Observation of a new $\Xi_b^-$ resonance

From samples of $pp$ collision data collected by the LHCb experiment at $\sqrt{s}=7$, $8$ and $13$ TeV corresponding to integrated luminosities of 1.0, 2.0 and 1.5 fb$^{-1}$, respectively, a peak in both the $\Lambda_b^0K^-$ and $\Xi_b^0\pi^-$ invariant mass spectra is observed. In the quark model, radially and orbitally excited $\Xi_b^-$ resonances with quark content $bds$ are expected. Referring to this peak as $\Xi_b(6227)^-$, the mass and natural width are measured to be $m_{\Xi_{b}(6227)^-}=6226.9\pm2.0\pm0.3\pm0.2$ MeV/$c^2$ and $\Gamma_{\Xi_b(6227)^-}=18.1\pm5.4\pm1.8$ MeV/$c^2$, where the first uncertainty is statistical, the second is systematic, and the third, on $m_{\Xi_b(6227)^-}$, is due to the knowledge of the $\Lambda_b^0$ baryon mass. Relative production rates of the ${\Xi_b(6227)^-\to\Lambda_b^0K^-}$ and ${\Xi_b(6227)^-\to\Xi_b^0\pi^-}$ decays are also reported.

In the constituent quark model [1,2], baryonic states form multiplets according to the symmetry of their flavor, spin, and spatial wave functions.The masses, widths and decay modes of these states give insight into their internal structure [3].The Ξ 0 b and Ξ − b states form an isodoublet of bsq bound states, where q is a u or d quark, respectively.Three such isodoublets, which are neither radially nor orbitally excited, should exist [4], and include one with spin j qs = 0 and J P = (1/2) + (Ξ b ), a second with j qs = 1 and J P = (1/2) + (Ξ b ), and a third with j qs = 1 and J P = (3/2) + (Ξ b * ).Here, j qs is the spin of the light diquark system qs, and J P represents the spin and parity of the state.Three of the four j qs = 1 states have been recently observed through their decays to Ξ 0 b π − and Ξ − b π + [5][6][7].Beyond these lowest-lying states, a spectrum of heavier states is expected [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], where there are either radial or orbital excitations amongst the constituent quarks.The only such states discovered thus far in the b-baryon sector are the Λ b (5912) 0 and Λ b (5920) 0 resonances [24], which are consistent with being orbital excitations of the Λ 0 b baryon.In this Letter, we report the first observation of a new state, decaying into both Λ 0 b K − and Ξ 0 b π − , using samples of pp collision data collected with the LHCb experiment at 7, 8 and 13 TeV, corresponding to integrated luminosities of 1.0, 2.0 and 1.5 fb −1 , respectively.The observation of these decays is consistent with the strong decay of a radially or orbitally excited Ξ − b baryon, hereafter referred to as Ξ b (6227) − .Charge-conjugate processes are implicitly included throughout this Letter.
The mass and width of the Ξ b (6227) − baryon are measured using the Λ 0 b K − mode, where the Λ 0 b baryon is detected through its fully reconstructed hadronic (HAD) decay to Λ + c π − .Larger samples of semileptonic (SL) Λ 0 b and Ξ 0 b decays are used to measure the production ratios where f Ξ b (6227) − , f Ξ 0 b and f Λ 0 b are the fragmentation fractions of a b quark into each baryon and B represents a branching fraction.Here, the Λ 0 b and Ξ 0 b baryons are detected using Owing to much larger branching fractions, the SL signal yields are about an order of magnitude larger than that of any fully hadronic final state, which enables the observation of the Ξ b (6227) − → Ξ 0 b π − mode.The SL decays are not used in the Ξ b (6227) − mass or width determination, as they have larger systematic uncertainties due to modeling of the mass resolution.
The LHCb detector [25,26] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks [25,26].The tracking system provides a measurement of the 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 (IP), 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 [27].The online event selection is performed by a trigger, which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction [28,29].Simulated data samples are produced using the software packages described in Refs.[30][31][32][33][34][35][36].
Samples of The left column is for 7, 8 TeV and the right is for 13 TeV data.Fits are overlaid, as described in the text.Here, the Λ 0 b → Λ + c µ − X mode has been prescaled by a factor of ten.
meson that has small χ 2 IP , consistent with being produced in the strong decay of the Ξ b (6227   To improve the resolution on the Ξ b (6227) − mass, we use the mass differences where the decay width is set to a negligible value.For the Λ 0 b → Λ + c π − mode, the δm K resolution model is approximately Gaussian with a width of 2.4 MeV/c 2 .For the SL decays, the missing momentum, p miss , is estimated by assuming it is carried by a zero-mass particle that balances the momentum transverse to the H 0 b direction (formed from its decay vertex and PV), and satisfies the mass constraint (p . Mass resolution shape parameters are obtained by fitting the δm K(π) spectra from simulated decays, which include contributions from excited charm baryons and final states with τ − leptons.The core of the resolution function has a half-width at half-maximum of about 20 MeV/c 2 , and has a tail toward larger mass (see Appendix).The obtained shape parameters are fixed in the fits to data.
