Observation of the decay B ¯ ¯ ¯ ¯ 0 s →ψ(2S) K + π −
LHCb collaboration, R. Aaij, B. Adeva, M. Adinolfi, A. Affolder, Z. Ajaltouni, S. Akar, J. Albrecht, F. Alessio, M. Alexander, S. Ali, G. Alkhazov, P. Alvarez Cartelle, A.A. Alves Jr, S. Amato, S. Amerio, Y. Amhis, L. An, L. Anderlini, J. Anderson, M. Andreotti, J.E. Andrews, R.B. Appleby, O. Aquines Gutierrez, F. Archilli, A. Artamonov, M. Artuso, E. Aslanides, G. Auriemma, M. Baalouch, S. Bachmann, J.J. Back, A. Badalov, C. Baesso, W. Baldini, R.J. Barlow, C. Barschel, S. Barsuk, W. Barter, V. Batozskaya, V. Battista, A. Bay, L. Beaucourt, J. Beddow, F. Bedeschi, I. Bediaga, L.J. Bel, I. Belyaev, E. Ben-Haim, G. Bencivenni, S. Benson, J. Benton, A. Berezhnoy, R. Bernet, A. Bertolin, M.-O. Bettler, M. van Beuzekom, A. Bien, S. Bifani, T. Bird, A. Bizzeti, T. Blake, F. Blanc, J. Blouw, S. Blusk, V. Bocci, A. Bondar, N. Bondar, W. Bonivento, S. Borghi, M. Borsato, T.J.V. Bowcock, E. Bowen, C. Bozzi, S. Braun, D. Brett, M. Britsch, T. Britton, J. Brodzicka, N.H. Brook, A. Bursche, J. Buytaert, S. Cadeddu, R. Calabrese, M. Calvi, M. Calvo Gomez, P. Campana, D. Campora Perez, L. Capriotti, A. Carbone, G. Carboni, R. Cardinale, A. Cardini, P. Carniti, L. Carson, K. Carvalho Akiba, R. Casanova Mohr, G. Casse, L. Cassina, L. Castillo Garcia, et al. (604 additional authors not shown)
EEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2015-072LHCb-PAPER-2015-010June 12, 2015
Observation of the decay B s → ψ (2 S ) K + π − The LHCb collaboration † Abstract
The decay B s → ψ (2 S ) K + π − is observed using a data set corresponding to anintegrated luminosity of 3 . − collected by the LHCb experiment in pp collisionsat centre-of-mass energies of 7 and 8 TeV. The branching fraction relative to the B → ψ (2 S ) K + π − decay mode is measured to be B ( B s → ψ (2 S ) K + π − ) B ( B → ψ (2 S ) K + π − ) = 5 . ± .
36 (stat) ± .
22 (syst) ± .
31 ( f s /f d ) % , where f s /f d indicates the uncertainty due to the ratio of probabilities for a b quark to hadronise into a B s or B meson. Using an amplitude analysis, thefraction of decays proceeding via an intermediate K ∗ (892) meson is measured tobe 0 . ± .
049 (stat) ± .
049 (syst) and its longitudinal polarisation fraction is0 . ± .
056 (stat) ± .
029 (syst). The relative branching fraction for this componentis determined to be B ( B s → ψ (2 S ) K ∗ (892) ) B ( B → ψ (2 S ) K ∗ (892) ) = 5 . ± .
57 (stat) ± .
40 (syst) ± .
32 ( f s /f d ) % . In addition, the mass splitting between the B s and B mesons is measured as M ( B s ) − M ( B ) = 87 . ± .
44 (stat) ± .
