Measurement of the properties of the $\Xi_b^{*0}$ baryon

We perform a search for near-threshold $\Xi_b^0$ resonances decaying to $\Xi_b^- \pi^+$ in a sample of proton-proton collision data corresponding to an integrated luminosity of 3 fb$^{-1}$ collected by the LHCb experiment. We observe one resonant state, with the following properties: \begin{eqnarray*} m(\Xi_b^{*0}) - m(\Xi_b^-) - m(\pi^+)&=&15.727 \pm 0.068 \, (\mathrm{stat}) \pm 0.023 \, (\mathrm{syst}) \, \mathrm{MeV}/c^2, \Gamma(\Xi_b^{*0})&=&0.90 \pm 0.16 \, (\mathrm{stat}) \pm 0.08 \, (\mathrm{syst}) \, \mathrm{MeV} . \end{eqnarray*} This confirms the previous observation by the CMS collaboration. The state is consistent with the $J^P=3/2^+$ $\Xi_b^{*0}$ resonance expected in the quark model. This is the most precise determination of the mass and the first measurement of the natural width of this state. We have also measured the ratio \begin{align*} \frac{\sigma(pp \to \Xi_b^{*0} X){\cal{B}}(\Xi_b^{*0} \to \Xi_b^- \pi^+)}{\sigma(pp \to \Xi_b^- X)} = 0.28 \pm 0.03 \, (\mathrm{stat}) \pm 0.01 \, (\mathrm{syst}) . \end{align*}


Introduction
Precise measurements of the properties of hadrons provide important metrics by which models of quantum chromodynamics (QCD), including lattice QCD and potential models employing the symmetries of QCD, can be tested. Studies of hadrons containing a heavy quark play a special role since the heavy quark symmetry can be exploited, for example to relate properties of charm hadrons to beauty hadrons. Measurements of the masses and mass splittings between the ground and excited states of beauty and charm hadrons provide a valuable probe of the interquark potential [1].
There are a number of b baryon states that contain both beauty and strange quarks. The singly strange states form isodoublets: Ξ 0 b (bsu) and Ξ − b (bsd). Theoretical estimates of the properties of these states are available (see, e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12]). There are five known Ξ b states which, in the constituent quark model, correspond to five of the six low-lying states that are neither radially nor orbitally excited: one isodoublet of weakly-decaying ground states (Ξ 0 b and Ξ − b ) with J P = 1 2 + , one isodoublet (Ξ 0 b and Ξ − b ) with J P = 1 2 + but different symmetry properties from the ground states, and one isodoublet (Ξ * 0 b and Ξ * − b ) with J P = 3 2 + . The large data samples collected at the Large Hadron Collider have allowed these states to be studied in detail in recent years. These studies include precise measurements of the masses and lifetimes of the Ξ 0 b and Ξ − b baryons [13,14] by the LHCb collaboration, the observation of a peak in the Ξ − b π + mass spectrum interpreted as the Ξ * 0 b baryon [15] by the CMS collaboration, and the observation of two structures in the Ξ 0 b π − mass spectrum, consistent with the Ξ − b and Ξ * − b baryons [16] by LHCb. 1 The Ξ 0 b state was not observed by CMS; it is assumed to be too light to decay into Ξ − b π + . In this paper, we present the results of a study of the Ξ − b π + mass spectrum, where the Ξ − b baryon is reconstructed through its decay to Ξ 0 c π − , with Ξ 0 c → pK − K − π + . The measurements use a pp collision data sample recorded by the LHCb experiment, corresponding to an integrated luminosity of 3 fb −1 , of which 1 fb −1 was collected at √ s = 7 TeV and 2 fb −1 at 8 TeV. We observe a single peak in the Ξ − b π + mass spectrum, consistent with the state reported in Ref. [15]. A precise determination of its mass and the first determination of a non-zero natural width are reported. We also measure the relative production rate between the Ξ * 0 b and Ξ − b baryons in the LHCb acceptance. The LHCb detector [17,18] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of 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 of the magnet.
The tracking system provides a measurement of momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV/c. The minimum distance of a track to a primary vertex (PV), the impact parameter, is measured with a resolution of (15 + 29/p T ) µm, where p T is the component of the momentum transverse to the beam, in GeV/c. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The online event selection is performed by a trigger [19], which consists of a hardware stage (L0), based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. The software trigger requires a two-, three-or four-track secondary vertex which is significantly displaced from all primary pp vertices and for which the scalar p T sum of the charged particles is large. At least one particle should have p T > 1.7 GeV/c and be inconsistent with coming from any of the PVs. A multivariate algorithm [20] is used to identify secondary vertices consistent with the decay of a b hadron. Only events that fulfil these criteria are retained for this analysis.
