Observation of a new $\Xi_b^0$ state

Using a proton-proton collision data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 8.5~fb$^{-1}$, the observation of a new excited $\Xi_b^0$ resonance decaying to the $\Xi_b^-\pi^+$ final state is presented. The state, referred to as $\Xi_b(6227)^0$, has a measured mass and natural width of $m(\Xi_b(6227)^0) = 6227.1^{\,+1.4}_{\,-1.5}\pm0.5$ MeV, $\Gamma(\Xi_b(6227)^0) = 18.6^{\,+5.0}_{\,-4.1}\pm1.4$ MeV, where the uncertainties are statistical and systematic. The production rate of the $\Xi_b(6227)^0$ state relative to that of the $\Xi_b^-$ baryon in the kinematic region $2<\eta<5$ and $p_{\rm T}<30$ GeV is measured to be $\frac{f_{\Xi_b(6227)^0}}{f_{\Xi_b^-}}{\mathcal{B}}(\Xi_b(6227)^0\to\Xi_b^-\pi^+) = 0.045\pm0.008\pm0.004$, where ${\mathcal{B}}(\Xi_b(6227)^0\to\Xi_b^-\pi^+)$ is the branching fraction of the decay, and $f_{\Xi_b(6227)^0}$ and $f_{\Xi_b^-}$ represent fragmentation fractions. Improved measurements of the mass and natural width of the previously observed $\Xi_b(6227)^-$ state, along with the mass of the $\Xi_b^-$ baryon, are also reported. Both measurements are significantly more precise than, and consistent with, previously reported values.


Introduction
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, natural 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 the Ξ b state with spin j qs = 0 and J P = (1/2) + , the Ξ b with j qs = 1 and J P = (1/2) + , and the Ξ b * with j qs = 1 and J P = (3/2) + . 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 observed through their decays to Ξ 0 b π − and Ξ − b π + final states [5][6][7].
In this article, the observation of a new beauty-baryon resonance, referred to as Ξ b (6227) 0 , is reported using samples of proton-proton (pp) collision data collected with the LHCb experiment at center-of-mass energies of √ s = 7, 8 TeV (Run 1) and 13 TeV (Run 2), corresponding to integrated luminosities of 1.0, 2.0 and 5.5 fb −1 , respectively. The resonance is seen through its decay to the Ξ − b π + final state, where the Ξ − b baryon is reconstructed in the fully hadronic decay channels Ξ 0 c π − and Ξ 0 c π − π + π − , with Ξ 0 c → pK − K − π + . Charge-conjugate processes are implicitly included throughout this paper.
Using the 13 TeV data, the production rate of the Ξ b (6227) 0 state is measured relative to that of the Ξ − b baryon as Here, f Ξ b (6227) 0 and f Ξ − b are the fragmentation fractions for b → Ξ b (6227) 0 and b → Ξ − b , which include contributions from the decays of higher-mass b-hadrons, and is the branching fraction of the decay. The same pp collision data set is used to improve the precision on the mass and width of the recently observed Ξ b (6227) − state [23] using the Ξ b (6227) − → Λ 0 b K − decay mode. The analysis presented here benefits greatly from the larger data sample, but also by using both Λ 0 b → Λ + c π − and Λ 0 b → Λ + c π − π + π − decays, leading to about a four-fold increase in the Λ 0 b yield over that which was used in Ref. [23]. Lastly, with the large samples of Ξ − b and Λ 0 b decays obtained in this analysis, the most precise measurement of the Ξ − b mass to date is presented. The Ξ − b mass obtained in this analysis is then used to obtain the mass of the Ξ b (6227) 0 resonance.