The δm K and δm π spectra in data are shown in Fig. 2. The Ξ b (6227) − mass and width are obtained from a simultaneous unbinned maximum-likelihood fit to the δm K spectra in 7, 8 and 13 TeV data, using the Λ 0 b → Λ + c π − mode.The signal shape is described by a P -wave relativistic Breit-Wigner function [40] with a Blatt-Weisskopf barrier factor [41], convoluted with a Gaussian resolution function of width 2.4 MeV/c 2 .The mass and width are common parameters in the fit.The background shape is described by a smooth threshold function [42] with shape parameters that are freely and independently varied in the fits to the two data sets.A peak is observed in both data sets, with a mean δm peak K = 607.3± 2.0 MeV/c 2 and width Γ Ξ b (6227) − = 18.1 ± 5.4 MeV/c 2 .The peak has a local statistical significance of about 7.9σ for the combined fit, based on the difference in log-likelihoods between a fit with zero signal and the best fit.The signal yields are given in Table 1.
The Ξ b (6227 is fit in a similar way, except for the different resolution function (see Appendix).A Gaussian constraint on the width of Γ Ξ b (6227) − = 18.1 ± 5.4 MeV/c 2 is applied, as obtained from the fit to the hadronic mode, and the mean is freely varied.A peak is observed at a mass difference of 610.8 ± 1.0 (stat) MeV/c 2 , which is consistent with that of the hadronic mode, and it contains a yield about 15 times larger, as expected.The statistical significance of this peak is about 25σ, thus clearly establishing this peaking structure.
The Ξ 0 b π − final state is investigated by examining the δm π spectra in  Ξ b (6227) − → Ξ 0 b π − candidate decays, as shown in the bottom row of Fig. 2. The fit is performed in an analogous way to the δm K spectra, except for a different resolution function (see Appendix for δm π resolution).The fitted mean of 440±5 MeV/c 2 is consistent with the value expected from the hadronic mode of δm peak The statistical significance of the peak is 9.2σ.The production ratios are computed using where N represents the yields in Table 1, and rel is the relative efficiency between the Ξ b (6227) − and H 0 b selections, reported in Table 2.The quantity κ ( ) represents corrections to the N (H 0 b ) SL signal yields to account for (i) random A number of sources of systematic uncertainty have been considered.For the mass and width, the momentum scale uncertainty of 0.03% [43] leads to a 0.1 MeV/c 2 uncertainty on δm K .A fit bias on the mass of 0.1 MeV/c 2 is observed in simulation, and is corrected for and a systematic uncertainty of equal size is assigned.Uncertainty due to the signal shape model is estimated by using a nonrelativistic Breit-Wigner signal shape and varying the Gaussian resolution by ±10% about its nominal value.With these variations, systematic uncertainties of 0.2 MeV/c 2 on δm K , and 0.9 MeV/c 2 on Γ Ξ b (6227) − are obtained.Sensitivity to the background function is assessed by varying the fit range by 100 MeV/c 2 on both ends, from which maximum shifts of 0.2 MeV/c 2 in the mass and 1.6 MeV/c 2 in the width are observed; these values are assigned as systematic uncertainties.Adding these systematic uncertainties in quadrature, leads to a total systematic uncertainty of 0.3 MeV/c 2 on the mass and 1.8 MeV/c 2 on the width.
The systematic uncertainties affecting the production ratio measurements are listed in Table 3.The background shape affects the yield determination, and the associated systematic uncertainty is estimated by varying the fit range as described above.(Different  background models give smaller deviations.)For the signal shape, the uncertainty is dominated by the resolution function.In an alternative fit, the resolution parameters are allowed to vary within twice the expected uncertainty and we take the difference with respect to the nominal result as the uncertainty.To assess the dependence on the kinematical properties of the Ξ b (6227) − resonance, the p T spectrum in simulation is weighted by 1 ± 0.01 × p Ξ b (6227) − T /( GeV/c); the relative change in efficiency is assigned as a systematic uncertainty.The charged-particle tracking efficiency, obtained using large samples of J/ψ → µ + µ − decays [44], contributes an uncertainty of 1% to ( ) rel .The systematic uncertainty of the PID requirement on the K − or π − from the Ξ b (6227) − baryon is determined by comparing the PID response of kaons and pions in the Λ + c → pK − π + decay between data and simulation, where the latter are obtained from calibration data, as described previously.The uncertainty on N (H 0 b ) is taken as the quadratic sum of the uncertainties on the fitted yields and the uncertainties on the κ ( ) corrections.Lastly, the finite size of the simulated samples is taken into account.
In summary, we report the first observation of a new state, assumed to be an excited Ξ − b state, using pp collision data samples collected by LHCb at √ s = 7 , 8 and 13 TeV.The mass and width are measured to be where for the last result we have used m Λ 0 b = 5619.58± 0.17 MeV/c 2 [39].We have also measured the relative production rates to two final states, Λ 0 b K − and Ξ 0 b π − , as summarized in Table 4.The R(Λ 0 b K − ) values from the hadronic mode are consistent with those obtained in the SL mode, and are about an order of magnitude smaller than R(Ξ 0 b π − ).Assuming f Ξ 0 b 0.1f Λ 0 b [45][46][47], we find that the ratio of branching fractions B(Ξ b (6227 , albeit with sizable uncertainty (≈ ±0.5) due to theoretical assumptions and the values of experimental inputs.