In the simulation, pp collisions are generated using Pythia [21] with a specific LHCb configuration [22]. Decays of hadrons are described by EvtGen [23], in which final-state radiation is generated using Photos [24]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [25] as described in Ref. [26].

Candidate selection
Candidate Ξ − b decays are formed by combining Ξ 0 c → pK − K − π + and π − candidates in a kinematic fit [27]. All tracks used to reconstruct the Ξ − b candidate are required to have good track fit quality, have p T > 100 MeV/c, and have particle identification information consistent with the hypothesis assigned. The large lifetime of the Ξ − b baryon is exploited to reduce combinatorial background by requiring all of its final-state decay products to have χ 2 IP > 4 with respect to all of the PVs in the event, where χ 2 IP , the impact parameter χ 2 , is defined as the difference in the vertex fit χ 2 of the PV with and without the particle under consideration. The Ξ 0 c candidates are required to have invariant mass within 20 MeV/c 2 of the known value [28], corresponding to about three times the mass resolution. To further suppress background, the Ξ − b candidate must have a trajectory that points back to one of the PVs (χ 2 IP ≤ 10) and must have a decay vertex that is significantly displaced from the PV with respect to which it has the smallest χ 2 IP (decay time > 0.2 ps and flight distance χ 2 > 100). The invariant mass spectra of selected Ξ 0 c and Ξ − b candidates are displayed in Fig. 1.
The Ξ − b candidates are then required to have invariant mass within 60 MeV/c 2 of the peak value, corresponding to about four times the mass resolution. In a given event, each combination of Ξ − b and π + candidates is considered, provided that the pion has p T greater than 100 MeV/c and is consistent with coming from the same PV as the Ξ − b candidate. The Ξ − b π + vertex is constrained to coincide with the PV in a kinematic fit, which is required to be of good quality. The Ξ − b π + system is also required to have p T > 2.5 GeV/c. The mass difference δm is defined as where m cand represents the reconstructed mass. The δm spectrum of Ξ − b π + candidates passing all selection requirements is shown in Fig. 2. A clear peak is seen at about 16 MeV/c 2 , whereas no such peak is seen in the wrong-sign (Ξ − b π − ) combinations, also shown in Fig. 2.
To determine the properties of the Ξ − b π + peak, we consider only candidates with δm < 45 MeV/c 2 ; this provides a large enough region to constrain the combinatorial background shape. There are on average 1.16 candidates per selected event in this mass region; all candidates are kept. In the vast majority of events with more than one candidate, a single Ξ − b candidate is combined with different π + tracks from the same PV.
3 Mass and width of Ξ − b π + peak Accurate determination of the mass, width, and signal yield requires knowledge of the signal shape, and in particular the mass resolution. This is obtained from simulated Ξ * 0 b decays in which the δm value is set to the approximate peak location seen in data. In this simulation, the natural width of the Ξ − b π + state is fixed to a negligible value so that the shape of the distribution measured is due entirely to the mass resolution. The resolution function is parameterised as the sum of three Gaussian distributions with a common mean value. The weighted average of the three Gaussian widths is 0.51 MeV/c 2 . In the fits to data, all of the resolution shape parameters are fixed to the values obtained from simulation.
Any Ξ − b π + resonance in this mass region would be expected to have a non-negligible natural width Γ. The signal shape in fits to data is therefore described using a P -wave relativistic Breit-Wigner (RBW) line shape [29] with a Blatt-Weisskopf barrier factor [30], convolved with the resolution function described above.
The combinatorial background is modelled by an empirical threshold function of the where A and C are freely varying parameters determined in the fit to the data and δm is in units of MeV/c 2 . The mass, width and yield of events in the observed peak are determined from an unbinned, extended maximum likelihood fit to the δm spectrum using the signal and background shapes described above. The mass spectrum and the results of the fit are shown in Fig. 3. The fitted signal yield is 232 ± 19 events. The nonzero value of the natural width of the peak, Γ = 0.90 ± 0.16 MeV (where the uncertainty is statistical only), is also highly significant: the change in log-likelihood when the width is fixed to zero exceeds 30 units. No other statistically significant structures are seen in the data.