09 (syst) MeV /c . Published in Phys. Lett. B c (cid:13) CERN on behalf of the LHCb collaboration, license CC-BY-4.0. † Authors are listed at the end of this paper. a r X i v : . [ h e p - e x ] N ov i Introduction
The large data set collected by the LHCb experiment has allowed precision measurements oftime-dependent CP violation in the B s → J/ψφ and B s → J/ψf (980) decay modes [1,2]. The results are interpreted assuming that these decays are dominated by colour-suppressedtree-level amplitudes (Fig. 1). Higher-order penguin amplitudes, which are difficultto calculate in QCD, also contribute (Fig. 1). Reference [3] suggests that the size ofcontributions from these processes can be determined by studying decay modes such as B s → J/ψK ∗ (892) where they dominate. The B s → J/ψK ∗ (892) decay mode was firstobserved by the CDF collaboration [4] and subsequently studied in detail by the LHCbcollaboration [5]. W + ¯ cc ¯ d (¯ s ) ss ¯ b J/ψ ( ψ (2 S ))¯ K ∗ ( φ ) W + s s ¯ b ¯ u, ¯ c, ¯ t ¯ cc ¯ d (¯ s ) J/ψ ( ψ (2 S ))¯ K ∗ ( φ ) Figure 1: Tree (left) and penguin (right) topologies contributing to the B s ) → ψV decays where ψ = J/ψ, ψ (2 S ) and V = φ, K ∗ (892) . Recently, interest in b -hadron decays to final states containing charmonia has beengenerated by the observation of the Z (4430) − → ψ (2 S ) π − state in the B → ψ (2 S ) K + π − decay chain by the Belle [6–8] and LHCb collaborations [9]. As this state is chargedand has a minimal quark content of ccdu , it is interpreted as evidence for the existenceof non- qq mesons [10]. Evidence for similar exotic structures in B → χ c ,c K + π − and B → J/ψK + π − decays has been reported by the Belle collaboration [11, 12]. If thesestructures correspond to real particles they should be visible in other decay modes.This letter reports the first observation of the decay B s → ψ (2 S ) K + π − and presentsmeasurements of the inclusive branching fraction and the fraction of decays that proceedvia an intermediate K ∗ (892) resonance, as determined from an amplitude analysis ofthe final state. The amplitude analysis also allows the determination of the longitudinalpolarisation fraction of the K ∗ (892) meson. Additionally a measurement of the massdifference between B s and B mesons is reported that improves the current knowledge ofthis observable. The LHCb detector [13,14] is a single-arm forward spectrometer covering the pseudorapidityrange 2 < η <
5, designed for the study of particles containing b or c quarks. The detector Charge-conjugatation is implicit unless stated otherwise. pp interaction region, a large-area silicon-strip detector located upstreamof a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-stripdetectors and straw drift tubes [15] placed downstream of the magnet. The tracking systemprovides a measurement of momentum, p , of charged particles with a relative uncertaintythat varies from 0.5% at low momentum to 1.0% at 200 GeV /c . The minimum distanceof a track to a primary vertex, the impact parameter, is measured with a resolution of(15 + 29 /p T ) µ m, where p T is 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 concurrentlywith the data set used here, were used to calibrate the momentum scale of the spectrometerto 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 acalorimeter system consisting of scintillating-pad and preshower detectors, an electromag-netic calorimeter and a hadronic calorimeter. Muons are identified by a system composedof alternating layers of iron and multiwire proportional chambers [18]. The online eventselection is performed by a trigger [19], which consists of a hardware stage, based oninformation from the calorimeter and muon systems, followed by a software stage, whichapplies a full event reconstruction. In this analysis candidates are first required to passthe hardware trigger, which selects muons and dimuon pairs based on the transversemomentum. At the subsequent software stage, events are triggered by a ψ (2 S ) → µ + µ − candidate where the ψ (2 S ) is required to be consistent with coming from the decay of a b hadron by either using impact parameter requirements on daughter tracks or detachmentof the ψ (2 S ) candidate from the primary vertex.The analysis is performed using data corresponding to an integrated luminosity of1.0 fb − collected in pp collisions at a centre-of-mass energy of 7 TeV and 2.0 fb − collectedat 8 TeV. In the simulation, pp collisions are generated using Pythia [20] with a specificLHCb configuration [21]. Decays of hadronic particles are described by
EvtGen [22],in which final state radiation is generated using
Photos [23]. The interaction of thegenerated particles with the detector and its response are implemented using the
Geant4 toolkit [24] as described in Ref. [25].