Detector and simulation
The LHCb detector [39,40] 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 siliconstrip 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 the momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV. 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. 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 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 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.
Simulation is required to model the effects of the detector acceptance and the imposed selection requirements. It is also used to determine the expected invariant-mass resolution. In the simulation, pp collisions are generated using Pythia [41] with a specific LHCb configuration [42]. Decays of unstable particles are described by EvtGen [43], in which final-state radiation is generated using Photos [44]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [45] as described in Ref. [46].
To improve the agreement of the simulation with the data in modeling the kinematics of beauty baryons within the acceptance of the LHCb detector, the simulated beauty-baryon momentum components, p T and p z , are transformed to match the distributions obtained from background-subtracted data [47]. Here, p z is the momentum component along the beam axis. In particular, the p T and p z are transformed according to For the Λ 0 b and Ξ − b simulations, the values κ T = 0.98 and κ z = 0.99 bring the simulated p T and p z distributions into good agreement with those of the data, while for the Ξ b (6227) 0 and Ξ b (6227) − simulations, the values κ T = 0.99 and κ z = 1.0 are found. Values of κ less than unity indicate that the given momentum component needs to be scaled to lower values to bring the simulation into agreement with the data. In the optimization of specific selections and the determination of selection efficiencies, these tunings are employed, as discussed below.
The particle identification (PID) response of charged hadrons produced in simulated signal decays is obtained from dedicated calibration samples from the data where no PID requirements are imposed [48,49]. The D * + → D 0 π + mode is used for the K − and π + meson PID responses and the Λ 0 b → Λ + c π − and Λ → pπ − decays are used for the proton PID response. Each final-state signal hadron has its PID response drawn from a three-dimensional probability distribution function that depends on the hadron's p and p T , and the number of reconstructed charged particles in the event.
3 Selection requirements The Ξ − b candidates are reconstructed using the Ξ 0 c π − and Ξ 0 c π − π + π − decay modes, while the Λ 0 b sample uses the Λ + c π − and Λ + c π − π + π − final states. The charm baryons are detected through the decays Ξ 0 c → pK − K − π + and Λ + c → pK − π + . In what follows, H b refers to either the Λ 0 b or Ξ − b baryon, and H c signifies the corresponding charm baryon, Λ + c or Ξ 0 c , according to the above decay sequences.
Charged hadrons used to reconstruct the H b candidates are required to be significantly detached from all PVs in the event using the quantity χ 2 IP , which is the difference in χ 2 of the vertex fit of a given PV when the particle is included or excluded from the fit. Each track is required to have χ 2 IP > 4, which corresponds to an IP that is at least twice as large as the expected IP resolution. Loose PID requirements are also imposed on all the H b decay products to ensure that they are consistent with the intended decay sequence.
The H c candidates are required to have a good-quality vertex fit, have significant displacement from all PVs in the event, and satisfy the invariant-mass requirements, MeV, corresponding to about three times the mass resolution. Here, and throughout this paper, M represents the invariant mass of the particle(s) indicated in parentheses, and m represents the measured mass of the indicated particle, using Ref. [50] for known particles.
One or three charged pions, with total charge −1, are combined with H c candidates to form the H b samples. The fitted decay vertex is required to be consistent with a single point in space, evidenced by having good fit quality. To suppress combinatorial background, the H b decay vertex is required to be significantly displaced from all PVs in the event and have small χ 2 IP to at least one PV. The H b candidates are assigned to the PV for which χ 2 IP is minimum. After these selections, clear Ξ − b and Λ 0 b peaks can be seen in the data. The Λ 0 b → Λ + c π − decay mode has an excellent signal-to-background (S/B) ratio, and no further selections are applied. For the decays, a boosted decision tree (BDT) discriminant [51][52][53] is used to further improve the S/B ratio. The set of variables used by the BDT is similar for the three modes. Those common to all three modes include: the χ 2 values of the fitted H c and H b decay vertices, the angle between the H b momentum direction and the vector pointing from the PV to the H b decay vertex, the H b and H c decay times, and for each final-state hadron, p, p T , χ 2 IP and a PID response variable. For the H b → H c π − π + π − modes, three additional variables are included: M (π − π + π − ), the χ 2 of the π − π + π − vertex fit, and the χ 2 of the vertex separation between the 3π vertex and the associated PV. The BDT is trained using simulated decays for the signal distributions in these variables, and the background distributions are taken from a combination of the H c or H b mass sidebands in data. The requirements on the BDT discriminant are chosen based on optimizing the product of signal efficiency and signal purity. The resulting BDT selection requirement is ∼100%, 94% and 93% efficient for   In anticipation that the Ξ − b → Ξ 0 c π − decay mode will be used to measure the relative production rate, R(Ξ − b π + ), Ξ − b candidates are restricted to lie in the kinematic region p T < 30 GeV and 2 < η < 5; this selection retains 99.7% of the signal decays.
With all of the selections applied, the resulting Ξ − b and Λ 0 b candidate invariant-mass spectra are shown in Figs. 1 and 2, respectively. The fits, as described below, are overlaid.

Ξ b (6227) 0 selection
The Ξ b (6227) 0 candidates are formed by combining a Ξ − b candidate with a π + meson consistent with coming from the same PV.
candidates are required to have their masses in the intervals 5737 < M (Ξ 0 c π − ) < 5847 MeV and 5750 < M (Ξ 0 c π − π + π − ) < 5840 MeV, respectively, corresponding to about three times the mass resolution about the Ξ − b mass [50]. The majority of particles from the PV are pions, and therefore only a loose requirement is applied to the pion PID hypothesis, sufficient to render the contribution from misidentified kaons and protons to be at the few percent level. To suppress background from random π + mesons, which tend to have lower p T than those from b-hadron decays, the selection on the p T of the π + candidate is optimized as follows. The Punzi figure-ofmerit [54] FOM = (p T )/( N B (p T ) + a/2) with a = 5 is used, where (p T ) and N B (p T ) are the signal efficiency and background yield as a function of the applied π + meson p T requirement. For the signal efficiency, (p T ), the π + meson p T is scaled by the ratio p T /p T , as given in Eq. (2). The optimal requirements are p T > 700 MeV and 900 MeV for the modes, respectively. The higher p T requirement on the latter is due to the higher average momentum required of the Ξ b (6227) 0 baryon in order for all of its decay products to be within the LHCb detector acceptance. These selections provide an expected signal efficiency of about 55% and reduce the background by an order of magnitude.