We perform a number of cross-checks to ensure the robustness of the result. These include splitting the data by magnet polarity, requiring that one or more of the decay products of the signal candidate pass the L0 trigger requirements, dividing the data into subsamples in which the π + candidate has p T < 250 MeV/c and p T > 250 MeV/c, varying the fit range in δm, and applying a multiple candidate rejection algorithm in which only one candidate, chosen at random, is retained in each event. In each of these cross-checks, the variation in fit results is consistent with statistical fluctuations. Several sources of systematic effects are considered and are summarised in Table 1. Other than the first two systematic uncertainties described below, all are determined by making variations to the baseline selection or fit procedure, repeating the analysis, and taking the maximum change in δm or Γ. A small correction (16 keV, estimated with pseudoexperiments) to Γ is required due to the systematic underestimation of the width in a fit with limited yield; an uncertainty of the same size is assigned. This correction is already included in the value of Γ quoted earlier. The limited size of the sample of simulated events leads to uncertainties on the resolution function parameters. These uncertainties are propagated to the final results using the full covariance matrix. We assign a systematic uncertainty for a particular class of events with multiple Ξ * 0 b candidates in which the Ξ − b or Ξ 0 c baryon is misreconstructed. This uncertainty is determined by applying a limited multiple candidate rejection procedure in which only one Ξ 0 b candidate is accepted per event (but may be combined with multiple pions). The robustness of the resolution model is verified with control samples of Ξ − b → Ξ 0 b π − (see Ref. [16]) and D * + → D 0 π + ; based on these tests, the uncertainty is assessed by increasing the Ξ * 0 b resolution width by 11%. This is the dominant uncertainty on Γ. An alternative background description is used in the fit to check the dependence of the signal parameters on the background model. The calibration of the momentum scale has an uncertainty of 0.03% [31,32], the effect of which is propagated to the mass and width of the Ξ * 0 b baryon. As in Ref. [16], this is validated by measuring m(D * + ) − m(D 0 ) in a large sample of D * + , D 0 → K − K + decays. The mass difference agrees with a recent BaBar measurement [33] within 6 keV/c 2 , corresponding to 1.3σ when including the mass scale uncertainty for that decay. Finally, the dependence of the results on the relativistic Breit-Wigner lineshape is tested: other values of the assumed angular momentum (spin 0, 2) and radial parameter (1-5 GeV −1 ) of the Blatt-Weisskopf barrier factor are used, and an alternative parameterisation of the mass-dependent width (from appendix A of Ref. [29]) is tested. Taking these effects into account, the mass difference and width are measured to be .727 ± 0.068 ± 0.023 MeV/c 2 , Γ(Ξ * 0 b ) = 0.90 ± 0.16 ± 0.08 MeV, where the first uncertainties are statistical and the second are systematic. Given these values, those of the other Ξ b resonances reported previously [16], and the absence of other structures in the δm spectrum, the observed peak is compatible with the J P = 3 2 + state expected in the quark model [2], and we therefore refer to it as the Ξ * 0 b baryon.

Relative production rate
In addition to the mass and width of the Ξ * 0 b state, we measure the rate at which it is produced in the LHCb acceptance relative to the Ξ − b baryon. The quantity that is measured is where rel is the ratio of the Ξ * 0 b to Ξ − b selection efficiencies, and N is a measured yield. Any variation in the ratio of cross-sections [σ(pp → Ξ * 0 b X)] / σ(pp → Ξ − b X) between √ s = 7 TeV and 8 TeV would be far below the sensitivity of our measurements, and is therefore neglected.
