Observation of the decay B0s→ψ(2S)K+π−

Physics Letters B 747 (2015) 484–494 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Observation of the decay B0 s→ψ(2S)K+π− .LHCb Collaboration a r t i c l e i n f o a b s t r a c t Article history: Received 24 March 2015 Received in revised form 12 June 2015 Accepted 16 June 2015 Available online 17 June 2015 Editor: M. Doser The decay B0 s→ψ(2S)K+π−is observed using a data set corresponding to an integrated luminosity of 3.0fb −1collected by the LHCb experiment in pp collisions at centre-of-mass energies of 7 and 8 TeV. The branching fraction relative to the B0→ψ(2S)K+π−decay mode is measured to be B(B0 s→ψ(2S)K+π−) B(B0→ψ(2S)K+π−)=5.38 ±0.36(stat)±0.22 (syst)±0.31(fs/fd)%, where fs/fdindicates the uncertainty due to the ratio of probabilities for a bquark to hadronise into a B0 sor B0meson. Using an amplitude analysis, the fraction of decays proceeding via an intermediate K∗(892)0meson is measured to be 0.645 ±0.049 (stat) ±0.049 (syst)and its longitudinal polarisation fraction is 0.524 ±0.056 (stat) ±0.029 (syst). The relative branching fraction for this component is determined to be B(B0 s→ψ(2S)K∗(892)0) B(B0→ψ(2S)K∗(892)0)=5.58 ±0.57(stat)±0.40 (syst)±0.32(fs/fd)%. In addition, the mass splitting between the B0 sand B0mesons is measured as M(B0 s)−M(B0)=87.45 ±0.44(stat)±0.09 (syst)MeV/c2. ©2015 CERN for the benefit of the LHCb Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction The large data set collected by the LHCb experiment has allowed precision measurements of time-dependent CP violation in the B0 s→J/ψφ and B0 s→J/ψ f0(980)decay modes [1,2].1The results are interpreted assuming that these decays are dominated by colour-suppressed tree-level amplitudes (Fig. 1). Higher-order penguin amplitudes, which are difficult to calculate in QCD, also contribute (Fig. 1). Ref. [3] suggests that the size of contributions from these processes can be determined by studying decay modes such as B0 s→J/ψ K∗(892)0where they dominate. The B0 s→J/ψ K∗(892)0decay mode was first observed by the CDF Collaboration [4] and subsequently studied in detail by the LHCb Collaboration [5]. Recently, interest in b-hadron decays to final states containing charmonia has been generated by the observation of the Z(4430)−→ψ(2S)π−state in the B0→ψ(2S)K+π−decay chain by the Belle [6–8] and LHCb Collaborations [9]. As this state is charged and has a minimal quark content of ccdu, it is in1Charge-conjugation is implicit unless stated otherwise. terpreted as evidence for the existence of non-qq mesons [10]. Evidence for similar exotic structures in B0→χc1,c2K+π−and B0→J/ψ K+π−decays has been reported by the Belle Collaboration [11,12]. If these structures correspond to real particles they should be visible in other decay modes. This letter reports the first observation of the decay B0 s→ ψ(2S)K+π−and presents measurements of the inclusive branching fraction and the fraction of decays that proceed via an intermediate K∗(892)0resonance, as determined from an amplitude analysis of the final state. The amplitude analysis also allows the determination of the longitudinal polarisation fraction of the K∗(892)0 meson. Additionally a measurement of the mass difference between B0 sand B0mesons is reported that improves the current knowledge of this observable. 2. Detector and simulation The LHCb detector [13,14] is a single-arm forward spectrometer covering the pseudorapidity range 2 <η<5, designed for the study of particles containing bor cquarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area http://dx.doi.org/10.1016/j.physletb.2015.06.038 0370-2693/©2015 CERN for the benefit of the LHCb Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. LHCb Collaboration / Physics Letters B 747 (2015) 484–494 485 Fig. 1. Tree (left) and penguin (right) topologies contributing to the B0 (s)→ψVdecays where ψ=J/ψ, ψ(2S)and V=φ,K∗(892)0. silicon-strip detector located upstream of a dipole magnet with a bending power of about 4Tm, and three stations of siliconstrip detectors and straw drift tubes [15] 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, the impact parameter, is measured with a resolution of (15 +29/pT)μm, where pTis the component of the momentum transverse to the beam, in GeV/c. Large samples of B+→J/ψ K+and J/ψ →μ+μ−decays, collected concurrently with the data set used here, were used to calibrate the momentum scale of the spectrometer to a precision of 0.03 %[16]. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors [17]. 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 [18]. The online event selection is performed by a trigger [19], which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. In this analysis candidates are first required to pass the hardware trigger, which selects muons and dimuon pairs based on the transverse momentum. At the subsequent software stage, events are triggered by a ψ(2S) →μ+μ−candidate where the ψ(2S)is required to be consistent with coming from the decay of a bhadron by either using impact parameter requirements on daughter tracks or detachment of the ψ(2S)candidate from the primary vertex. The analysis is performed using data corresponding to an integrated luminosity of 1.0fb −1collected in pp collisions at a centre-of-mass energy of 7TeV and 2.0fb −1collected at 8TeV. In the simulation, pp collisions are generated using Pythia [20] with a specific LHCb configuration [21]. Decays of hadronic particles are described by EvtGen [22], in which final state radiation is generated using Photos [23]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [24] as described in Ref. [25]. 3. Event selection The selection of candidates is divided into two parts. First, a loose selection is performed that retains the majority of signal events whilst reducing the background substantially. After this the B0→ψ(2S)K+π−peak is clearly visible. Subsequently, a multivariate method is used to further improve the signalto-background ratio and to allow the observation of the B0 s→ ψ(2S)K+π−decay. The selection starts by reconstructing the dimuon decay of the ψ(2S)meson. Pairs of oppositely charged particles identified as muons with pT>550 MeV/care combined to form ψ(2S)candidates. The invariant mass of the dimuon pair is required to be within 60 MeV/c2of the known ψ(2S)mass [26]. To form B0 (s) candidates, the selected ψ(2S)mesons are combined with oppositely charged kaon and pion candidates. Tracks that do not correspond to actual trajectories of charged particles are suppressed by requiring that they have pT>250 MeV/cand by selecting on the output of a neural network trained to discriminate between these and genuine tracks associated to particles. Combinatorial background from hadrons originating in the primary vertex (PV) is suppressed by requiring that both hadrons are significantly displaced from any PV. Well-identified hadrons are selected using the information provided by the Cherenkov detectors. This is combined with kinematic information using a neural network to provide a probability that a particle is a kaon (PK), pion (Pπ) or proton (Pp). It is required that PKis larger than 0.1 for the K+candidate and that Pπis larger than 0.2 for the π−candidate. A kinematical vertex fit is applied to the B0 (s)candidates [27]. To improve the invariant mass resolution, the fit is performed with the requirement that the B0 (s)candidate points to the PV and the ψ(2S)is mass constrained to the known value [26]. A good quality of the vertex fit χ2, χ2 DTF, is required. To ensure good separation between the B0and B0 ssignals, the uncertainty on the reconstructed mass returned by the fit must be less than 11 MeV/c2. Combinatorial background from particles produced in the primary vertex is further reduced by requiring the decay time of the B0 (s)meson to exceed 0.3ps. Four criteria are applied to reduce background from specific b-hadron decay modes. First, the candidate is rejected if the invariant mass of the hadron pair calculated assuming that both particles are kaons is within 10 MeV/c2of the known φmeson mass [26], suppressing B0 s→ψ(2S)φ decays where one of the kaons is misidentified as a pion. Second, to