First observation of the decay $B_{s2}^*(5840)^0 \to B^{*+} K^-$ and studies of excited $B_s$ mesons

Properties of the orbitally excited (L=1) $B_s$ states are studied using 1.0 fb$^{-1}$ of pp collisions at $\sqrt{s} =7$ TeV collected with the LHCb detector. The first observation of the $B_{s2}^*(5840)^0$ meson decaying to $B^{*+} K^-$ is reported, and the corresponding branching fraction measured relative to the $B^+ K^-$ decay mode. The $B_{s1}(5830)^0 \to B^{*+} K^-$ decay is observed as well. The width of the $B_{s2}^*(5840)^0$ state is measured for the first time and the masses of the two states are determined with the highest precision to date. The observation of the $B_{s2}^*(5840)^0 \to B^{*+} K^-$ decay favours the spin-parity assignment $J^P = 2^+$ for the $B_{s2}^*(5840)^0$ meson. In addition, the most precise measurement of the mass difference $m(B^{*+})-m(B^+) = 45.01 \pm 0.30 (stat) \pm 0.23 (syst)$ MeV/$c^2$ is obtained.

Heavy quark effective theory (HQET) describes mesons with one heavy and one light quark where the heavy quark is assumed to have infinite mass [1]. It is an important tool for calculating meson properties which may be modified by physics beyond the Standard Model, such as CP violation in charm meson decays [2] or the mixing and lifetimes of B mesons [3]. It also predicts the properties of excited B and B 0 s mesons [4][5][6][7], and precise measurements of these properties are a sensitive test of the validity of the theory. Within HQET the B 0 s mesons are characterised by three quantum numbers: the relative orbital angular momentum L of the two quarks, the total angular momentum of the light quark j q = |L± 1 2 |, and the total angular momentum of the B 0 s meson J = |j q ± 1 2 |. For L = 1 there are four different possible (J, j q ) combinations, all with even parity. These are collectively termed the orbitally excited states. Such states can decay to B + K − and/or B * + K − (the inclusion of charge-conjugate states is implied throughout this Letter), depending on their quantum numbers and mass values. The two states with j q = 1/2, named B * s0 and B ′ s1 , are expected to decay through an S-wave transition and to have a large O(100 MeV/c 2 ) decay width. In contrast, the two states with j q = 3/2, named B s1 (5830) 0 and B * s2 (5840) 0 (henceforth B s1 and B * s2 for brevity), are expected to decay through a D-wave transition and to have a narrow O(1 MeV/c 2 ) decay width. Table 1 gives an overview of these states. In this Letter a 1.0 fb −1 sample of data collected by the LHCb detector is used to search for the orbitally excited B 0 s mesons in the mass distribution of B + K − pairs, where the B + mesons are selected in the four decay modes: B + → J/ψ(µ + µ − )K + , B + → D 0 (K + π − )π + , B + → D 0 (K + π − π + π − )π + , and B + → D 0 (K + π − )π + π − π + . Two narrow peaks were observed in the B + K − mass distribution by the CDF collaboration [9]. Putatively, they are identified with the states of the j q = 3/2 doublet expected in HQET [4] and are named B s1 and B * s2 . As the B s1 → B + K − decay is forbidden, one of the mass peaks observed is interpreted as the B s1 → B * + K − decay followed by B * + → B + γ, where the photon is not observed. This peak is shifted by the B * + − B + mass difference due to the missing momentum of the photon in the B * + → B + γ decay. While the B * s2 → B + K − decay has been observed by the D0 collaboration as well [10], a confirmation of the B s1 meson is still missing. The identification of the B s1 and B * s2 mesons in the B + K − mass spectrum is based on the expected mass splitting between the j q = 3/2 states. The B s1 and B * s2 widths are very sensitive to their masses, due to their proximity to the BK and B * K thresholds. Measurements of the widths thus provide fundamental information concerning the nature of these states. In addition the B s1 and B * s2 quantum numbers have not yet been directly determined and the observation of other decay modes can constrain the spin-parity combinations of the states. In particular the B * s2 → B * + K − decay has not yet been observed but could manifest itself in the B + K − mass spectrum in a similar fashion to the corresponding B s1 meson decay. The B * s2 → B * + K − branching fraction relative to B * s2 → B + K − is predicted to be between 2% and 10%, depending on the B * s2 mass [11][12][13][14].
