Precise measurements of the properties of the B1(5721)0,+ and B *2(5747)0,+ states and observation of B+,0π−,+ mass structures

JHEP04(2015)024 Published for SISSA by Springer Received:February 11, 2015 Accepted:March 11, 2015 Published:April 7, 2015 Precise measurements of the properties of the B1(5721)0,+and B∗ 2(5747)0,+states and observation of B+,0π−,+mass structures The LHCb collaboration E-mail: [email protected] Abstract: Invariant mass distributions of B+π−and B0π+combinations are investigated in order to study excited Bmesons. The analysis is based on a data sample corresponding to 3.0 fb−1of pp collision data, recorded by the LHCb detector at centre-of-mass energies of 7 and 8 TeV. Precise measurements of the masses and widths of the B1(5721)0,+and B∗ 2(5747)0,+states are reported. Clear enhancements, particularly prominent at high pion transverse momentum, are seen over background in the mass range 5850–6000 MeV in both B+π−and B0π+combinations. The structures are consistent with the presence of four excited Bmesons, labelled BJ(5840)0,+and BJ(5960)0,+, whose masses and widths are obtained under different hypotheses for their quantum numbers. Keywords: Spectroscopy, Hadron-Hadron Scattering, QCD, B physics, Flavor physics ArXiv ePrint: 1502.02638 Open Access, Copyright CERN, for the benefit of the LHCb Collaboration. Article funded by SCOAP3. doi:10.1007/JHEP04(2015)024 JHEP04(2015)024 Contents 1 Introduction 1 2 Detector and dataset 4 3 Event selection 4 4 Fit model 6 5 Fit results 9 6 Systematic uncertainties 10 7 Interpretation and conclusions 14 A Covariance matrices 18 The LHCb collaboration 22 1 Introduction The properties of excited Bmesons containing a light quark can be described in the context of heavy quark effective theory (HQET) [1]. Since the mass of the bquark is much larger than the QCD scale, the Lagrangian can be expanded in powers of 1/mb, where the leading term defines the static limit (mb→ ∞). In the heavy quark approximation, the Bmesons are characterised by three quantum numbers: the orbital angular momentum L(S, P, D for L= 0,1,2 respectively) of the light quark, its total angular momentum jq=|L±1 2|, and the total angular momentum J=|jq±1 2|of the Bmeson. The spectroscopic notation has the form n2S+1LJ, where S= 0 or 1 is the sum of the quark spins and where the quantum number ndescribes the radial excitations of the state. The PDG notation [2] (which is used in this paper) has the form B(∗) J(m) or B(∗) J(nL), where mis the mass in units of MeV,1the ∗superscript is given to those states with natural spin-parity P= (−1)J (JP= 0+,1−,2+, . . .), and the subscript Jis omitted for pseudoscalar and vector states. A prime may be used to distinguish two states with the same quantum numbers. For L= 0, there are two possible (J;jq) combinations, both parity-odd, corresponding to the Bmeson ground state with JP= 0−and to the excited B∗state with JP= 1−. Higher excitations are collectively referred to as B∗∗ states and decay strongly to lighter Bmesons and pions. For L= 1 there are four different possible (J;jq) combinations, all parity-even. Predictions for the masses of such states and higher excitations spread over – 1 – JHEP04(2015)024 Mass [GeV] 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 πB π*B B *B (2S)B*(2S)B (3S)B*(3S)B * 0 B ' 1 B1 B* 2 B *(2P) 0 B'(2P) 1 B(2P) 1 B*(2P) 2 B * 1 B' 2 B 2 B * 3 B *(2D) 1 B'(2D) 2 B(2D) 2 B*(2D) 3 B J L +1S2 q j P J 0 S 1 1/2 - 0 1 S 3 1/2 - 1 0 P 1 1/2 + 0 1 P 3 1/2 + 1 1 P 1 3/2 + 1 2 P 3 3/2 + 2 1 D 1 3/2 - 1 2 D 3 3/2 - 2 2 D 1 5/2 - 2 3 D 3 5/2 - 3 Figure 1. Mass predictions of the excited Bstates [3–10]. The boxes cover the range of predictions for the masses of each state, and the red dots indicate the measured values. The horizontal lines correspond to the Bπ (red) and B∗π(blue) thresholds. a wide range of values, as shown in figure 1[3–10]. As can be seen in figure 1, the states