The selection of candidates is divided into two parts. First, a loose selection is performedthat retains the majority of signal events whilst reducing the background substantially. Af-ter this the B → ψ (2 S ) K + π − peak is clearly visible. Subsequently, a multivariate methodis used to further improve the signal-to-background ratio and to allow the observation ofthe B s → ψ (2 S ) K + π − decay.The selection starts by reconstructing the dimuon decay of the ψ (2 S ) meson. Pairsof oppositely charged particles identified as muons with p T >
550 MeV /c are combined toform ψ (2 S ) candidates. The invariant mass of the dimuon pair is required to be within20 MeV /c of the known ψ (2 S ) mass [26]. To form B s ) candidates, the selected ψ (2 S )mesons are combined with oppositely charged kaon and pion candidates. Tracks that donot correspond to actual trajectories of charged particles are suppressed by requiring thatthey have p T >
250 MeV /c and by selecting on the output of a neural network trainedto discriminate between these and genuine tracks associated to particles. Combinatorialbackground from hadrons originating in the primary vertex (PV) is suppressed by requiringthat both hadrons are significantly displaced from any PV. Well-identified hadrons areselected using the information provided by the Cherenkov detectors. This is combinedwith kinematic information using a neural network to provide a probability that a particleis a kaon ( P K ), pion ( P π ) or proton ( P p ). It is required that P K is larger than 0.1 for the K + candidate and that P π is larger than 0.2 for the π − candidate.A kinematical vertex fit is applied to the B s ) candidates [27]. To improve the invariantmass resolution, the fit is performed with the requirement that the B s ) candidate pointsto the PV and the ψ (2 S ) is mass constrained to the known value [26]. A good quality ofthe vertex fit χ , χ , is required. To ensure good separation between the B and B s signals, the uncertainty on the reconstructed mass returned by the fit must be less than11 MeV /c . Combinatorial background from particles produced in the primary vertex isfurther reduced by requiring the decay time of the B s ) meson to exceed 0 . b -hadron decay modes.First, the candidate is rejected if the invariant mass of the hadron pair calculated assumingthat both particles are kaons is within 10 MeV /c of the known φ meson mass [26],suppressing B s → ψ (2 S ) φ decays where one of the kaons is misidentified as a pion. Second,to suppress B → ψ (2 S ) π + π − events where one of the pions is incorrectly identified asa kaon, it is required that P K > P π for the kaon candidate. This rejects 80 % of thebackground from this source whilst retaining 90 % of B s ) signal candidates. Third, tosuppress background from Λ b → ψ (2 S ) pπ − decays where the proton is misidentifed asa kaon, candidates with P p > . /c of the known Λ b mass [26] are discarded. Finally, to reduce background from a B + → ψ (2 S ) K + decaycombined with a random pion, candidates where the reconstructed ψ (2 S ) K + invariantmass is within 16 MeV /c of the known B + mass [26] are rejected. Background from thedecay Λ b → ψ (2 S ) pK − with misidentified hadrons does not peak at the B s mass and ismodelled in the fit.To further improve the signal-to-background ratio, a multivariate analysis based ona neural network is used. This is trained using simulated B signal events togetherwith candidates from data with a mass between 5500 and 5600 MeV /c that are not usedfor subsequent analysis. Eight variables that give good separation between signal andbackground are used: the number of clusters in the large-area silicon tracker upstreamof the magnet, P K for the kaon candidate, P π for the pion candidate, the transversemomentum of the B s ) , the minimum impact parameter to any primary vertex for each ofthe two hadrons, χ and the flight distance in the laboratory frame of the B s ) candidatedivided by its uncertainty. The ratio N S / √ N S + N B is used as a figure of merit, where N S ( N B ) is the number of signal (background) events determined from the