Observation of a new excited beauty strange baryon decaying to $\Xi^-_\mathrm{b} \pi^+ \pi^-$

The $\Xi^-_\mathrm{b} \pi^+ \pi^-$ invariant mass spectrum is investigated with an event sample of proton-proton collisions at $\sqrt{s} = $ 13 TeV, collected by the CMS experiment at the LHC in 2016-2018 and corresponding to an integrated luminosity of 140 fb$^{-1}$. The ground state $\Xi^-_\mathrm{b}$ is reconstructed via its decays to J$/\psi$ $\Xi^-$ and J$/\psi$ $\Xi^-$ $\Lambda$ K$^-$. A narrow resonance, labeled $\Xi_\mathrm{b}$(6100)$^-$, is observed at a $\Xi^-_\mathrm{b} \pi^+ \pi^-$ invariant mass of 6100.3 $\pm$ 0.2 (stat) $\pm$ 0.1 (syst) $\pm$ 0.6 ($\Xi^-_\mathrm{b}$) MeV, where the last uncertainty reflects the precision of the $\Xi^-_\mathrm{b}$ baryon mass. The upper limit on the $\Xi_\mathrm{b}$(6100)$^-$ natural width is determined to be 1.9 MeV at 95% confidence level. Following analogies with the established excited $\Xi_\mathrm{c}$ baryon states, the new $\Xi_\mathrm{b}$(6100)$^-$ resonance and its decay sequence are consistent with the orbitally excited $\Xi^-_\mathrm{b}$ baryon, with spin and parity quantum numbers $J^P$ $=$ 3/2$^-$.

The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [25].
Events of interest are selected using a two-tiered trigger system. The first level (L1), composed of custom hardware processors, uses information from the calorimeters and muon detectors [26]. The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing [27]. The events used in the analysis were selected at L1 by requiring the presence of at least two muons, and at HLT by requiring that the two muons have opposite sign (OS), with various thresholds on the pseudorapidity η and momentum transverse to the beam axis p T , compatible with being produced in the dimuon decay of J/ψ mesons.
Several simulated event samples are used in the analysis. The PYTHIA 8.230 package [28] is used to simulate the production of the Ξ b (6100) − state, where the Σ − b baryon, with a modified mass value, is used as a proxy for an excited   of the CMS detector, including the same trigger and reconstruction algorithms as used for the collision data. The simulation includes effects from multiple pp interactions in the same or nearby bunch crossings (pileup) with a multiplicity distribution matching the measured one.
The selection criteria are optimized using the Punzi figure of merit [33], which does not rely on the signal normalization. The expected background is estimated from data using the same-sign (SS) control region described below, while the signal efficiency is obtained from the simulated Events are required to have two OS muons passing the CMS soft-muon selection criteria [34] and satisfying p T (µ ± ) > 3 GeV and |η(µ ± )| < 2.4. The muons must form a common vertex with χ 2 probability P vtx above 1%. The dimuon invariant mass must be within 100 MeV of m PDG J/ψ (hereafter, m PDG X denotes the world-average mass of hadron X [20]), corresponding to about three times the mass resolution. The Λ candidates are formed from displaced two-prong vertices, assuming the decay Λ → pπ − , as described in Ref. [35]. The pπ − reconstructed mass is required to be within 10 MeV of m PDG Λ , corresponding to about three times the mass resolution. The two tracks are then refitted with their invariant mass constrained to m PDG Λ . The obtained Λ candidates are required to have p T > 1 GeV and P vtx > 1%.
For the Ξ − b → J/ψΞ − channel, the Ξ − → Λπ − candidates are obtained by combining charged particles of p T > 0.25 GeV with the selected Λ candidates. The reconstructed Ξ − must have P vtx > 1%, p T > 3 GeV, and invariant mass within 9.5 MeV of m PDG Ξ − , corresponding to about three times the mass resolution. The Ξ − b candidates are obtained by performing a µ + µ − Ξ − kinematic vertex fit, constraining the dimuon invariant mass to m PDG J/ψ .
