−553 ±30 0.0423 ±0.0059 286 ±20 0.0166 ±0.0023 B0→K0 SK+K−181 ±15 0.0263 ±0.0052 119 ±12 0.0149 ±0.0029 B0 s→K0 SK±π∓205 ±18 0.0395 ±0.0060 99 ±13 0.0155 ±0.0023 B0→K0 SK±π∓63 ±11 0.0306 ±0.0047 45 ±10 0.0143 ±0.0022 B0 s→K0 Sπ+π−17 ±8 0.0493 ±0.0068 15 ±6 0.0145 ±0.0021 B0 s→K0 SK+K−2±3 0.0290 ±0.0039 1 ±2 0.0092 ±0.0030 Table 4. Signal yields obtained for the 2011 category from the simultaneous fit to the data. The yields shown are those obtained when fitting the data sample selected using the BDT optimisation chosen for the given decay mode. The uncertainties are statistical only. The average selection efficiencies, described in section 5, are also shown for each decay mode together with the corresponding total uncertainty due to the limited simulation sample size and systematic effects in their determination. – 16 – JHEP11(2017)027 downstream long Decay Yield Efficiency (%) Yield Efficiency (%) B0→K0 Sπ+π−1410 ±46 0.0455 ±0.0063 654 ±30 0.0161 ±0.0022 B0→K0 SK+K−671 ±30 0.0395 ±0.0076 344 ±20 0.0128 ±0.0025 B0 s→K0 SK±π∓562 ±29 0.0401 ±0.0059 262 ±19 0.0138 ±0.0020 B0→K0 SK±π∓122 ±17 0.0402 ±0.0056 65 ±10 0.0100 ±0.0015 B0 s→K0 Sπ+π−86 ±14 0.0335 ±0.0045 38 ±5 0.0108 ±0.0015 B0 s→K0 SK+K−5±4 0.0291 ±0.0034 2 ±2 0.0083 ±0.0017 Table 5. Signal yields obtained for the 2011 category from the simultaneous fit to the data. The yields shown are those obtained when fitting the data sample selected using the BDT optimisation chosen for the given decay mode. The uncertainties are statistical only. The average selection efficiencies, described in section 5, are also shown for each decay mode together with the corresponding total uncertainty due to the limited simulation sample size and systematic effects in their determination. – 17 – JHEP11(2017)027 ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 20 40 60 80 100 120 LHCb Downstream ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 60 70 LHCb Downstream ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 60 70 80 90 LHCb Downstream ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 50 100 150 200 250 300 LHCb Downstream Figure 3. Results of the simultaneous fit to data (downstream, 2011) with the BDT optimisation corresponding to the favoured decay modes. The modes K0 SK+K−,K0 SK+π−,K0 Sπ+K−and K0 Sπ+π−are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in figure 1. – 18 – JHEP11(2017)027 ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 60 70 80 90 LHCb Downstream ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Downstream ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 60 LHCb Downstream ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Downstream ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 60 LHCb Downstream ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 50 100 150 200 250 LHCb Downstream Figure 4. Results of the simultaneous fit to data (downstream, 2012a) with the BDT optimisation corresponding to the favoured decay modes. The modes K0 SK+K−,K0 SK+π−,K0 Sπ+K−and K0 Sπ+π−are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in figure 1. – 19 – JHEP11(2017)027 ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 50 100 150 200 250 LHCb Downstream ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 20 40 60 80 100 120 LHCb Downstream ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 20 40 60 80 100 120 LHCb Downstream ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 100 200 300 400 500 LHCb Downstream Figure 5. Results of the simultaneous fit to data (downstream, 2012b) with the BDT optimisation corresponding to the favoured decay modes. The modes K0 SK+K−,K0 SK+π−,K0 Sπ+K−and K0 Sπ+π−are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in figure 1. – 20 – JHEP11(2017)027 ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Long ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 20 40 60 80 100 LHCb Long ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Long ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 5 10 15 20 25 30 35 LHCb Long ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Long ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 LHCb Long ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Long ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 20 40 60 80 100 120 140 160 LHCb Long Figure 6. Results of the simultaneous fit to data (long, 2011) with the BDT optimisation corresponding to the favoured decay modes. The modes K0 SK+K−,K0 SK+π−,K0 Sπ+K−and K0 Sπ+π− are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in figure 1. – 21 – JHEP11(2017)027 ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Long ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 LHCb Long ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Long ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 5 10 15 20 25 LHCb Long ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Long ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 5 10 15 20 25 30 LHCb Long ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Long ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 20 40 60 80 100 LHCb Long Figure 7. Results of the simultaneous fit to data (long, 2012a) with the BDT optimisation corresponding to the favoured decay modes. The modes K0 SK+K−,K0 SK+π−,K0 Sπ+K−and K0 Sπ+π− are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in figure 1. – 22 – JHEP11(2017)027 ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Long ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 20 40 60 80 100 120 140 LHCb Long ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Long ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 LHCb Long ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Long ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 60 LHCb Long ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Long ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 50 100 150 200 250 LHCb Long Figure 8. Results of the simultaneous fit to data (long, 2012b) with the BDT optimisation corresponding to the favoured decay modes. The modes K0 SK+K−,K0 SK+π−,K0 Sπ+K−and K0 Sπ+π− are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in figure 1. – 23 – JHEP11(2017)027 ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Downstream ] 2 c) [MeV/ − K + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 LHCb Downstream ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Downstream ] 2 c) [MeV/ − π + K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 LHCb Downstream ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 LHCb Downstream ] 2 c) [MeV/ + π − K 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 10 20 30 40 50 60 LHCb Downstream ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 1 10 2 10 LHCb Downstream ] 2 c) [MeV/ − π + π 0 S K(m 5200 5400 5600 5800 ) 2 Candidates / ( 16.25 MeV/c 0 20 40 60 80 100 120 140 160 180 LHCb Downstream Figure 9. Results of the simultaneous fit to data (downstream, 2011) with the BDT optimisation corresponding to the suppressed modes. The modes K0 SK+K−,K0 SK+π−,K0 Sπ+K−and K0 Sπ+π− are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in figure 1. – 24 – JHEP11(2017)027 Relative B(2011 sample) B(B0 →K0 SK±π∓) B(B0 →K0 Sπ+π−) B(B0 →K0 SK+K−) B(B0 →K0 Sπ+π−) B(B0 s→K0 Sπ+π−) B(B0 →K0 Sπ+π−) B(B0 s→K0 SK±π∓) B(B0 →K0 Sπ+π−) B(B0 s→K0 SK+K−) B(B0 →K0 Sπ+π−) Fit model (uncorrelated) [%] 9.7 0.9 6.7 1.6 32.7 Fit model (correlated) [%] 8.9 1.9 9.8 5.9 20.2 Selection (statistics) [%] 2.9 1.6 3.3 2.5 8.0 Selection (binning) [%] 3.2 1.0 2.6 1.4 2.9 Tracking [%] 0.1 0.1 0.2 0.1 0.4 Trigger (overlap) [%] 0.3 0.2 0.1 0.1 0.2 Trigger (calibration sample) [%] 3.7 3.7 6.1 4.2 7.5 PID [%] 1.1 1.1 1.1 1.1 1.1 fs/fd[%] · · · · · · 5.8 5.8 5.8 Relative B(2012a sample) B(B0 →K0 SK±π∓) B(B0 →K0 Sπ+π−) B(B0 →K0 SK+K−) B(B0 →K0 Sπ+π−) B(B0 s→K0 Sπ+π−) B(B0 →K0 Sπ+π−) B(B0 s→K0 SK±π∓) B(B0 →K0 Sπ+π−) B(B0 s→K0 SK+K−) B(B0 →K0 Sπ+π−) Fit model (uncorrelated) [%] 5.2 1.8 5.4 4.3 42.9 Fit model (correlated) [%] 8.9 1.9 9.8 5.9 20.2 Selection (statistics) [%] 5.2 2.8 4.5 2.1 21.1 Selection (binning) [%] 2.0 1.1 2.8 2.4 7.5 Tracking [%] 0.3 0.1 0.3 0.2 0.9 Trigger (overlap) [%] 0.2 0.0 0.2 0.1 0.5 Trigger (calibration sample) [%] 2.8 5.9 6.4 2.6 12.8 PID [%] 1.1 1.1 1.1 1.1 1.1 fs/fd[%] · · · · · · 5.8 5.8 5.8 Relative B(2012b sample) B(B0 →K0 SK±π∓) B(B0 →K0 Sπ+π−) B(B0 →K0 SK+K−) B(B0 →K0 Sπ+π−) B(B0 s→K0 Sπ+π−) B(B0 →K0 Sπ+π−) B(B0 s→K0 SK±π∓) B(B0 →K0 Sπ+π−) B(B0 s→K0 SK+K−) B(B0 →K0 Sπ+π−) Fit model (uncorrelated) [%] 4.4 2.8 9.2 4.5 80.3 Fit model (correlated) [%] 4.6 1.4 9.1 4.0 15.0 Selection (statistics) [%] 4.0 1.0 2.8 1.6 11.0 Selection (binning) [%] 1.6 1.5 1.2 1.7 8.8 Tracking [%] 0.3 0.1 0.2 0.1 0.4 Trigger (overlap) [%] 0.1 0.1 0.1 0.1 0.1 Trigger (calibration sample) [%] 2.8 5.9 6.4 2.6 12.8 PID [%] 1.1 1.1 1.1 1.1 1.1 fs/fd[%] · · · · · · 5.8 5.8 5.8 Table 7. Systematic uncertainties on the ratios of branching fractions for long K0 Sreconstruction. All uncertainties are relative and are quoted as percentages. C Dalitz-plot distributions of signal events Dalitz-plot distributions of signal events as extracted using the sPlot technique are shown for each signal mode are shown in figure 15. – 31 – JHEP11(2017)027 ] 4 c/ 2 [MeV 2 ) + K 0 S Km( 0 10 20 30 6 10× ] 4 c/ 2 [MeV 2 ) − K 0 S Km( 0 5 10 15 20 25 30 6 10× LHCb − K + K 0 S K → 0 B ] 4 c/ 2 [MeV 2 ) + K 0 S Km( 0 10 20 30 6 10× ] 4 c/ 2 [MeV 2 ) − K 0 S Km( 0 5 10 15 20 25 30 6 10× LHCb − K + K 0 S K → 0 s B ] 4 c/ 2 [MeV 2 ) + K 0 S Km( 0 10 20 30 6 10× ] 4 c/ 2 [MeV 2 ) − π 0 S Km( 0 5 10 15 20 25 30 6 10× LHCb − π + K 0 S K → 0 B ] 4 c/ 2 [MeV 2 ) + K 0 S Km( 0 10 20 30 6 10× ] 4 c/ 2 [MeV 2 ) − π 0 S Km( 0 5 10 15 20 25 30 6 10× LHCb − π + K 0 S K → 0 s B ] 4 c/ 2 [MeV 2 ) + π 0 S Km( 0 10 20 30 6 10× ] 4 c/ 2 [MeV 2 ) − K 0 S Km( 0 5 10 15 20 25 30 6 10× LHCb − K + π 0 S K → 0 B ] 4 c/ 2 [MeV 2 ) + π 0 S Km( 0 10 20 30 6 10× ] 4 c/ 2 [MeV 2 ) − K 0 S Km( 0 5 10 15 20 25 30 6 10× LHCb − K + π 0 S K → 0 s B ] 4 c/ 2 [MeV 2 ) + π 0 S Km( 0 10 20 30 6 10× ] 4 c/ 2 [MeV 2 ) − π 0 S Km( 0 5 10 15 20 25 30 6 10× LHCb − π + π 0 S K → 0 B ] 4 c/ 2 [MeV 2 ) + π 0 S Km( 0 10 20 30 6 10× ] 4 c/ 2 [MeV 2 ) − π 0 S Km( 0 5 10 15 20 25 30 6 10× LHCb − π + π 0 S K → 0 s B Figure 15. Distribution of sPlot weights in data. The K0 SK+K−,K0 SK+π−,K0 Sπ+K−, and K0 Sπ+π−final states are shown from top to bottom, with a B0parent on the left, and a B0 son the right. All data-taking periods and K0 Sreconstruction categories are added. – 32 – JHEP11(2017)027 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. References [1] N. Cabibbo, Unitary symmetry and leptonic decays,Phys. Rev. Lett. 10 (1963) 531 [INSPIRE]. [2] M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction,Prog. Theor. Phys. 49 (1973) 652 [INSPIRE]. [3] M. Beneke, Corrections to sin(2β)from CP asymmetries in B0→(π0, ρ0, η, η0, ω, φ)K0 S decays,Phys. Lett. B 620 (2005) 143 [hep-ph/0505075] [INSPIRE]. [4] G. Buchalla, G. Hiller, Y. Nir and G. 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Physikalisches Institut, RWTH Aachen University, Aachen, Germany 10 Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany 11 Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany 12 Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany 13 School of Physics, University College Dublin, Dublin, Ireland 14 Sezione INFN di Bari, Bari, Italy – 39 – JHEP11(2017)027 15 Sezione INFN di Bologna, Bologna, Italy 16 Sezione INFN di Cagliari, Cagliari, Italy 17 Sezione INFN di Ferrara, Ferrara, Italy 18 Sezione INFN di Firenze, Firenze, Italy 19 Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy 20 Sezione INFN di Genova, Genova, Italy 21 Sezione INFN di Milano Bicocca, Milano, Italy 22 Sezione INFN di Milano, Milano, Italy 23 Sezione INFN di Padova, Padova, Italy 24 Sezione INFN di Pisa, Pisa, Italy 25 Sezione INFN di Roma Tor Vergata, Roma, Italy 26 Sezione INFN di Roma La Sapienza, Roma, Italy 27 Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland 28 AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Krak´ow, Poland 29 National Center for Nuclear Research (NCBJ), Warsaw, Poland 30 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania 31 Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia 32 Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia 33 Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia 34 Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia 35 Yandex School of Data Analysis, Moscow, Russia 36 Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia 37 Institute for High Energy Physics (IHEP), Protvino, Russia 38 ICCUB, Universitat de Barcelona, Barcelona, Spain 39 Universidad de Santiago de Compostela, Santiago de Compostela, Spain 40 European Organization for Nuclear Research (CERN), Geneva, Switzerland 41 Institute of Physics, Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland 42 Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland 43 Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands 44 Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands 45 NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine 46 Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 47 University of Birmingham, Birmingham, United Kingdom 48 H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom 49 Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 50 Department of Physics, University of Warwick, Coventry, United Kingdom 51 STFC Rutherford Appleton Laboratory, Didcot, United Kingdom 52 School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 53 School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 54 Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 55 Imperial College London, London, United Kingdom 56 School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 57 Department of Physics, University of Oxford, Oxford, United Kingdom 58 Massachusetts Institute of Technology, Cambridge, MA, United States 59 University of Cincinnati, Cincinnati, OH, United States 60 University of Maryland, College Park, MD, United States 61 Syracuse University, Syracuse, NY, United States 62 Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2 – 40 –