invariant mass3t (see Sect. 4). The maximum value of this ratio is found for a threshold on the neuralnetwork output that rejects 98% of the background and retains 81% of the signal forsubsequent analysis. A maximum likelihood fit is made to the unbinned ψ (2 S ) K + π − invariant mass distribution, m ( ψ (2 S ) K + π − ), to extract the B and B s signal yields. The B signal component ismodelled by the sum of two Crystal Ball functions [28] with common tail parameters andan additional Gaussian component, all with a common mean. All parameters are fixedto values determined from the simulation apart from the common mean and an overallresolution scale factor. The simulation is tuned to match the invariant mass resolutionseen in data for the B + → J/ψK + and B → J/ψ K + π − decay modes. Consequently, theresolution scale factor is consistent with unity in the fit to data. The B s component ismodelled with the same function, with the mean value of the B s meson mass left free in thefit. The resolution parameters in this case are multiplied by a factor of 1.06, determinedfrom 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 B s → ψ (2 S ) φ decays is visible at lower masses thanthe B peak. This is modelled in the fit by a bifurcated Gaussian function where theshape parameters are constrained to the values obtained in the simulation and the yieldconstrained to the value determined in data under the hypothesis that both hadrons arekaons. Additional small components from B s ) → ψ (2 S ) π + π − and Λ b → ψ (2 S ) pK − decaysare modelled by bifurcated Gaussian functions. The shapes of these components are fixedusing the simulation and the yields are determined by normalising the simulation samplesto the number of candidates for each modes found in data using dedicated selections.Contributions from partially reconstructed decays are accounted for in the combinatorialbackground. In total, the fit has ten free parameters. Variations of this fit model areconsidered as systematic uncertainties.Figure 2 shows the invariant mass distribution observed in the data together with theresult of a fit to the model described above. Binning the data, a χ -probability of 0.30is found. The moderate mismodelling of the B peak is accounted for in the systematicuncertainties. The fit determines that there are 329 ± B s decays and 24207 ± B decays. The B s → ψ (2 S ) K + π − mode is observed with high significance.The precision of the momentum scale calibration of 0 .
03% translates to an uncertaintyon the B and B s meson masses of 0 . /c . Therefore, it is chosen to quote only themass difference in which this uncertainty largely cancels, M ( B s ) − M ( B ) = 87 . ± .
44 (stat) ± .
09 (syst) MeV /c . This procedure has been checked using the simulation, which gives the input mass differencewith a bias of 0 .
05 MeV /c that is assigned as a systematic uncertainty. Further systematicuncertainties arise from the momentum scale and mass fit model. Varying the momentum4 c ) [MeV/ − π + (2S) K ψ m( ) c C a nd i d a t e s / ( M e V / LHCb P u ll -6-4-20246 Figure 2: Invariant mass distribution for selected ψ (2 S ) K + π − candidates in the data. A fit tothe 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 theexclusive b → ψ (2 S ) X modes considered in the text by the shaded (blue) area. The maximum ofthe y -scale is restricted so as to be able to see more clearly the B s → ψ (2 S ) K + π − signal. Thelower plot shows the differences between the fit and measured values divided by the correspondinguncertainty of the measured value, the so-called pull distribution. scale by 0 .
03% leads to an uncertainty of 0 .
04 MeV /c . The effect of the fit model isevaluated by considering several variations: the relative fraction of the two Crystal Ballfunctions is left free; the slope of the combinatorial background is constrained usingcandidates where the kaon and pion have the same charge; the Gaussian constraintson the background from the B s → ψ (2 S ) φ mode are removed; and the tail parametersof the Crystal Ball functions are left free. The largest variation in the mass splittingis 0 .