come in doublets (two values of Jfor each jq), and within each doublet, one has natural and one unnatural spin-parity quantum numbers. States with natural spin-parity (except for 0+) can decay to both Bπ and B∗πfinal states. States with unnatural spin-parity cannot decay to the pseudoscalar-pseudoscalar Bπ final state due to parity conservation, but may decay to B∗π(table 1). Since the B∗meson decays to Bγ, the signature from a doublet of B∗∗ states is given by three peaks in the Bπ mass spectrum (unless the doublet includes a 0+state): one from the natural spin-parity state decay to Bπ, and two from both states decaying to B∗πwith a missing photon. Due to the missing photon, the peaks from B∗πdecays are shifted down from the true B∗∗ mass by the difference between the B∗and Bmasses (this feature recently allowed a precise determination of the B∗−Bmass difference from the B+K−spectrum [11]). Depending on the widths of the states and the mass resolution, two or all three of these peaks may overlap and be hard to distinguish experimentally. The B∗ 0and B0 1states are predicted to be very broad [3,10] since they decay via S-wave (the comparable states in the charm sector have widths of around 300 MeV [2]). However, the B1and B∗ 2states decay only via D-wave and are predicted [3,10] and observed [2] to be much narrower. Higher states such as the B(2S), 1Natural units where ~=c= 1 are used. – 2 – JHEP04(2015)024 JPAllowed decay mode Bπ B∗π 0+yes no 0−,1+,2−, . . . no yes 1−,2+,3−, . . . yes yes Table 1. Allowed decay modes for the excited Bstates. B∗(2S), B2(1D) and B∗ 3(1D) are predicted to have widths in the 100–200 MeV range [10], consistent with the recent measurement of the properties of the D∗ s3(1D) state [12,13]. In contrast to the situation in the charm sector, there is relatively little experimental information concerning Bmeson spectroscopy. The B1(5721)0and B∗ 2(5747)0states have been observed by the CDF [14] and D0 [15] experiments, and recently the CDF collaboration has presented results on the charged isospin partners, together with evidence for a higher mass resonance [16]. This result has prompted theoretical speculation about the origin of the new state [17–21]. While in the Dmeson system amplitude analyses of excited states produced in Bdecays can be used to determine their spin and parity (see, for example, refs. [12,13,22]), in the Bmeson system it is very difficult to assign with certainty quantum numbers to observed states. The labelling of the states follows the quark-model expectations for the quantum numbers, which have not been experimentally verified. In this paper, the results of a study of B+π−and B0π+combinations are presented. The inclusion of charge-conjugate processes is implied throughout. The analysis is based on a data sample corresponding to 3.0 fb−1of LHC pp collision data recorded with the LHCb detector at centre-of-mass energies of 7 and 8 TeV. The Bmesons are reconstructed in the J/ψK+,D0π+,D0π+π+π−,J/ψK∗0,D−π+ and D−π+π+π−channels, with subsequent J/ψ →µ+µ−,D0→K+π−and K+π−π+π−, D−→K+π−π−and K∗0→K+π−decays. The Bmeson candidates are required to originate from a primary pp collision vertex (PV), and are combined with pions originating from the same PV (referred to as “companion pions”). Both “right-sign” (RS) and “wrongsign” (WS) combinations are considered, where the latter are those with quark-content that precludes that the pair originates from the strong decay of an excited Bmeson (e.g. B+π+) and are used to model the combinatorial background. Excited Bmesons are seen as peaks in the RS invariant mass distributions, and are fitted with relativistic Breit-Wigner (RBW) functions. An additional very broad component, observed in the RS and not in the WS combinations, is referred to as “associated production” (AP) in this paper. The AP contribution may originate from very broad resonances or from correlated nonresonant production