For the Ξ − b → J/ψΛK − decay channel, the Λ candidates must pass stricter requirements: p T > 2 GeV and |M(pπ − ) − m PDG Λ | < 9 MeV. The charged kaon candidates are particle tracks with kaon mass assignment satisfying high purity tracking requirements [36] and p T > 1.2 GeV. The Ξ − b candidates are reconstructed by fitting the µ + µ − ΛK − vertex with the J/ψ mass constraint. Since the photon from the Σ 0 → Λγ decay is not detected, both From all reconstructed pp collision vertices, the primary vertex (PV) is chosen as the one with the smallest pointing angle, as done in Refs. [37][38][39][40]. The pointing angle is the three-dimensional angle between the Ξ − b candidate momentum and the vector joining the PV with the reconstructed Ξ − b candidate decay vertex. The decay length L xy of the Ξ − b candidate in the transverse plane, computed as the two-dimensional distance between the PV and the Ξ − b decay vertex, is required to be at least three times larger than its uncertainty σ L xy . The p T (Ξ − b ) is required to be aligned with the transverse displacement vector: is the pointing angle in the plane transverse to the beams. Two additional topological requirements are applied: the cosine of the pointing angle, cos(α(Ξ − , Ξ − b )), must be larger than 0.999 for the Besides, the pion emitted in the Ξ − → Λπ − decay and the kaon emitted in the Ξ − b → J/ψΛK − decay must have d xy /σ d xy > 0.9 and 0.6, respectively, where d xy is the impact parameter in the transverse plane with respect to the PV, and σ d xy is its uncertainty.
The invariant mass distributions of the selected Ξ − b candidates are shown in Fig. 2 for the J/ψΞ − (left) and J/ψΛK − (right) channels. The two plots also show the results of independent unbinned extended maximum-likelihood fits. In both cases, the fully reconstructed Ξ − b signal is described by a double-Gaussian function with two free parameters: the common mean and the total yield; the two width parameters and the proportion of each Gaussian are fixed from simulation studies. The background is described by a first-order polynomial in the J/ψΞ − fit and an exponential function in the J/ψΛK − fit. In the latter fit, the signal contribution from the partially reconstructed Ξ − b → J/ψΣ 0 K − decays is taken into account by including an asymmetric Gaussian in the fit model, with the shape parameters fixed from simulation studies. All normalization values (signals and backgrounds) are free parameters of the fit.
The signal yields from the fits described above are 859 ± 36 and 815 ± 74 for the Ξ − b → J/ψΞ − and fully reconstructed Ξ − b → J/ψΛK − decay modes, respectively, with the uncertainties being statistical only. The fitted Ξ − b masses of 5797.0 ± 0.7 and 5800.1 ± 1.2 MeV, respectively for the J/ψΞ − and J/ψΛK − channels, the uncertainties being statistical only, are consistent with each other and with the world-average value, 5797.0 ± 0.6 MeV [20]. The signal components corresponding to fully reconstructed Ξ − b candidates are shown by the solid green curves. The fitted yield of the partially reconstructed Ξ − b → J/ψΣ 0 K − contribution, reconstructed as J/ψΛK − , is 820 ± 158, represented by the dotted-dashed curve in Fig. 2 (right). The Ξ − b fit results illustrate this part of the reconstruction procedure and provide the first confirmation of the When reconstructing Ξ − b π + π − candidates, we select events with Ξ − b invariant mass within 54 (27) MeV of the fitted Ξ − b mass for the J/ψΞ − (J/ψΛK − ) channel, corresponding to approximately 2.8 (1.8) times the mass resolution, as shown by the vertical solid lines in Fig. 2. The 5.63 < M(J/ψΛK − ) < 5.76 GeV mass region is used for the partially reconstructed Ξ − b → J/ψΣ 0 K − decay mode, shown by the dashed vertical lines in Fig. 2 (right). These mass ranges are selected through the same optimization procedure as used for the other selection criteria.