06 MeV /c . The total systematic uncertainty is given by summing the individualcomponents in quadrature. Figure 3 shows the Dalitz plot of the selected B s → ψ (2 S ) K + π − candidates in the signalrange, m ( ψ (2 S ) K + π − ) ∈ [5350 , /c . There is a clear enhancement around theknown K ∗ (892) mass [26] and no other significant enhancements elsewhere. To determinethe fraction of decays that proceed via the K ∗ (892) resonance, an amplitude analysis5 c / ) [GeV - p + (K m ] c / ) [ G e V -p ( S ) y ( m Figure 3: Dalitz plot for the selected B s → ψ (2 S ) K + π − candidates in the signal window m ( ψ (2 S ) K + π − ) ∈ [5350 , /c .Figure 4: Definition of the helicity angles. is performed, similar to that used in Ref. [9] for the analysis of the B → ψ (2 S ) K + π − mode. The final-state particles are described using three angles Ω ≡ (cos θ K , cos θ µ , φ )in the helicity basis, defined in Fig. 4, and the invariant K + π − mass, m Kπ ≡ m ( K + π − ).The total amplitude is S ( m Kπ , Ω) ε ( m Kπ , Ω) + B ( m Kπ , Ω), where S ( m Kπ , Ω) representsthe coherent sum over the helicity amplitudes for each considered K + π − resonance ornon-resonant component. The detection efficiency, ε ( m Kπ , cos θ K , cos θ µ , φ ), is evaluatedusing simulation and parameterised using a combination of Legendre polynomials andspherical harmonic moments, given by ε ( m Kπ , cos θ K , cos θ µ , φ ) = (cid:88) a,b,c,d c abcd P a (cos θ K ) Y bc (cos θ µ , φ ) P d (cid:18) m Kπ − m min Kπ ) m max Kπ − m min Kπ − (cid:19) , (1) where m min(max) Kπ is the minimum (maximum) value allowed for m Kπ in the available phasespace of the decay. The coefficients of the efficiency parameterisation are computed by6 q cos -1 -0.5 0 0.5 1 A r b it r a r y un it s [rad] f -2 0 2 A r b it r a r y un it s K q cos -1 -0.5 0 0.5 1 A r b it r a r y un it s ] c ) [GeV/ - p + m(K A r b it r a r y un it s (a) (b)(c) (d) Figure 5: Distributions of (a) cos θ µ , (b) φ , (c) cos θ K and (d) m ( K + π − ) of simulated B s → ψ (2 S ) K + π − decays in a phase space configuration (black points) with the parameterisation ofthe efficiency overlaid (blue lines). summing over the N MC events simulated uniformly in the phase-space as c abcd = 1 N MC N MC (cid:88) i a + 12 2 d + 12 P a (cos θ K i ) Y bc (cos θ µi , φ i ) P d (cid:18) m Kπi − m min Kπ ) m max Kπ − m min Kπ − (cid:19) Cg i , (2)where g i = p i q i , with p i ( q i ) being the momentum of the K + π − system ( K + meson) inthe B ( K + π − ) rest frame and C is a normalising constant with units GeV /c . Thisapproach provides a description of the multidimensional correlations without assumingfactorisation. In practice, the sum is over a finite number of moments ( a ≤ b ≤ c ≤ d ≤
2) and only coefficients with a statistical significance larger than five standarddeviations from zero are retained. The one-dimensional projections of the parameterisedefficiency are shown in Fig. 5, superimposed on the simulated event distributions.The background probability density function, B ( m Kπ , Ω), is determined using a similarmethod as for the efficiency parameterisation. In this case the sum in Eq. (2) is over theselected events with m ( ψ (2 S ) K + π − ) > /c and g i ≡
1. Only moments with a ≤ b = 0, c = 0 and d ≤ q cos -1 -0.5 0 0.5 1 A r b it r a r y un it s [rad] f -2 0 2 A r b it r a r y un it s K q cos -1 -0.5 0 0.5 1 A r b it r a r y un it s ] c ) [GeV/ - p + m(K A r b it r a r y un it s (a) (b)(c) (d) Figure 6: Distributions of (a) cos θ µ , (b) φ , (c) cos θ K and (d) m ( K + π − ) of B s ) → ψ (2 S ) K + π − candidates with m ( ψ (2 S ) K + π − ) > /c (black points), with the parameterisation of thebackground distribution overlaid (blue lines). distribution are shown in Fig. 6, superimposed on the sideband data. As a consistencycheck, the ( m Kπ , Ω) distributions for events with m ( ψ (2 S ) K + π − ) > /c are foundto be compatible with the same distributions obtained from a like-sign ( ψ (2 S ) K ± π ± )sample.The default amplitude model is constructed using contributions from the K ∗ (892) resonance and a K + π − S-wave modelled using the LASS parameterisation [29]. Themagnitudes and phases of all components are measured relative to those of the zero helicitystate of the K ∗ (892) meson and the masses and widths of the resonances are fixed totheir known values [26]. The remaining eight free parameters are determined using amaximum likelihood fit of the amplitude to the data in the signal window. The backgroundfraction is fixed to 0 .