of Bmesons and companion pions in the fragmentation chain. The remainder of the paper is organised as follows. A brief description of the LHCb detector is given in section 2. The selection requirements are described in section 3, the fit model is discussed in section 4, and the nominal fit results are given in section 5, with the evaluation of the systematic uncertainties in section 6. Interpretation of the results and a summary are given in section 7. – 3 – JHEP04(2015)024 2 Detector and dataset The LHCb detector [23,24] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing bor c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector [25] 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 [26] placed downstream of the magnet. The tracking system provides a momentum measurement with relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV, and an impact parameter measurement with resolution of 20 µm for tracks with large momentum transverse to the beamline (pT). Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors [27]. Photon, electron and hadron candidates 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 [28]. The trigger [29] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which uses information from the vertex detector and tracking system. In the simulation, pp collisions are generated using Pythia [30] with a specific LHCb configuration [31]. Decays of hadronic particles are described by EvtGen [32], in which final-state radiation is generated using Photos [33]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [34, 35] as described in ref. [36]. 3 Event selection The Bmeson candidates in each decay mode are reconstructed using a set of loose selection requirements to suppress the majority of the combinatorial backgrounds. The selection criteria are similar to those used in previous analyses of the same channels [37–40]. The B+→J/ψK+and B0→J/ψK∗0selections require a Bcandidate with pT>3 GeV and a decay time of at least 0.3 ps. For the other decay modes, the selection explicitly requires that the software trigger decision is based only on tracks from which the Bmeson candidate is formed. No requirement is imposed on how the event was selected at the hardware trigger stage. Additional loose selection requirements are placed on variables related to the Bmeson production and decay, such as transverse momentum and quality of the track fits for the decay products, detachment of the Bcandidate from the PV, and whether the momentum of the Bcandidate points back to the PV. Because B0mesons oscillate, the distinction between RS and WS combinations is clearest at short B0decay times, and hence only B0candidates with decay time below 2 ps are used in the analysis. The mass distributions for the B+and B0candidates are shown in figure 2. Only B meson candidates falling within 25 MeV of the nominal Bmass for the decay modes containing J/ψ mesons, or within 50 MeV for the other modes, are selected for further analysis. – 4 – JHEP04(2015)024 [MeV] ]π,3π [ 0 D m 5200 5250 5300 5350 Candidates / ( 4 MeV ) 0 20 40 60 80 100 120 3 10× LHCb (a) [MeV] KψJ/ m 5200 5250 5300 5350 Candidates / ( 4 MeV ) 0 50 100 150 200 250 3 10× LHCb (b) [MeV] ]π,3π [ ± D m 5200 5250 5300 5350 Candidates / ( 4 MeV ) 0 10000 20000 30000 40000 50000 60000 70000 80000 LHCb (c) [MeV] * KψJ/ m 5200 5250 5300 5350 Candidates / ( 4 MeV ) 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 LHCb (d) Figure 2. Mass distributions of the B+and B0candidates reconstructed through (a) B+→ D0(π+, π+π+π−), (b) B+→J/ψK+, (c) B0→D−(π+, π+π+π−), and (d) B0→J/ψK∗0decays. The J/ψ,D0and D−masses are constrained to their world average values [2]. Results of fits are superimposed for illustration. The signal (dot-dashed red line) is modelled with a double Crystal Ball [41] distribution, while the background (dashed black line) is modelled with a second-order polynomial. The total fit is shown as