To minimize systematic uncertainties, all aspects of the Ξ − b selection are chosen to be common to the inclusive Ξ − b and Ξ * 0 b samples. Therefore an additional requirement, not applied to the sample used in the mass and width measurements, is imposed that at least one of the Ξ − b decay products passes the L0 hadron trigger requirements. The relative efficiency rel includes the efficiency of detecting the π + from the Ξ * 0 b decay and the selection criteria imposed on it. It is evaluated using simulated decays, and small corrections (discussed below) are applied to account for residual differences between data and simulation. Including only the uncertainty due to the finite sizes of the simulated samples, the value of rel is found to be 0.598 ± 0.014. The yields in data are obtained by fitting the δm and m cand (Ξ − b ) spectra after applying all selection criteria. For the Ξ * 0 b yield, the data are fitted using the same functional form as was used for the full sample. The fit is shown in Fig. 4, and the yield obtained is N (Ξ * 0 b ) = 133 ± 14. The results of an unbinned, extended maximum likelihood fit to the Ξ − b sample are shown in Fig. 5. The shapes used to describe the signal and backgrounds are identical to those described in Ref. [14]. In brief, the signal shape is described by the sum of two Crystal Ball functions [34] with a common mean. The background components are due to misidentified contribution is also described by the sum of two Crystal Ball functions with a common mean. Its shape parameters are fixed to the values from simulation, and the fractional yield relative to that of Ξ − b → Ξ 0 c π − is fixed to 3.1%, based on previous studies of this mode [14]. The Ξ − b → Ξ 0 c ρ − mass shape is described by an ARGUS function [35], convolved with a Gaussian resolution function. The threshold and shape parameters are fixed based on simulation, and the resolution is fixed to 14 MeV/c 2 , the approximate mass resolution for signal decays. The yield is freely varied in the fit. The combinatorial background is described by an exponential function with freely varying shape parameter and yield. To match the criteria used for the Ξ * 0 b selection, only Ξ − b candidates within ±60 MeV/c 2 of the known mass contribute to the yield, which is found to be N (Ξ − b ) = 808 ± 32. Several sources of uncertainty contribute to the production ratio measurement, either in the signal efficiency or in the determination of the yields. Most of the selection requirements are common to both the signal and normalization modes, and therefore the corresponding efficiencies cancel in the production ratio measurement. Effects related to the detection and selection of the π + from the Ξ * 0 b decay do not cancel, and therefore contribute to the systematic uncertainty. The tracking efficiency is measured using a tag and probe procedure with J/ψ → µ + µ − decays [36], and for this momentum range a correction of (+7.0 ± 3.0)% is applied. Fit quality requirements on the π + track lead to an additional correction of (−1.5 ± 1.5)%. The simulation is used to estimate the loss of Ξ * 0 b efficiency from decays in which the π + is reconstructed but has p T < 100 MeV/c. This loss, 2.7%, is already included in the efficiency, and does not require an additional correction. Since the simulation reproduces the p T spectrum well for p T > 100 MeV/c, we assign half of the value, 1.4%, as a systematic uncertainty associated with the extrapolation to p T < 100 MeV/c. Finally, the limited sample sizes of simulated events contribute an uncertainty of 2.4% to the relative efficiency. With these systematic sources included, the relative efficiency is found to be rel For the Ξ * 0 b signal yield in data, we assign a 1% systematic uncertainty due to a potential peaking background in which a genuine For the normalization mode, independent variations in the signal and background shapes are investigated, and taken together correspond to a systematic uncertainty in the normalisation mode yield of 2%.
Combining the relative efficiency, the yields, and the systematic uncertainties described above, we find where the statistical uncertainty takes into account the correlation between N (Ξ * 0 b ) and

Summary
Using pp collision data from the LHCb experiment corresponding to an integrated luminosity of 3 fb −1 , we observe one highly significant structure in the Ξ − b π + mass spectrum near threshold. There is no indication of a second state above the Ξ − b π + mass threshold that would indicate the presence of the Ξ 0 b resonance; from this we conclude that The mass difference and width of the Ξ * 0 b are measured to be: We interpret the structure as the J P = 3 2 + Ξ * 0 b state observed previously by the CMS collaboration through the decay chain Our results are consistent with and about a factor of ten more precise than their measurements, δm = 14.84 ± 0.74 ± 0.28 MeV/c 2 and Γ = 2.1 ± 1.7 (stat) MeV [15]. The measured width of the state is in line with theory expectations: a calculation based on lattice QCD predicted a width of 0.51 ± 0.16 MeV [37], and another using the 3 P 0 model obtained a value of 0.85 MeV [38].
Combining our measured value for δm with the most precise measured value of the Ξ − b mass, 5797.72 ± 0.46 ± 0.16 ± 0.26 MeV/c 2 [14], and the pion mass [28], we obtain In combining the above measurements, the systematic uncertainties on the mass scale and the RBW shape are treated as fully correlated between the two δm measurements.
We have also measured the inclusive ratio of production cross-sections to be This value is similar to the previously measured value from the isospin partner mode, = 0.21 ± 0.03 ± 0.01 [16]. Taking into account the neutral modes, e.g. Ξ * 0 b → Ξ 0 b π 0 and Ξ * − b → Ξ − b π 0 , and contributions from Ξ b states [16], it is evident that in pp collisions at 7 and 8 TeV a large fraction of Ξ − b and Ξ 0 b baryons are produced through feed-down from higher-mass states.