Recently the Belle collaboration has reported observation of charged bottomoniumlike Z b (10610) + and Z b (10650) + states [15,16], that could be interpreted as BB * and B * B * molecules respectively [17]. To test this interpretation, improved measurements of the B * + mass are necessary, and can be obtained from the difference in peak positions between B * s2 → B * + K − and B * s2 → B + K − decays in the B + K − mass spectrum. The LHCb detector [18] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for studying particles containing b or c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream. The combined tracking system has a momentum resolution (∆p/p), that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c, and a decay time resolution of 50 fs. The resolution of the impact parameter, the transverse distance of closest approach between the track and a primary interaction, is about 20 µm for tracks with large transverse momentum. The transverse component is measured in the plane normal to the beam axis. Charged hadrons are identified using two ring-imaging Cherenkov detectors. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and pre-shower detectors, an electromagnetic calorimeter, and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers.
The trigger system [19] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage that applies a full event reconstruction. Events likely to contain a B meson are selected by searching for a dimuon vertex detached from the primary interaction or two-, three-, and four-track vertices detached from the primary interaction which have high total transverse momentum. These are respectively referred to as dimuon and topological triggers.
The samples of simulated events used in this analysis are based on the Pythia 6.4 generator [20], with a choice of parameters specifically configured for LHCb [21]. The EvtGen package [22] describes the decay of the B mesons, and the Geant4 toolkit [23,24] is used to simulate the detector response. QED radiative corrections are generated with the Photos package [25].
In the offline analysis the B mesons are reconstructed using a set of loose selection criteria to suppress the majority of the combinatorial backgrounds. The B + → J/ψK + selection requires a B + candidate with a transverse momentum of at least 2 GeV/c and a decay time of at least 0.3 ps. For the other decay modes, the selection explicitly requires that the topological trigger, which selected the event, is based exclusively on tracks from and (d) B + → D 0 (K + π − )π + π − π + decays. The J/ψ and D 0 masses are constrained to their world average values.
which the B meson candidate is formed. Additional loose selection requirements are placed on variables related to the B meson production and decay such as transverse momentum and quality of the track fits for the decay products, detachment of the B + candidate from the primary interaction, whether the momentum of the B + candidate points back to the primary interaction, and the impact parameter χ 2 . The impact parameter χ 2 is defined as the difference between the χ 2 of the primary vertex reconstructed with and without the considered track.
Following these selections, B + signals are visible above backgrounds in all four decay modes. In order to improve their purity, four boosted decision tree classifiers [26] are trained on variables common to all four decay modes: the transverse momenta and impact parameters of the final state tracks, the transverse momentum and impact parameter of the B + candidate, the detachment of the B + candidate from the primary interaction, the cosine of the angle between the B + candidate momentum and the direction of flight from the primary vertex to the decay vertex, the fit χ 2 of the tracks, and particle identification information. The classifier is trained on data using the sWeights technique [27], with the B + candidate mass as a discriminating variable, to unfold the signal and background distributions. The cut on the classifier response is chosen by optimizing the significance of each B + signal. The final mass distributions for the B + candidates are shown in Fig. 1. The B + candidate mass spectra are fitted using a double Gaussian function for the signal and a second order polynomial for the background. The average mass resolution, σ B + , is defined as the weighted average of the Gaussian widths. The purities of the samples, defined as the fraction of the signal events in a ±2σ B + mass region, are 96%, 91%, 90%, and 85% for the B + → J/ψK + , B + → D 0 (K + π − )π + , B + → D 0 (K + π − π + π − )π + , and B + → D 0 (K + π − )π + π − π + decays respectively. The B + candidates, within a ±2σ B + mass region, are selected for each decay mode. A sample of about 1 000 000 B + candidates is obtained and combined with any track of opposite charge that is identified as a kaon.