suppress B0→ψ(2S)π+π− events where one of the pions is incorrectly identified as a kaon, it is required that PK>Pπfor the kaon candidate. This rejects 80 %of the background from this source whilst retaining 90 %of B0 (s)signal candidates. Third, to suppress background from Λ0 b→ ψ(2S)pπ−decays where the proton is misidentifed as a kaon, candidates with Pp>0.3 and an invariant mass within 15 MeV/c2of the known Λ0 bmass [26] are discarded. Finally, to reduce background from a B+→ψ(2S)K+decay combined with a random pion, candidates where the reconstructed ψ(2S)K+invariant mass is within 16 MeV/c2of the known B+mass [26] are rejected. Background from the decay Λ0 b→ψ(2S)pK−with misidentified hadrons does not peak at the B0 smass and is modelled in the fit. To further improve the signal-to-background ratio, a multivariate analysis based on a neural network is used. This is trained using simulated B0signal events together with candidates from data with a mass between 5500 and 5600 MeV/c2that are not used for subsequent analysis. Eight variables that give good separation between signal and background are used: the number of clusters in the large-area silicon tracker upstream of the magnet, PKfor the kaon candidate, Pπfor the pion candidate, the transverse momentum of the B0 (s), the minimum impact parameter to any primary vertex for each of the two hadrons, χ2 DTF and the flight 486 LHCb Collaboration / Physics Letters B 747 (2015) 484–494 distance in the laboratory frame of the B0 (s)candidate divided by its uncertainty. The ratio NS/√NS+NBis used as a figure of merit, where NS(NB)is the number of signal (background) events determined from the invariant mass fit (see Section 4). The maximum value of this ratio is found for a threshold on the neural network output that rejects 98% of the background and retains 81% of the signal for subsequent analysis. 4. Invariant mass fit A maximum likelihood fit is made to the unbinned ψ(2S)K+π− invariant mass distribution, m(ψ(2S)K+π−), to extract the B0and B0 ssignal yields. The B0signal component is modelled by the sum of two Crystal Ball functions [28] with common tail parameters and an additional Gaussian component, all with a common mean. All parameters are fixed to values determined from the simulation apart from the common mean and an overall resolution scale factor. The simulation is tuned to match the invariant mass resolution seen in data for the B+→J/ψ K+and B0→J/ψ K+π− decay modes. Consequently, the resolution scale factor is consistent with unity in the fit to data. The B0 scomponent is modelled with the same function, with the mean value of the B0 smeson mass left free in the fit. The resolution parameters in this case are multiplied by a factor of 1.06, determined from simulation, which accounts for the additional energy release in this decay. The dominant background is combinatorial and modelled by an exponential function. A significant component from B0 s→ψ(2S)φ decays is visible at lower masses than the B0peak. This is modelled in the fit by a bifurcated Gaussian function where the shape parameters are constrained to the values obtained in the simulation and the yield constrained to the value determined in data under the hypothesis that both hadrons are kaons. Additional small components from B0 (s)→ψ(2S)π+π−and Λ0 b→ψ(2S)pK−decays are modelled by bifurcated Gaussian functions. The shapes of these components are fixed using the simulation and the yields are determined by normalising the simulation samples to the number of candidates for each modes found in data using dedicated selections. Contributions from partially reconstructed decays are accounted for in the combinatorial background. In total, the fit has ten free parameters. Variations of this fit model are considered as systematic uncertainties. Fig. 2 shows the invariant mass distribution observed in the data together with the result of a fit to the model described above. Binning the data, a χ2-probability of 0.30 is found. The moderate mismodelling of the B0peak is accounted for in the systematic uncertainties. The