a solid blue line. Samples of about 1.2 million B0and 2.5 million B+candidates are obtained, with purity depending on decay mode and always larger than 80%. Each candidate is combined with any track that originates from the same PV and that is identified as a pion. The particle identification requirements on the companion pion are chosen to reduce potential backgrounds from misidentified particles to a level where they can be neglected in the analysis. Over the momentum range relevant for this analysis, the pion identification requirements are 81% efficient at identifying pions, while they have 3.1% and 2.6% probabilities respectively to misidentify a kaon or a proton as a pion. Since the production of B∗∗0 smesons is likely to be suppressed relative to the production of B∗∗ states, as has been observed for the ground states [42,43], these requirements are expected to reduce background from the decays Bs1(5830)0→B∗+K−and B∗ s2(5840)0→B∗+K−or B+K−, where the kaon is misidentified as a pion, to a negligible level. Further selection requirements are placed on the B∗∗ candidate. The invariant mass and χ2/ndf (ndf is the number of degrees of freedom) of the B∗∗ candidate vertex fit are calculated constraining the Bcandidates and companion pion to originate from the PV, and also constraining the known Bmeson mass, and the masses of intermediate J/ψ,D0 and D−mesons in the Bdecay. The χ2/ndf of the B∗∗ candidate vertex fit is then required to be below 3.5. In order to reduce combinatorial backgrounds, the PV associated with the B∗∗ candidate is required to have fewer than 75 charged particles associated with it. – 5 – JHEP04(2015)024 [MeV]) - π)-m( + -m(B) - π + m(B 200 400 600 800 1000 1200 1400 Candidates/(8 MeV) 8000 10000 12000 14000 16000 LHCb [MeV]) - π)-m( + -m(B) - π + m(B 200 400 600 800 1000 1200 1400 Candidates/(8 MeV) 0 100 200 300 400 500 600 LHCb > 2 GeV T Companion p ) [MeV] + π)-m( 0 )-m(B + π 0 m(B 200 400 600 800 1000 1200 1400 Candidates/(8 MeV) 1500 2000 2500 3000 3500 4000 4500 LHCb ) [MeV] + π)-m( 0 )-m(B + π 0 m(B 200 400 600 800 1000 1200 1400 Candidates/(8 MeV) 0 20 40 60 80 100 120 140 160 180 200 220 LHCb > 2 GeV T Companion p Figure 3. Distributions of the Qvalues of the B∗∗ candidates after the selection for the (top) B+and (bottom) B0candidates. The white histograms represent the RS combinations, while the overlaid shaded red histograms represent the WS combinations. The right hand plots are made after applying an additional requirement of pT>2 GeV on the companion pion. The angle θis required to satisfy cos θ > −0.5, where θis the angle between the pion in the Bπ rest frame and the opposite direction of the boost vector from the Bπ rest frame to the laboratory frame. Finally, the companion pion is required to have more than (0.5) 5 GeV of (transverse) momentum, while the Bcandidate is required to have pT>10 GeV for candidates where the companion pion has pT>2 GeV. In any selected event, the Bcandidate can potentially be combined with several different pions to create B∗∗ candidates. The average number of candidates per selected event is 1.4 and all of them are used for the subsequent analysis. 4 Fit model The distributions of the mass difference, Q≡m(Bπ)−m(B)−m(π), following these selection requirements are shown in figure 3for both RS and WS B∗∗ candidates, where mBand mπare the known masses of the Bmeson and the pion [2]. All Bdecay modes are combined in figure 3and in the subsequent analysis. Two narrow peaks are seen in both B+π−and B0π+mass difference distributions, corresponding to the B1(5721)0,+→B∗π signal overlapping with the B∗ 2(5747)0,+→B∗πdecay, and the B∗ 2(5747)0,+→Bπ decay. In addition, an excess of RS over WS combinations around Q∼500 MeV is particularly prominent after requiring the companion pion to have pT>2 GeV. This peak could result from a combination of two heavier B∗∗ resonances, consistent with the expectation that