28, as determined from the fit described in Sect. 4. The fit fraction forany resonance R is defined in the full phase space, as f R = (cid:82) S R d m Kπ dΩ / (cid:82) S d m Kπ dΩ,where S R is the signal amplitude with all amplitude terms set to zero except those for R .The fractions of each component determined by the fit are f K ∗ (892) = 0 . ± . f S − wave = 0 . ± . K + π − resonances, including the introduction of the8 q cos -1 -0.5 0 0.5 1 C a nd i d a t e s / ( . ) -1 -0.5 0 0.5 1 P u ll -3-2-10123 (a) [rad] f -2 0 2 C a nd i d a t e s / ( . r a d ) -2 0 2 P u ll -2-1012 (b) K q cos -1 -0.5 0 0.5 1 C a nd i d a t e s / ( . ) -1 -0.5 0 0.5 1 P u ll -3-2-10123 (c) ] c ) [GeV/ - p + m(K ) c C a nd i d a t e s / ( . G e V / P u ll -6-4-202 (d) Figure 7: Distributions of (a) cos θ µ , (b) φ , (c) cos θ K and (d) m ( K + π − ) for selected B s → ψ (2 S ) K + π − candidates (black points) with the projections of the fitted amplitude model overlaid.The following components are included in the model: K ∗ (892) (red dashed), LASS S-wave(green dotted), and background (grey dashed-dotted). The residual pulls are shown below eachdistribution. spin-2 K ∗ (1430) meson or an exotic Z − c meson, are considered but found to give largervalues of the Poisson likelihood χ [30] per degree of freedom or lead to components with fitfractions that are consistent with zero. For each model the number of degrees of freedom iscalibrated using simulated experiments. The variations in amplitude model are consideredas sources of systematic uncertainty. The longitudinal polarisation fraction of the K ∗ (892) meson is defined as f L = H / ( H + H + H − ), where H , + , − are the magnitudes of the K ∗ (892) helicity amplitudes. This is measured to be f L = 0 . ± . K + π − mass are shown in Fig. 7. A summary of possible sources of systematic uncertainties that affect the amplitudeanalysis is reported in Table 1. The size of each contribution is determined using a set of9 able 1: Summary of systematic uncertainties on the K ∗ (892) fit fraction and f L . Rows markedwith (*) refer to uncorrelated sources of uncertainty between the B s and B modes for thecomputation of the ratio of branching fractions. Source K ∗ (892) fit fraction f L (*) K + π − amplitude model 0.028 0.017(*) S-wave model 0.018 0.010 K ∗ resonance widths 0.005 0.008Blatt-Weisskopf radius 0.014 0.003Breit-Wigner parameters ( m R vs . m Kπ ) 0.026 0.005(*) Background parameterisation 0.014 0.012(*) Background normalisation 0.007 0.011Efficiency model (parameterisation) 0.011 0.007Efficiency model (neural net) 0.002 0.004Quadrature sum of systematic uncertainties 0.049 0.029Quadrature sum of uncorrelated systematic uncertainties 0.037 0.026Statistical uncertainty 0.049 0.056simulated experiments, of the same size as the data, generated under the hypothesis ofan alternative amplitude model. These are fitted once with the default model and againwith the alternative model. The experiment-by-experiment difference in the measured fitfractions and f L is then computed and the sum in quadrature of the mean and standarddeviation is assigned as a systematic uncertainty to the corresponding parameter.The systematic dependence on the K + π − amplitude model is determined using theabove procedure, where the alternative model also contains a spin-2 K ∗ (1430) component.This leads to the dominant systematic uncertainty on the K ∗ (892) fit fraction and f L .The systematic dependence on the K + π − S-wave model is determined using simulatedexperiments where a combination of a non-resonant term and a K ∗ (1430) contribution isused in place of the LASS parameterisation. In addition, the amplitude model containsparameters that are fixed in the default fit such as the masses and widths of the