fit determines that there are 329 ±22 B0 sdecays and 24 207 ±160 B0decays. The B0 s→ψ(2S)K+π−mode is observed with high significance. The precision of the momentum scale calibration of 0.03% translates to an uncertainty on the B0and B0 smeson masses of 0.3MeV/c2. Therefore, it is chosen to quote only the mass difference in which this uncertainty largely cancels, M(B0 s)−M(B0)=87.45 ±0.44 (stat)±0.09 (syst)MeV/c2. This procedure has been checked using the simulation, which gives the input mass difference with a bias of 0.05 MeV/c2that is assigned as a systematic uncertainty. Further systematic uncertainties arise from the momentum scale and mass fit model. Varying the momentum scale by 0.03% leads to an uncertainty of 0.04 MeV/c2. The effect of the fit model is evaluated by considering several variations: the relative fraction of the two Crystal Ball functions is left free; the slope of the combinatorial background is constrained using candidates where the kaon and pion have the same charge; the Gaussian constraints on the background from the B0 s→ψ(2S)φ mode are removed; and the tail parameters of the Fig. 2. Invariant mass distribution for selected ψ(2S)K+π−candidates in the data. A fit to the model described in the text is superimposed. The full fit model is shown by the solid (red) line, the combinatorial background by the solid (yellow) and the sum of background from the exclusive b →ψ(2S)Xmodes considered in the text by the shaded (blue) area. The maximum of the y-scale is restricted so as to be able to see more clearly the B0 s→ψ(2S)K+π−signal. The lower plot shows the differences between the fit and measured values divided by the corresponding uncertainty of the measured value, the so-called pull distribution. Fig. 3. Dalitz plot for the selected B0 s→ψ(2S)K+π−candidates in the signal window m(ψ(2S)K+π−) ∈[5350, 5380]MeV/c2. Crystal Ball functions are left free. The largest variation in the mass splitting is 0.06 MeV/c2. The total systematic uncertainty is given by summing the individual components in quadrature. 5. Amplitude analysis Fig. 3 shows the Dalitz plot of the selected B0 s→ψ(2S)K+π− candidates in the signal range, m(ψ(2S)K+π−) ∈[5350, 5380] MeV/c2. There is a clear enhancement around the known K∗(892)0 mass [26] and no other significant enhancements elsewhere. To determine the fraction of decays that proceed via the K∗(892)0 resonance, an amplitude analysis is performed, similar to that used in Ref. [9] for the analysis of the B0→ψ(2S)K+π−mode. The final-state particles are described using three angles  ≡ (cosθK, cos θμ, φ) in the helicity basis, defined in Fig. 4, and the invariant K+π−mass, mKπ≡m(K+π−). The total amplitude is S(mKπ, )ε(mKπ, ) +B(mKπ, ), where S(mKπ, ) represents the coherent sum over the helicity amplitudes for each considered K+π−resonance or non-resonant component. The detection efficiency, ε(mKπ, cos θK, cos θμ, φ), is evaluated using simulation and parameterised using a combination of Legendre polynomials and spherical harmonic moments, given by LHCb Collaboration / Physics Letters B 747 (2015) 484–494 487 Fig. 4. Definition of the helicity angles. Fig. 5. Distributions of (a) cosθμ, (b) φ, (c) cosθKand (d) m(K+π−)of simulated B0 s→ψ(2S)K+π−decays in a phase space configuration (black points) with the parameterisation of the efficiency overlaid (blue lines). ε(mKπ,cosθK,cos θμ,φ)= a,b,c,d cabcd Pa(cos θK)Ybc(cosθμ,φ) ×Pd2(mKπ−mmin Kπ) mmax Kπ−mmin Kπ−1,(1) where mmin(max) Kπis the minimum (maximum) value allowed for mKπin the available phase space of the decay. The coefficients of the efficiency parameterisation are computed by summing over the NMC events simulated uniformly in the phase-space as cabcd =1 NMC NMC  i 2a+1 2 2d+1 2Pa(cosθKi)Ybc(cos θμi,φi) ×Pd2(mKπi−mmin Kπ) mmax Kπ−mmin Kπ−1C gi ,(2) where gi=piqi, with pi(qi)being the momentum of the K+π− system (K+meson) in the B0(K+π−)rest frame and Cis a normalising constant with units GeV2/c2. This approach provides a description of the multidimensional correlations without assuming factorisation. In practise, the sum is over