Since the lifetime of the excited Ξ b states is expected to be negligible, the Ξ − b π + π − candidates are formed by combining the selected Ξ − b candidates with two OS tracks originating from the PV, as in Refs. [37][38][39][40]. Combinations of a Ξ − b candidate with two SS pions from the PV are used as a control channel and form the SS control region. The analysis is performed using the mass difference variable which has a better mass resolution than M( According to the simulation studies, this variable also has the advantage of being insensitive to a potential mass shift caused by the fact that the photon emitted in the Ξ − b → J/ψΣ 0 K − , Σ 0 → Λγ decay sequence is not reconstructed. Following the technique developed in Ref. [40], the selected Ξ − b candidate and all tracks forming the PV are refit to a common vertex, further improving the Ξ − b π + π − invariant mass resolution of the fully reconstructed channels from 1.39 ± 0.11 to 0.94 ± 0.06 MeV (statistical uncertainties only), as obtained from simulation studies.
Theoretical studies [12,13,21] and analogous decays of excited charm baryons [20,41] suggest that the decay Therefore, an additional requirement is applied to enhance this contri-bution. As the Ξ * 0 b state has a mass of 5952.3 ± 0.6 MeV, the mass difference M( π + will peak at 15.73 MeV [20]. To avoid complications in understanding the Ξ − b π + π − threshold, we do not apply a minimum cut on this mass difference but simply require it to be less than 20.73 MeV, with the 5 MeV addition found to be optimal when considering the Ξ * 0 b natural width and our detector resolution. The invariant mass distribution of the selected Ξ − b π + π − candidates is shown in Fig. 3, using the mass difference variable ∆M. The left plot combines the data from the Ξ − b → J/ψΞ − and  [MeV]  A narrow peak is seen near the threshold of the Ξ − b π + π − system in both plots of Fig. 3. The excess is also visible in each of the two independent decay channels, J/ψΞ − and J/ψΛK − . We have also studied the OS and SS distributions in a wider range of ∆M (up to 280 MeV) and found no other significant peaks. A simultaneous unbinned extended maximum-likelihood fit is performed on the two data samples shown in Fig. 3, the result being represented by the red curves. The signal component is described with a relativistic Breit-Wigner (RBW) function [42,43] for the Ξ b (6100) − → Ξ * 0 b π − decay, convolved with a double-Gaussian resolution function. The mass and natural width of the signal function are the two parameters of interest in the fit. The normalization and background parameters are different for the fully and partially reconstructed channels, as are the resolution parameters, which are fixed from the simulation studies. The background component is modeled with the threshold function (∆M) α , where α is a free parameter.

CMS
The fitted mass difference of the new Ξ b (6100) − state is ∆M Ξ b (6100) − = 24.14 ± 0.22 MeV, where the uncertainty is statistical only. The fitted signal yields are 26 ± 7 and 34 ± 9 for the fully reconstructed and the Ξ − b → J/ψΣ 0 K − channels, respectively. The relative yield of the Ξ b (6100) − , w.r.t. the Ξ − b yield, is found to be noticeably larger in the partially reconstructed Ξ − b channel, compared to the fully reconstructed channels. Given the large uncertainties in the observed small Ξ b (6100) − signal yields, this discrepancy is consistent with being a statistical fluctuation. The order-of-magnitude larger signals of the Ξ * 0 b → Ξ − b π + decays, with respect to the Ξ − b ground state signals, are found to be consistent between all three Ξ − b reconstruction channels.
The natural width of the Ξ b (6100) − is too small to be measured with the present data sample and experimental resolution. An upper limit on Γ(Ξ b (6100) − ) has been obtained through a scan of the profiled likelihood, assuming an asymptotic distribution. The measured upper limit, at 95% confidence level, is Γ(Ξ b (6100) − ) < 1.9 MeV, where the systematic uncertainties, discussed below, are taken into account.