B∗∗ states come in doublets, as described in section 1; the structure is further analysed as – 6 – JHEP04(2015)024 described below. Furthermore, a comparison with the WS distributions shows a very broad excess of RS combinations lying under the resonances, corresponding to AP as discussed in section 1. The Q-value distributions of B+π−and B0π+candidates are fitted independently to determine the masses and widths of the various resonant signals. In order to increase sensitivity to the parameters of the high mass states, the fits are performed in three bins of companion pion pT: 0.5< pT≤1 GeV, 1 < pT≤2 GeV and pT>2 GeV. The fits minimise the total χ2of the Q-value distributions (in bins of width 1 MeV) simultaneously for the three companion pion pTbins. The combinatorial background shape is obtained from WS combinations. It has been checked that the WS background consists of purely combinatorial background by studying Bπ combinations in which a Bmeson from one event is combined with a companion pion from another event; consistent shapes are found. The WS Q-value distributions are fitted with piecewise-defined, smooth polynomial (“spline”) functions. The shape is fixed in the subsequent fit to the RS distribution, but the yield is allowed to vary. Resonances are modelled with RBW lineshapes [44], given by ARBW(m) = Γ(m) m2−m2 02+m2 0Γ2(m),(4.1) where mis the Bπ invariant mass (which is trivially related to the Qvalue), m0is the mass value for the resonance2and Γ(m) is the mass dependent width Γ(m) = Γ0 m0 mq(m) q(m0)2l+1 F2 l.(4.2) In the latter equation Γ0is the natural width, q(m) is the Bor πmomentum in the rest frame of the resonance and lis the orbital angular momentum between the Band πmesons. The Blatt-Weisskopf form factors Fl[45,46] account for the fact that the maximum angular momentum is limited by the phase-space in the decay. Defining the dimensionless quantity z(m) = q2(m)R2, where Ris the effective radius, Flis defined as F0= 1 , F1=s1 + z(m0) 1 + z(m), F2=s(z(m0)−3)2+ 9z(m0) (z(m)−3)2+ 9z(m).(4.3) Depending on the fit model, the B∗∗ resonances are described by five or six RBW shapes: •one for the B1(5721)0,+→B∗πfeed-down into the left narrow peak with width, yield, and mean free to vary in the fits; 2The mass difference m0−m(B)−m(π) is referred to as the mean µhereafter. – 7 – JHEP04(2015)024 •one for the B∗ 2(5747)0,+→Bπ signal (the right narrow peak) with width, yield, and mean free to vary in the fits; •one for the B∗ 2(5747)0,+→B∗πfeed-down into the left narrow peak with width fixed to be the same as that of the B∗ 2(5747)0,+→Bπ signal, mean shifted from the B∗ 2(5747)0,+→Bπ peak by the known B∗−Bmass difference, 45.0±0.4 MeV [2], and relative yield in pTbins constrained as described later; •two (or three) for the higher mass components, with widths, means, and yields free to vary in the fits (except in the three RBW case, where two of the means are constrained by the B∗−Bmass difference). The alternative descriptions for the higher mass resonances are motivated by the lack of knowledge of their quantum numbers. As described in section 1, a doublet of states is expected to give rise to three peaks. For example, for the (B(2S), B∗(2S)) doublet the higher (lower) mass of the pair has natural (unnatural) spin-parity. The description with three RBW shapes, two of which are constrained to have means offset by the B∗−Bmass difference, is therefore a physically motivated choice, obtained by applying quark-model expectations to the new states. However, there are two possibilities for this configuration, since it may be either the lower or the higher of the states that gives rise to two peaks. The alternative, with only two RBW shapes, is an empirical model, that corresponds to the minimal choice necessary to obtain a satisfactory description of the data. This is taken as the default and is referred to hereafter as the empirical model, but results of