a finite number of moments (a ≤2, b ≤2, c≤2 and d ≤2) and only coefficients with a statistical significance larger than five standard deviations from zero are retained. The one-dimensional projections of the parameterised efficiency are shown in Fig. 5, superimposed on the simulated event distributions. The background probability density function, B(mKπ, ), is determined using a similar method as for the efficiency parameterisation. In this case the sum in Eq. (2) is over the selected events with m(ψ(2S)K+π−) >5390 MeV/c2and gi≡1. Only moments with a ≤2, b =0, c=0 and d ≤2 and a statistical significance larger than five standard deviations from zero are retained. The one-dimensional projections of the parameterised background distribution are shown in Fig. 6, superimposed on the sideband data. As a consistency check, the (mKπ, ) distributions for events with m(ψ(2S)K+π−) >5390 MeV/c2are found to be compatible with the same distributions obtained from a like-sign (ψ(2S)K±π±) sample. The default amplitude model is constructed using contributions from the K∗(892)0resonance and a K+π−S-wave modelled using the LASS parameterisation [29]. The magnitudes and phases of all components are measured relative to those of the zero helicity state of the K∗(892)0meson and the masses and widths of the resonances are fixed to their known values [26]. The remaining eight free parameters are determined using a maximum likelihood fit of the amplitude to the data in the signal window. The background fraction is fixed to 0.28, as determined from the fit described in Section 4. The fit fraction for 488 LHCb Collaboration / Physics Letters B 747 (2015) 484–494 Fig. 6. Distributions of (a) cosθμ, (b) φ, (c) cos θKand (d) m(K+π−)of B0 (s)→ψ(2S)K+π−candidates with m(ψ(2S)K+π−) >5390 MeV/c2(black points), with the parameterisation of the background distribution overlaid (blue lines). any resonance Ris defined in the full phase space, as fR= SRdmKπd / SdmKπd, where SRis the signal amplitude with all amplitude terms set to zero except those for R. The fractions of each component determined by the fit are fK∗(892)0= 0.645 ±0.049, and fS-wave =0.339 ±0.052, where the uncertainty is statistical only. The fractions do not sum to unity due to interference between the different components. Variations of the S-wave description and default mixture of K+π−resonances, including the introduction of the spin-2 K∗ 2(1430)0meson or an exotic Z− cmeson, are considered but found to give larger values of the Poisson likelihood χ2[30] per degree of freedom or lead to components with fit fractions that are consistent with zero. For each model the number of degrees of freedom is calibrated using simulated experiments. The variations in amplitude model are considered as sources of systematic uncertainty. The longitudinal polarisation fraction of the K∗(892)0meson is defined as fL=H2 0/(H2 0+H2 ++H2 −), where H0,+,−are the magnitudes of the K∗(892)0helicity amplitudes. This is measured to be fL=0.524 ±0.056, where the uncertainty is statistical. The projections of the default fit for the helicity angles and invariant K+π− mass are shown in Fig. 7. 5.1. Systematic uncertainties of amplitude analysis A summary of possible sources of systematic uncertainties that affect the amplitude analysis is reported in Table 1. The size of each contribution is determined using a set of simulated experiments, of the same size as the data, generated under the hypothesis of an alternative amplitude model. These are fitted once with the default model and again with the alternative model. The experiment-by-experiment difference in the measured fit fractions and fLis then computed and the sum in quadrature of the mean and standard deviation is assigned as a systematic uncertainty to the corresponding parameter. The systematic dependence on the K+π−amplitude model is determined using the above procedure, where the alternative model also contains a spin-2 K∗ 2(1430)component. This leads to the dominant systematic uncertainty on the K∗(892)0fit fraction and fL. The systematic dependence on the