resonancesand the Blatt-Weisskopf radius. The radius controls the effective hadron size and is setto 1 . /c ) − by default. Alternative models are considered where this is changed to3 . /c ) − and 0 . /c ) − .A large source of systematic uncertainty comes from the choice of convention for themass, m , in the ( p/m ) L R terms of the amplitude. The default amplitude model follows theconvention in Ref. [26] by using the resonance mass. This is different to that in Ref. [9]where the running resonance mass ( m Kπ ) is used in the denominator. This choice ismotivated by the improved fit quality obtained when using the resonance mass.The systematic uncertainty related to the combinatorial background parameterisationis determined using an amplitude model with an alternative background description thatallows for higher moment contributions ( a ≤ b ≤ c ≤ d ≤ m ( ψ (2 S ) K + π − ) distributionand is fixed in the amplitude fit. The systematic uncertainty related to the level ofthe background is estimated by using an amplitude model with the background fractionmodified by ± a ≤ b ≤ c ≤ d ≤ B and B s mesons. Two ratios of branching fractions are calculated, B ( B s → ψ (2 S ) K + π − ) / B ( B → ψ (2 S ) K + π − ) and B ( B s → ψ (2 S ) K ∗ (892) ) / B ( B → ψ (2 S ) K ∗ (892) ). These are deter-mined from the signal yields given in Sect. 4 correcting for the relative detector acceptanceusing simulation. The simulated B s samples are reweighted with the results of the angularanalysis presented in Sect. 5. Similarly, the B simulated data are reweighted to matchthe results given in Ref. [9]. For the inclusive branching ratio, the relative efficiencybetween the two modes is found to be 0 . ± .
014 whilst for the K ∗ (892) component it is1 . ± . . p T spectra of the B meson areseen comparing data and the reweighted simulation. If the p T spectrum in the simulationis further reweighted to match the data, the efficiency ratio changes by 0 . K + π − amplitude model for the B s channel, thesimulated events are reweighted using a model consisting of the K ∗ (892) resonance,the LASS [29] description of the S-wave and the K ∗ (1430) resonance. This changes theefficiency ratio by 0 . K ∗ (892) branching ratio, the fraction of candidates from this source is needed. For the B s channel this is determined from the amplitude analysis to be 0 . ± . ± .
049 and thecorresponding fraction for the B channel is 0 . ± .
009 [9], leading to a 6 .
0% systematicuncertainty. All of the uncertainties discussed above are summarised in Table 2. Thelimited knowledge of the fragmentation fractions, f s /f d = 0 . ± .
015 [31–33], results inan uncertainty of 5 . able 2: Systematic uncertainties on the ratio of branching fractions.Relative uncertainty %Source Inclusive K ∗ (892) Simulation sample size 1.4 2.2Fit model 3.7 3.7Detector acceptance 0.7 0.7 K + π − amplitude model 0.6 – K ∗ (892) fit fraction – 6.0Quadrature sum 4.1 7.4 Using a data set corresponding to an integrated luminosity of 3 . − collected in pp collisions at centre-of-mass energies of 7 and 8 TeV, the decay B s → ψ (2 S ) K + π − isobserved. The mass splitting between the B s and B mesons is measured to be M ( B s ) − M ( B ) = 87 . ± .
44 (stat) ± .
09 (syst) MeV /c . This is consistent with, though less precise than, the value 87 . ± .
31 MeV /c obtainedby averaging the results in Refs. [34, 35]. Averaging the two numbers gives M ( B s ) − M ( B ) = 87 . ± .
26 MeV /c . The ratio of branching fractions between the B s and B modes is measured to be B ( B s → ψ (2 S ) K + π − ) B ( B → ψ (2 S ) K + π − ) = 5 . ± .
36 (stat) ± .
22 (syst) ± .
31 ( f s /f d ) % . The fraction of decays proceeding via an intermediate K ∗ (892) meson is measured withan amplitude analysis to be 0 . ± .