Multiple pp interactions can occur in LHC bunch crossings. In order to reduce combinatorial backgrounds, the B + and kaon candidates are required to be consistent with coming from the same interaction point. The signal purity is improved by a boosted decision tree classifier, whose inputs are the B + and the kaon transverse momenta, the log-likelihood difference between the kaon and pion hypotheses, and the vertex fit and impact parameter χ 2 . The training is performed using simulated events for the signal and the like-charge B + K + candidates in the data for the background. The same selection is subsequently applied to all B + decay modes. The cut on the classifier response is chosen by optimizing the significance of the B * s2 → B + K − signal. It retains 57% of the signal events and rejects 92% of the background events. In order to improve the mass resolution, the B + K − mass fits are performed constraining the J/ψ (or D 0 ) and B + particles to their respective world average masses [8] and constraining the B + and K − momenta to point to the associated primary vertex. Figure 2 shows the mass difference for the selected candidates, summed over all B + decay modes. The mass difference is defined as Q ≡ m(B + K − ) − m(B + ) − m(K − ) where m(B + ) and m(K − ) are the known masses of the B + and K − mesons [8], respectively. The two narrow peaks at 10 and 67 MeV/c 2 are identified as the B s1 → B * + K − and B * s2 → B + K − signals, respectively, as previously observed. In addition, a smaller structure is seen around 20 MeV/c 2 , identified as the previously unobserved B * s2 → B * + K − decay mode.
Simulated events are used to compute the detector resolutions corresponding to the three signals. The values obtained are increased by 20% to account for differences between the B + resolutions in data and simulated events. The corrected resolutions are 0.4 MeV/c 2 , 0.6 MeV/c 2 and 1.0 MeV/c 2 for the B s1 → B * + K − , B * s2 → B * + K − , and B * s2 → B + K − signals respectively. A discrepancy of 40% between the mass resolutions in data and simulated events is observed for decays with small Q values, such as D * + → D 0 π + . Therefore we assign an uncertainty of ±20% to the resolution in the systematic studies.
An unbinned fit of the mass difference distribution is performed to extract the Q values and event yields of the three peaks. The B * s2 → B + K − signal is parameterized by a relativistic Breit-Wigner function with natural width Γ convolved with a Gaussian function that accounts for the detector resolution. Its width is fixed to the value obtained from simulated events. The lineshapes of the B s1 /B * s2 → B * + K − signals, expected to be Breit-Wigner functions in the B * + K − mass spectrum, are affected by the phase space and the angular distribution of the decays as the photon is not reconstructed. The resulting shapes can not be properly simulated due to the lack of knowledge of the B s1 /B * s2 properties. Therefore a Gaussian function is used for each B s1 /B * s2 → B * + K − signals as effective parameterization. The background is modelled by a threshold function, f (Q) = Q α e βQ+δ , where α, β and δ are free parameters in the fit. Its analytical form is verified by fitting the like charge B + K + combinations where no signal is expected.
The parameters allowed to vary in the fit are: the yield N B * s2 →B + K − , the yield ratios signals, the mass difference between the B * s2 → B + K − and B * s2 → B * + K − peaks, the natural width of the B * s2 state, the Gaussian widths of B s1 /B * s2 → B * + K − signals and the parameters of the threshold function. From the yield ratios, the relative branching fraction (1) is measured. The B s1 to B * s2 ratio of production cross-sections times the ratio of branching fractions of B s1 → B * + K − relative to that of B * s2 → B + K − is also determined from These ratios are corrected by the relative selection efficiencies, ǫ rel 2,2 = 1.05 ± 0.02 and ǫ rel 1,2 = 1.03 ± 0.01, using simulated decays. The fit results are given in Table 2. The widths of the two Gaussian functions are 0.73 ± 0.04 MeV/c 2 and 1.9 ± 0.3 MeV/c 2 for the B s1 → B * + K − and B * s2 → B * + K − signals respectively. A binned χ 2 test gives a confidence level of 43% for the fit.