K+π−S-wave model is determined using simulated experiments where a combination of a non-resonant term and a K∗ 0(1430)contribution is used in place of the LASS parameterisation. In addition, the amplitude model contains parameters that are fixed in the default fit such as the masses and widths of the resonances and the Blatt–Weisskopf radius. The radius controls the effective hadron size and is set to 1.6(GeV/c)−1by default. Alternative models are considered where this is changed to 3.0(GeV/c)−1and 0.8(GeV/c)−1. A large source of systematic uncertainty comes from the choice of convention for the mass, m, in the (p/m)LRterms of the amplitude. The default amplitude model follows the convention in Ref. [26] by using the resonance mass. This is different to that in Ref. [9] where the running resonance mass (mKπ) is used in the denominator. This choice is motivated by the improved fit quality obtained when using the resonance mass. The systematic uncertainty related to the combinatorial background parameterisation is determined using an amplitude model with an alternative background description that allows for higher moment contributions (a ≤2, b ≤2, c≤2 and d ≤2). The combinatorial background normalisation is determined from the fit to the m(ψ(2S)K+π−)distribution and is fixed in the amplitude fit. The systematic uncertainty related to the level of the background is estimated by using an amplitude model with the background fraction modified by ±10%. The efficiency parameterisation is tested by re-evaluating the coefficients, allowing for higher order moments (a ≤4, b ≤4, c≤4 and d ≤4). Similarly, to test the dependence of the efficiency model on the neural network requirement, an alternative model is used with the efficiency parameterisation determined from the simulated events that are selected without applying the requirement. There is a negligible systematic uncertainty caused by the lifetime difference between the B0and B0 smesons. LHCb Collaboration / Physics Letters B 747 (2015) 484–494 489 Fig. 7. Distributions of (a) cosθμ, (b) φ, (c) cosθKand (d) m(K+π−)for selected B0 s→ψ(2S)K+π−candidates (black points) with the projections of the fitted amplitude model overlaid. The following components are included in the model: K∗(892)0(red dashed), LASS S-wave (green dotted), and background (grey dashed-dotted). The residual pulls are shown below each distribution. Table 1 Summary of systematic uncertainties on the K∗(892)0fit fraction and fL. Rows marked with (*) refer to uncorrelated sources of uncertainty between the B0 sand B0modes for the computation of the ratio of branching fractions. Source K∗(892)0fit fraction fL (*) K+π−amplitude model 0.028 0.017 (*) S-wave model 0.018 0.010 K∗resonance widths 0.005 0.008 Blatt–Weisskopf radius 0.014 0.003 Breit–Wigner parameters (mRvs.mKπ) 0.026 0.005 (*) Background parameterisation 0.014 0.012 (*) Background normalisation 0.007 0.011 Efficiency model (parameterisation) 0.011 0.007 Efficiency model (neural net) 0.002 0.004 Quadrature sum of systematic uncertainties 0.049 0.029 Quadrature sum of uncorrelated systematic uncertainties 0.037 0.026 Statistical uncertainty 0.049 0.056 6. Branching fraction results Two ratios of branching fractions are calculated, B(B0 s→ ψ(2S)K+π−)/B(B0→ψ(2S)K+π−)and B(B0 s→ψ(2S)K∗(892)0)/ B(B0→ψ(2S)K∗(892)0). These are determined from the signal yields given in Section 4correcting for the relative detector acceptance using simulation. The simulated B0 ssamples are reweighted with the results of the angular analysis presented in Section 5. Similarly, the B0simulated data are reweighted to match the results given in Ref. [9]. For the inclusive branching ratio, the relative efficiency between the two modes is found to be 0.975 ±0.014 whilst for the K∗(892)0component it is 1.027 ±0.021. The uncertainty on these values is propagated to the systematic uncertainty. Since the same final state is considered in the signal and normalisation mode, most sources of systematic uncertainty cancel in the ratio. The remaining sources are discussed in the following. The