Quantity [10
Ξ − b states expected in this mass region, the presence of more than one of these states contributing to this peak cannot be excluded.More precise measurements of the width and the relative branching fractions to Λ 0 b K − and Ξ 0 b π − , as well as Ξ b π − and Ξ b * π − , could help to determine the J P quantum numbers of this state [20].
The symbol M * represents the mass after the constraint (p is applied, as described in the text.The natural width used in the simulation is set to a negligible value, so that these spectra are due entirely to the mass resolution.Fits to the sum of a nonrelativistic Breit-Wigner function and a Crystal Ball function [48] with a common mean value are overlaid.

MeV/c 2
are considered, where HAD and SL indicate the sample from which the mass is determined.We require p K − T > 800 MeV/c and p π − T > 900 MeV/c, based on an optimization of the expected statistical uncertainty on the Ξ b (6227) − signal yield, using simulation to model the signal and either wrong-sign (Λ 0 b K + , Ξ 0 b π + ) or Ξ b (6227) − mass sideband samples in data to . After all selections the dominant source of background is due to combinations of real Λ 0 b (Ξ 0 b ) decays with a random K − (π − ) meson.All candidates satisfying these selections are retained.

2 H 0 b
Figure 2: Spectra of mass differences for Ξ b (6227) − candidates, reconstructed in the final states(top) Λ 0 b K − , with Λ 0 b → Λ + c π − , (middle) Λ 0 b K − , with Λ 0 b → Λ + c µ − X, and (bottom) Ξ 0 b π − , with Ξ 0 b → Ξ + c µ − X,along with the results of the fits.The left column is for 7, 8 TeV and the right is for 13 TeV data.The symbol M * represents the mass after the constraint (p H + c + p µ − + p miss ) 2 = m 2 H 0 b and (iii) slightly different integrated luminosities used for the Ξ b (6227) − and H 0 b samples.The contribution from random H + c µ − combinations is estimated from a study of the wrong-sign (H + c µ + ) and right-sign (H + c µ − ) yields, from which a correction of 1.010 ± 0.002 to both R(Ξ 0 b π − ) and R(Λ 0 b K − ) is found.Cross-feeds from SL Ξ − b decays, which must be subtracted from N (Ξ 0 b ), are inferred by adding a π − meson to the Ξ + c µ − candidate and searching for excited Ξ 0 c states.Mass peaks associated with the Ξ c (2645) 0 and Ξ c (2790) 0 resonances are observed, although for the former about half is due to Ξ c (2815) + → Ξ c (2645) 0 π + decays, as determined through a study of the Ξ + c π + mass spectrum.Since the Ξ c (2815) + µ − final state is predominantly from Ξ 0 b decays, this contribution is not subtracted.After correcting for the pion detection efficiency, we estimate that R(Ξ 0 b π − ) must be corrected by 1.11±0.03.Slightly different-size data samples are used for the Ξ b (6227) − and inclusive H 0 b yield determinations, which amounts to corrections of less than 3%.

a
Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil b Laboratoire Leprince-Ringuet, Palaiseau, France c P.N.Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia d Università di Bari, Bari, Italy e Università di Bologna, Bologna, Italy f Università di Cagliari, Cagliari, Italy g Università di Ferrara, Ferrara, Italy h Università di Genova, Genova, Italy i Università di Milano Bicocca, Milano, Italy j Università di Roma Tor Vergata, Roma, Italy k Università di Roma La Sapienza, Roma, Italy l AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland m LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain n Hanoi University of Science, Hanoi, Vietnam o Università di Padova, Padova, Italy p Università di Pisa, Pisa, Italy q Università degli Studi di Milano, Milano, Italy r Università di Urbino, Urbino, Italy s Università della Basilicata, Potenza, Italy t Scuola Normale Superiore, Pisa, Italy u Università di Modena e Reggio Emilia, Modena, Italy v MSU -Iligan Institute of Technology (MSU-IIT), Iligan, Philippines w Novosibirsk State University, Novosibirsk, Russia x National Research University Higher School of Economics, Moscow, Russia y Sezione INFN di Trieste, Trieste, Italy z Escuela Agrícola Panamericana, San Antonio de Oriente, Honduras aa School of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi'an, China ab Physics and Micro Electronic College, Hunan University, Changsha City, China † Deceased

Table 1 :
Uncorrected Ξ b (6227) − and H 0 b signal yields for 7, 8 and 13 TeV data.The H 0 b yields are limited to the signal regions used to form Ξ b (6227) − candidates (see text).

Table 2 :
Relative efficiencies ( ) for the SL modes.Uncertainties are due only to the finite size of the simulated samples. rel