alternative fits with three RBW shapes are also presented. The RBW shapes have several parameters which need to be fixed in the fits, in particular the spin and effective radius input to the Blatt-Weisskopf form factors. The B1(5721)0,+ and B∗ 2(5747)0,+resonances are assigned spin 1 and 2, respectively, and are both assumed to decay via D-wave (l= 2), while the two higher mass resonances are assigned spin 0 (l= 0) in the default fit. The effective radius is fixed to 4 GeV−1[13]. The mass resolution is around 2 MeV which is negligible compared to the natural widths (>20 MeV) of the resonances, and is therefore not modelled. The variation of the signal reconstruction efficiency with Qvalue is described with a fifth-order polynomial function with parameters determined from simulation. All signal parameters except the yields are shared between the different pTbins and Bmeson decay modes, though the efficiency function is determined independently for each pTbin. The AP component is caused by correlations between the Bmeson and the companion pion, and as such is not present in either the WS sample or in a sample obtained by mixing Bmesons and pions from different events. As there is no suitable data control sample from which it can be constrained, it must be empirically modelled. The AP is modelled by a sixth-order polynomial shape determined from simulation with an additional broad spin-0 RBW function to account for possible data-simulation differences. The latter component is introduced since the modelling of fragmentation effects in the simulation is expected to be imprecise. – 8 – JHEP04(2015)024 the Q-value distributions reported in section 5can be converted into absolute masses using the known Band πmeson masses and the B∗−Bmass difference [2], leading to mB1(5721)0= 5727.7±0.7±1.4±0.17 ±0.4 MeV , mB∗ 2(5747)0= 5739.44 ±0.37 ±0.33 ±0.17 MeV , mB1(5721)+= 5725.1±1.8±3.1±0.17 ±0.4 MeV , mB∗ 2(5747)+= 5737.20 ±0.72 ±0.40 ±0.17 MeV , ΓB1(5721)0= 30.1±1.5±3.5 MeV , ΓB∗ 2(5747)0= 24.5±1.0±1.5 MeV , ΓB1(5721)+= 29.1±3.6±4.3 MeV , ΓB∗ 2(5747)+= 23.6±2.0±2.1 MeV . The listed uncertainties are, from left to right: the statistical uncertainty, the experimental systematic uncertainty, and, where applicable, the uncertainty on the Bmeson mass and the uncertainty on the B∗−Bmass difference. Note that B1(5721)0,+and B∗ 2(5747)0,+ notations are maintained here for consistency with the previous literature, even though the values of the masses no longer agree with these labels within uncertainty. The results reported above are the most precise determinations of these quantities to date. The relative branching fractions for the B∗ 2(5747)0,+decays are measured to be BB∗ 2(5747)0→B∗+π− B(B∗ 2(5747)0→B+π−)= 0.71 ±0.14 ±0.30 , BB∗ 2(5747)+→B∗0π+ B(B∗ 2(5747)+→B0π+)= 1.0±0.5±0.8, where the uncertainties are statistical and systematic, respectively. The significances of the B∗ 2(5747)0,+→B∗πdecays are evaluated using a likelihood ratio test. Values of 6.5σand 1.8σare obtained for B∗+π−and B∗0π+, respectively, when only the statistical uncertainty is considered. The inclusion of systematic uncertainties reduces the significance for the B∗+π−case to 3.7σ. This result therefore corresponds to the first evidence for the B∗ 2(5747)0→B∗+π−decay. The relative branching fractions for the B∗ 2(5747)0,+decays are in agreement with theoretical predictions [10,47–50]. Structures at higher mass are clearly observed in the Q-value distributions. To investigate the significance of the high mass states, large samples of pseudoexperiments are generated and fitted with different configurations. To cover the dominant systematic uncertainty on the yield of these states which arises due to lack of knowledge of the shape of the AP component, the pseudoexperiments are generated with the AP shape that minimises the significance. A first ensemble is generated without any high mass states included. Each pseudoexperiment