049 (stat) ± .
049 (syst). No significant structure isseen in the distribution of m ( ψ (2 S ) π − ).The longitudinal polarisation fraction, f L , of the K ∗ (892) meson is determinedas 0 . ± .
056 (stat) ± .
029 (syst). This is consistent with the value measuredin the corresponding decay that proceeds through an intermediate
J/ψ meson, f L = 0 . ± .
08 (stat) ± .
02 (syst) [5]. The present data set does not allow a test ofthe prediction given in Ref. [36] that f L should be lower for decays closer to the kinematicendpoint.Using the K ∗ (892) fraction determined in this analysis for the B s component, thecorresponding number for the B mode from Ref. [9], and the efficiency ratio given inSect. 6, the following ratio of branching fractions is measured B ( B s → ψ (2 S ) K ∗ (892) ) B ( B → ψ (2 S ) K ∗ (892) ) = 5 . ± .
57 (stat) ± .
40 (syst) ± .
32 ( f s /f d ) % . B s → ψ (2 S ) K + π − mode may be useful for future studies that attempt to control thesize of loop-mediated processes that influence CP violation studies and offers promisingopportunities in the search for exotic resonances. Acknowledgements
We express our gratitude to our colleagues in the CERN accelerator departments forthe excellent performance of the LHC. We thank the technical and administrative staffat the LHCb institutes. We acknowledge support from CERN and from the nationalagencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3(France); BMBF, DFG, HGF and MPG (Germany); INFN (Italy); FOM and NWO (TheNetherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO(Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (UnitedKingdom); 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 themultiple open source software packages on which we depend. We are also thankful forthe computing resources and the access to software R&D tools provided by Yandex LLC(Russia). Individual groups or members have received support from EPLANET, MarieSk(cid:32)lodowska-Curie Actions and ERC (European Union), Conseil g´en´eral de Haute-Savoie,Labex ENIGMASS and OCEVU, R´egion Auvergne (France), RFBR (Russia), XuntaGaland GENCAT (Spain), Royal Society and Royal Commission for the Exhibition of 1851(United Kingdom).
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Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil Center for High Energy Physics, Tsinghua University, Beijing, China LAPP, Universit´e Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany School of Physics, University College Dublin, Dublin, Ireland Sezione INFN di Bari, Bari, Italy Sezione INFN di Bologna, Bologna, Italy Sezione INFN di Cagliari, Cagliari, Italy Sezione INFN di Ferrara, Ferrara, Italy Sezione INFN di Firenze, Firenze, Italy Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy Sezione INFN di Genova, Genova, Italy Sezione INFN di Milano Bicocca, Milano, Italy Sezione INFN di Milano, Milano, Italy Sezione INFN di Padova, Padova, Italy Sezione INFN di Pisa, Pisa, Italy Sezione INFN di Roma Tor Vergata, Roma, Italy Sezione INFN di Roma La Sapienza, Roma, Italy Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,Krak´ow, Poland National Center for Nuclear Research (NCBJ), Warsaw, Poland Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia Institute for High Energy Physics (IHEP), Protvino, Russia Universitat de Barcelona, Barcelona, Spain Universidad de Santiago de Compostela, Santiago de Compostela, Spain European Organization for Nuclear Research (CERN), Geneva, Switzerland Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, TheNetherlands NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine University of Birmingham, Birmingham, United Kingdom H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom Department of Physics, University of Warwick, Coventry, United Kingdom STFC Rutherford Appleton Laboratory, Didcot, United Kingdom School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom Imperial College London, London, United Kingdom School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom Department of Physics, University of Oxford, Oxford, United Kingdom Massachusetts Institute of Technology, Cambridge, MA, United States University of Cincinnati, Cincinnati, OH, United States University of Maryland, College Park, MD, United States Syracuse University, Syracuse, NY, United States Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to
Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China, associated to
Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia, associated to
Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to
National Research Centre Kurchatov Institute, Moscow, Russia, associated to
Yandex School of Data Analysis, Moscow, Russia, associated to
Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC, Valencia, Spain, associated to