The local statistical significance of the Ξ b (6100) − signal is evaluated with the likelihood ratio technique, comparing the background-only and signal-plus-background hypotheses (with four additional free parameters), using asymptotic formulas [44,45]. The resulting significance of the Ξ b (6100) − signal varies between 6.2 and 6.7 standard deviations, depending on the fit model variations used to evaluate the systematic uncertainties. The RBW function used in the signal modeling includes Blatt-Weisskopf barrier factors [43], which depend on the radial parameter r and on the angular momentum l (spin). In the baseline fit, r = 3.5 GeV −1 and l = 1. The corresponding systematic uncertainties are obtained by varying r between 1 and 5 GeV −1 or by assigning l = 0. The r variations have a negligible effect on the results, while fixing l = 0 changes the signal shape and induces a mass difference variation of 0.01 MeV, taken as the corresponding systematic uncertainty.
To account for a possible difference between the measured and simulated mass resolutions, the fits are repeated with resolutions scaled up or down by 1.074, a factor determined from the comparison of the Ξ − b resolutions in data and simulation. The resulting systematic uncertainty of the Ξ b (6100) − mass difference is 0.02 MeV.
Simulation studies show a shift of 0.07 MeV between the generated and reconstructed mass differences; this shift is treated as an additional systematic uncertainty in the ∆M Ξ b (6100) − measurement.
The systematic uncertainty reflecting the ∆M fit range is evaluated by changing the upper end of the ∆M fit range from its default 100 MeV to 80, 120, and 150 MeV. The largest mass difference change of 0.02 MeV is taken as the corresponding systematic uncertainty.
A potential bias due to a possible misalignment of the tracker detectors is evaluated by comparing the results obtained with the data collected in 2016, 2017, and 2018. This is a reasonable evaluation, given that the inner part of the CMS tracker was replaced between the 2016 and 2017 data-taking periods. The measured mass is found to be insensitive to alignment uncertainties.
The total systematic uncertainty in the measured mass difference ∆M Ξ b (6100) − , calculated as the sum in quadrature of the partial terms, is 0.09 MeV.
In summary, we report the observation of a new excited beauty strange baryon, decaying to Ξ − b π + π − . The analysis uses proton-proton collision data collected by the CMS experiment at √ s = 13 TeV, corresponding to an integrated luminosity of 140 fb −1 . The measured mass difference of this state is It is particularly remarkable that if the Ξ b (6100) − baryon were only 13 MeV heavier, it would be above the Λ 0 b K − mass threshold and could decay to this final state. The natural width of this resonance is compatible with zero and a 95% confidence level upper limit of 1.9 MeV has been determined.
Following analogies with the established excited Ξ c baryon states [20], and considering several theoretical predictions [12,13,21], the new Ξ b (6100) − resonance and its decay sequence are consistent with the lightest orbitally excited Ξ − b baryon, with the light diquark angular momentum j ds = 1 and J P = 3/2 − (excitation with orbital momentum L = 1 between the b quark and the ds diquark). This suggests that it is the beauty analogue of the Ξ c (2815) baryon [41]. Measuring a natural width of the Ξ b (6100) − smaller than 1.9 MeV comes as a surprise, given the larger values predicted by the theory calculations [12,13,21], based on the assumption that the Ξ b * * − → Ξ * 0 b π − decay proceeds predominantly via S-wave (3/2 − → 3/2 + 0 − ). The observation of this baryon and the measurement of its properties provide information that should help to distinguish between different theoretical models used to calculate the properties of the excited Ξ b states.

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid and other centers for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC, the CMS detector, and the supporting computing infrastructure provided by the following funding agencies:   [33] G. Punzi, "Sensitivity of searches for new signals and its optimization", in Proceedings of PHYSTAT 2003, Statistical problems in particle physics, astrophysics and cosmology, p. MODT002. 2003. arXiv:physics/0308063. eConf C030908.
INFN Sezione di Bari a , Università di Bari b , Politecnico di Bari c , Bari, Italy