in this ensemble is fitted twice, once with the same model as used for generation and once with an additional high mass resonance included. The distribution of the difference of χ2values between the two fits is extrapolated to obtain the p-value corresponding to the probability to find a χ2difference as large or larger than that obtained from the corresponding fits to data. This procedure gives significances of 9.6σfor the B+π−case and 4.8σfor the B0π+case. – 15 – JHEP04(2015)024 A second ensemble of pseudoexperiments is generated with a configuration that corresponds to the best fit to the data with a single high mass resonance. The pseudoexperiments in this ensemble are fitted both with the model used for generation and with a second high mass resonance included. The significances of the second peaks, again obtained from the difference in χ2values, are found to be 7.5σand 4.6σfor the B+π−and B0π+cases, respectively. Since isospin symmetry is expected to hold for these states, this shows that under the hypothesis that the high mass structures are due to resonances, two new pairs of particles are observed. Masses and widths of the BJ(5840)0,+and BJ(5960)0,+states are obtained with different fit models, as discussed in section 4, and the corresponding results are shown in table 6. The properties of the BJ(5960)0,+states are consistent with and more precise than those obtained by the CDF collaboration when assuming decay to Bπ [16]. If the BJ(5840)0,+ and BJ(5960)0,+states are considered under the quark model hypothesis, their properties are consistent with those expected for the B(2S) and B∗(2S) radially excited states. In summary, the B+π−and B0π+invariant mass distributions obtained from LHC pp collision data recorded at centre-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3.0 fb−1, have been investigated in order to study excited Bmesons. Precise measurements of the masses and widths of the B1(5721)0,+and B∗ 2(5747)0,+states are reported. Evidence is found for the B∗ 2(5747)0→B∗+π−decay. Clear enhancements over background are observed in the mass range 5850–6000 MeV in both B+π−and B0π+ combinations. Fits to the data, accounting for the apparent enhanced production of the high mass states in the high transverse momentum region, allow the parameters of these states, labelled BJ(5840)0,+and BJ(5960)0,+, to be determined under different hypotheses for their quantum numbers. Acknowledgments We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (U.S.A.). 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). Individual groups or members have received support from 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 (Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for the Exhibition of 1851 (United Kingdom). – 16 – JHEP04(2015)024 Empirical model mBJ(5840)05862.9 ±5.0 ±6.7 ±0.2 ΓBJ(5840)0127.4 ±16.7 ±34.2 mBJ(5960)05969.2 ±2.9 ±5.1 ±0.2 ΓBJ(5960)082.3 ±7.7 ±9.4 mBJ(5840)+5850.3 ±12.7 ±13.7 ±0.2 ΓBJ(5840)+224.4 ±23.9 ±79.8 mBJ(5960)+5964.9 ±4.1 ±2.5 ±0.2 ΓBJ(5960)+63.0 ±14.5 ±17.2 Quark model, BJ(5840)0,+natural mBJ(5840)05889.7 ±22.2 ±6.7 ±0.2 ΓBJ(5840)0107.0 ±19.6 ±34.2 mBJ(5960)06015.9 ±3.7 ±5.1 ±0.2 ±0.4 ΓBJ(5960)081.6 ±9.9 ±9.4 mBJ(5840)+5874.5 ±25.7 ±13.7 ±0.2 ΓBJ(5840)+214.6 ±26.7 ±79.8 mBJ(5960)+6010.6 ±4.0 ±2.5 ±0.2 ±0.4 ΓBJ(5960)+61.4 ±14.5 ±17.2 Quark model, BJ(5960)0,+natural mBJ(5840)05907.8 ±4.7 ±6.7 ±0.2 ±0.4 ΓBJ(5840)0119.4 ±17.2 ±34.2 mBJ(5960)05993.6 ±6.4 ±5.1 ±0.2 ΓBJ(5960)055.9 ±6.6 ±9.4 mBJ(5840)+5889.3 ±15.0 ±13.7 ±0.2 ±0.4 ΓBJ(5840)+229.3 ±26.9 ±79.8 mBJ(5960)+5966.4 ±4.5 ±2.5 ±0.2 ΓBJ(5960)+60.8 ±14.0 ±17.2 Table 6. Parameters of the BJ(5840)0,+and BJ(5960)0,+states obtained with different fit models. The empirical fit uses two, and the quark model fits three, RBW shapes to model the broad resonances. The listed uncertainties are, from left to right: the statistical uncertainty, the experimental systematic uncertainty, and, where