variations of the invariant mass fit model described in Section 4are considered. The largest change in the ratio of yields observed in these tests is 3.7%, which is assigned as a systematic uncertainty. Differences in the pTspectra of the B0meson are seen comparing data and the reweighted simulation. If the pTspectrum in the simulation is further reweighted to match the data, the efficiency ratio changes by 0.7%, which is assigned as a systematic uncertainty. To test the impact of the chosen K+π−amplitude model for the B0 schannel, the simulated events are reweighted using a model 490 LHCb Collaboration / Physics Letters B 747 (2015) 484–494 Table 2 Systematic uncertainties on the ratio of branching fractions. Source Relative uncertainty % Inclusive K∗(892)0 Simulation sample size 1.4 2.2 Fit model 3.7 3.7 Detector acceptance 0.7 0.7 K+π−amplitude model 0.6 – K∗(892)0fit fraction – 6.0 Quadrature sum 4.1 7.4 consisting of the K∗(892)0resonance, the LASS [29] description of the S-wave and the K∗ 2(1430)resonance. This changes the efficiency ratio by 0.6%, which is assigned as a systematic uncertainty. To calculate the K∗(892)0branching ratio, the fraction of candidates from this source is needed. For the B0 schannel this is determined from the amplitude analysis to be 0.645 ±0.049 ±0.049 and the corresponding fraction for the B0channel is 0.591 ±0.009 [9], leading to a 6.0% systematic uncertainty. All of the uncertainties discussed above are summarised in Table 2. The limited knowledge of the fragmentation fractions, fs/fd=0.259 ±0.015 [31–33], results in an uncertainty of 5.8%, which is quoted separately from the others. 7. Summary Using a data set corresponding to an integrated luminosity of 3.0fb −1collected in pp collisions at centre-of-mass energies of 7 and 8 TeV, the decay B0 s→ψ(2S)K+π−is observed. The mass splitting between the B0 sand B0mesons is measured to be M(B0 s)−M(B0)=87.45 ±0.44 (stat)±0.09 (syst)MeV/c2. This is consistent with, though less precise than, the value 87.21 ± 0.31 MeV/c2obtained by averaging the results in Refs. [34,35]. Averaging the two numbers gives M(B0 s)−M(B0)=87.29 ±0.26 MeV/c2. The ratio of branching fractions between the B0 sand B0modes is measured to be B(B0 s→ψ(2S)K+π−) B(B0→ψ(2S)K+π−)=5.38 ±0.36 (stat)±0.22 (syst) ±0.31(fs/fd)%. The fraction of decays proceeding via an intermediate K∗(892)0 meson is measured with an amplitude analysis to be 0.645 ± 0.049 (stat) ±0.049 (syst). No significant structure is seen in the distribution of m(ψ(2S)π−). The longitudinal polarisation fraction, fL, of the K∗(892)0meson is determined as 0.524 ±0.056 (stat) ±0.029 (syst). This is consistent with the value measured in the corresponding decay that proceeds through an intermediate J/ψ meson, fL=0.50 ± 0.08 (stat) ±0.02 (syst)[5]. The present data set does not allow a test of the prediction given in Ref. [36] that fLshould be lower for decays closer to the kinematic endpoint. Using the K∗(892)0fraction determined in this analysis for the B0 scomponent, the corresponding number for the B0mode from Ref. [9], and the efficiency ratio given in Section 6, the following ratio of branching fractions is measured B(B0 s→ψ(2S)K∗(892)0) B(B0→ψ(2S)K∗(892)0)=5.58 ±0.57 (stat)±0.40 (syst) ±0.32(fs/fd)%. The B0 s→ψ(2S)K+π−mode may be useful for future studies that attempt to control the size of loop-mediated processes that influence CP violation studies and offers promising opportunities in the search for exotic resonances. Acknowledgements 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, HGF and MPG (Germany); INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO (Russia); Ministerio de Economía y Competitividad (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). The Tier1 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom). We are indebted to the communities behind the multiple open source software packages on which we depend. We are also thankful for the computing resources and the access to software R&D tools provided by Yandex LLC (Russia). 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