To determine the significance of the B * s2 → B * + K − signal, a similar maximum likelihood fit is performed, where all parameters of the signal are fixed according to expectation, except its yield. The likelihood of this fit is compared to the result of a fit where the yield of the signal is fixed to zero. The statistical significance of the B * s2 → B * + K − signal is 8σ.
A number of systematic uncertainties are considered. For the signal model, the signal shape is changed to a double Gaussian function and an alternative threshold function is used for the background. The changes in the fit results are assigned as the associated uncertainties. The B + decay modes are fitted independently to test for effects that may be related to differences in their selection requirements. For each observable quoted in Table 2, the difference between the weighted average of these independent fits and the global fit is taken as a systematic uncertainty. Additional systematic uncertainties are assigned based on the change in the results when varying the selection criteria and the B + signal region. The detector resolution of B * s2 → B + K − signal is varied by ±20%. In addition, the momentum scale in the processing of the data used in this analysis is varied within the estimated uncertainty of 0.15%. The corresponding uncertainty on Table 3: Absolute systematic uncertainties for each measurement, which are assumed to be independent and are added in quadrature. the measured masses is assigned as a systematic uncertainty. The uncertainty on the determination of the selection efficiency ratios caused by finite samples of simulated events is taken as a systematic uncertainty for the branching fractions. Finally simulated events are used to estimate the mass shifts of the B s1 /B * s2 → B * + K − signals from the nominal values when the radiated photon is excluded from their reconstructed decays. The absolute systematic uncertainties are given in Table 3. The B * s2 → B * + K − signal is observed with the expected frequency in each of the four resconstructed decay modes and the systematic error for the B(B * s2 →B * + K − ) B(B * s2 →B + K − ) branching fraction ratio, related to the different B + decay modes, is small. The final results are shown in Table 2. The measured mass differences are more precise than the previous best measurements of a factor two at least. The measured B(B * s2 →B * + K − ) B(B * s2 →B + K − ) branching fraction ratio and B * s2 width are in good agreement with theoretical predictions [12][13][14].
The mass differences given in Table 2 are translated into absolute masses by adding the masses of the B + and kaon [8] and, in the case of the B s1 meson, the B * + − B + mass difference measured in this Letter. The results are m(B * + ) = 5324.26 ± 0.30 ± 0.23 ± 0.17 MeV/c 2 , m(B s1 ) = 5828.40 ± 0.04 ± 0.04 ± 0.41 MeV/c 2 , m(B * s2 ) = 5839.99 ± 0.05 ± 0.11 ± 0.17 MeV/c 2 , where the first uncertainty is statistical and the second is systematic. The third uncertainty corresponds to the uncertainty on the B + mass [8] and, in the case of the B s1 mass measurement, the uncertainty on the B * + − B + mass difference measured in this analysis.
The significance of the non-zero B * s2 width is determined by comparing the likelihood for the nominal fit with a fit in which the width is fixed to zero. To account for systematic effects, the minimum √ 2∆logL among all systematic variations is taken; the significance including systematic uncertainties is 9σ.
In conclusion, using 1.0 fb −1 of data collected with the LHCb detector at √ s = 7 TeV, the decay mode B * s2 → B * + K − is observed for the first time and its branching fraction measured relative to that of B * s2 → B + K − . The observation of the B * s2 meson decaying to two pseudoscalars (B * s2 → B + K − ) and to a vector and a pseudoscalar (B * s2 → B * + K − ) favours the assignment of J P = 2 + for this state. The B * s2 width is measured for the first time, while the masses of the B s1 and B * s2 states are measured with the highest precision to date and are consistent with previous measurements [9,10]. Finally, the observed B * s2 → B * + K − decay is used to make the most precise measurement to date of the B * + − B + mass difference. This measurement, unlike others reported in the literature, does not require the reconstruction of the soft photon from B * + decays and therefore has significantly smaller systematic uncertainty. High precision measurements of the B * + mass are important for the understanding of the exotic Z + b states recently observed [15]. Using the B * + mass measured in this analysis, we compute that the Z b (10610) + and Z b (10650) + masses are 3.69 ± 2.05 MeV/c 2 and 3.68 ± 1.71 MeV/c 2 above the BB * and B * B * thresholds respectively.