applicable, the uncertainty on the Bmeson mass and the uncertainty on the B∗−Bmass difference. Note that any state not explicitly labelled as “natural” is considered to have unnatural spin-parity (and not to be 0+); the reported mass can be converted into the corresponding result under the 0+spin-parity assumption by subtracting the B∗−Bmass difference. Units of MeV are implied. – 17 – JHEP04(2015)024 A Covariance matrices Tables 7and 8each show both statistical and systematic correlations between the main parameters of interest in the B+π−and B0π+fits, respectively. In each table, the masses and widths of the two broad states are seen to be heavily correlated with each other because they overlap, while the parameters of the narrow states are correlated because of the overlap between the B1(5721)0,+state and the B∗ 2(5747)0,+feed-down. B1(5721)0B∗ 2(5747)0BJ(5840)0BJ(5960)0 µΓ BF ratio µΓµΓµΓ B1(5721)0µ0.5 B1(5721)0Γ 0.8 2.3 B∗ 2(5747)0BF ratio −0.1−0.1 0.0 B∗ 2(5747)0µ0.1 0.1 0.0 0.1 B∗ 2(5747)0Γ−0.2−0.4 0.0 0.0 1.0 BJ(5840)0µ0.0−0.4 0.0 0.0 0.0 24.5 BJ(5840)0Γ−0.1 2.0 0.0−0.4−1.2 23.1 278.9 BJ(5960)0µ0.0 0.1 0.0 0.0 0.0 7.4 21.2 8.3 BJ(5960)0Γ 0.1 0.6 0.0 0.1 0.9−21.4−41.2−10.2 59.4 B1(5721)0µ1.9 B1(5721)0Γ 1.0 12.2 B∗ 2(5747)0BF ratio −0.1−0.1 0.1 B∗ 2(5747)0µ0.1 0.1 0.0 0.1 B∗ 2(5747)0Γ−0.2−0.3 0.0 0.0 2.2 BJ(5840)0µ0.1 0.1 0.0 0.0 0.0 44.6 BJ(5840)0Γ−0.2−0.4 0.0 0.0 0.1 0.0 1172 BJ(5960)0µ0.0 0.0 0.0 0.0 0.0 0.0 0.0 26.0 BJ(5960)0Γ 0.2 0.3 0.0 0.0 0.0 0.0−0.1 0.0 88.6 Table 7. Statistical (top) and systematic (bottom) covariance matrices of the nominal B+π−fit, where µand Γ stand for the mean and width respectively. The parameters related to the AP and WS shapes and the signal yields are suppressed for brevity. Units of MeV for µand Γ are implied. B1(5721)+B∗ 2(5747)+BJ(5840)+BJ(5960)+ µΓ BF ratio µΓµΓµΓ B1(5721)+µ3.3 B1(5721)+Γ 5.0 12.7 B∗ 2(5747)+BF ratio −0.9−1.5 0.3 B∗ 2(5747)+µ0.4 0.4−0.1 0.5 B∗ 2(5747)+Γ−0.8−1.9 0.2 0.1 4.0 BJ(5840)+µ0.5−3.2−0.1 1.6 8.8 161.3 BJ(5840)+Γ 2.2 9.4−0.7−0.9−7.6−42.5 571.2 BJ(5960)+µ0.1 0.0 0.0 0.2 1.0 20.7−7.8 16.6 BJ(5960)+Γ−0.3 1.0 0.0−0.4−2.0−95.8−107.4−22.4 210.2 B1(5721)+µ9.6 B1(5721)+Γ 3.7 18.3 B∗ 2(5747)+BF ratio −0.8−1.1 0.6 B∗ 2(5747)+µ0.2 0.3−0.1 0.2 B∗ 2(5747)+Γ−0.8−1.2 0.2−0.1 4.3 BJ(5840)+µ−0.2−0.3 0.0 0.0 0.1 187.7 BJ(5840)+Γ 3.0 4.3−0.9 0.2−1.0−0.3 6371 BJ(5960)+µ0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.4 BJ(5960)+Γ 0.0 0.0 0.0 0.0 0.0−0.1 0.0 0.0 295.2 Table 8. 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Zhong3 1Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil 2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil 3Center for High Energy Physics, Tsinghua University, Beijing, China 4LAPP, Universit´e Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France 5Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France 6CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France 7LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France 8LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France 9Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany 10 Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany 11 Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany 12 School of Physics, University College Dublin, Dublin, Ireland 13 Sezione INFN di Bari, Bari, Italy 14 Sezione INFN di Bologna, Bologna, Italy 15 Sezione INFN di Cagliari, Cagliari, Italy 16 Sezione INFN di Ferrara, Ferrara, Italy 17 Sezione INFN di Firenze, Firenze, Italy 18 Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy 19 Sezione INFN di Genova, Genova, Italy 20 Sezione INFN di Milano Bicocca, Milano, Italy 21 Sezione INFN di Milano, Milano, Italy 22 Sezione INFN di Padova, Padova, Italy 23 Sezione INFN di Pisa, Pisa, Italy 24 Sezione INFN di Roma Tor Vergata, Roma, Italy 25 Sezione INFN di Roma La Sapienza, Roma, Italy 26 Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland – 24 –