Ξ b (6227) − selection
The Ξ b (6227) − candidates are formed by combining Λ 0 b candidates in the mass interval 5560-5670 MeV and K − candidates consistent with emerging from the same PV. A similar optimization to that discussed above is performed to determine the optimal p T requirement on the K − candidate. A loose PID requirement on the K − candidate is applied in advance, which suppresses about 80% of the misidentified π − background. Since the is the expected signal yield based on an initial signal yield estimate, N S0 , and the efficiency, (p T ), obtained from simulation. The background yield, N B , is obtained from wrong-sign Λ 0 b K + combinations. The optimal requirement is p T > 1000 MeV. The efficiency of this selection is about 40% and reduces the combinatorial background by a factor of ten.
With the p T > 1000 MeV requirement applied, a more refined optimization is performed on the K − PID requirement. The PID tuning for the 7 and 8 TeV data differs from that of the 13 TeV data [49], so different requirements are imposed. Using the same FOM as above, except with the PID variable used in place of the p T , tighter PID requirements are imposed. The optimal PID requirement on the K − candidate provides an efficiency of 80% (95%) while suppressing the background by a factor of 2 (1.6) for the Run 1 (Run 2) data samples. The same p T and PID requirements are applied to the K − candidate in both the ) background shapes to determine the signal yields. The signal shapes are described by the sum of two Crystal Ball functions [55] with a common value for the peak mass. For the Ξ − b modes, the signal shapes are fixed to the values obtained from simulation, except for the widths, which are allowed to vary freely in the fit. For the Λ 0 b modes, the signal yields in data are significantly larger than in the simulated samples, and thus all signal shape parameters are freely varied in the fit. For Table 1: Signal yields of Ξ − b and Ξ b (6227) 0 decays for the full data set after all selection requirements, and the corresponding Run 2 signal yields used for the measurement of R(Ξ − b π + ) at 13 TeV.

All data
10 800 ± 400 5100 ± 300 8300 ± 300 where the kaon is misidentified as a pion. This Cabibbo-suppressed (CS) contribution is small compared to the Cabibbo-favored (CF) H b → H c π − π + π − decay. The CS to CF signal yield ratio is fixed to 1.8% based upon the PID efficiency of the K − meson to pass the π − PID requirement and the assumption that the CS/CF ratio of branching fractions is 7.3%, as is the case for

Fit to the
To search for the Ξ b (6227) 0 state, the mass difference, , is used, since the mass resolution on this difference is about eight times better than that of M (Ξ − b π + ). Moreover, systematic uncertainties, particularly that due to the momentum scale calibration, are greatly reduced. The resulting mass difference spectra, δM π , for both the right-sign and wrong-sign (Ξ − b π − ) combinations are shown in Fig. 3. The top row shows the spectra using Ξ − b → Ξ 0 c π − candidates and the bottom row shows the spectra using Ξ − b → Ξ 0 c π − π + π − candidates. A clear signal is observed at the same invariant mass in both right-sign final states, while there are no significant structures in the wrong-sign The left column shows the right-sign candidates and the right column shows the wrong-sign candidates. The fit projections are overlaid.

spectra.
The Ξ b (6227) 0 mass and natural width are obtained from a simultaneous unbinned maximum-likelihood fit to the four δM π spectra. The signal shape is described by a P -wave relativistic Breit-Wigner function [57] with a Blatt-Weisskopf barrier factor [58] of 3 GeV −1 , convolved with a resolution function. The mass resolution is parametrized as the sum of two Gaussian functions with a common mean of zero and widths that are fixed to the values obtained from simulation. The weighted average mass resolution is about 2.0 MeV, which is negligible compared to the apparent width of the observed peak. The background shape is described by a smooth threshold function with shape parameters that are common between the right-sign and wrong-sign spectra, but independent for the Ξ 0 c π − and Ξ 0 c π − π + π − final states. The threshold function takes the form The parameter δM 0 represents a threshold. Due to the low signal yield, the fit does not always converge when δM 0 is left to freely vary. Therefore, δM 0 is fixed to 240 MeV (10 MeV below the minimum of the fit range), and the value is varied as a source of systematic uncertainty. The parameters A and C are freely varied in the fit. The projection of the fit is superimposed on the data in Fig. 3. Using the difference in log-likelihoods between the nominal fit and a fit where the signal yield is fixed to zero, a statistical significance of about 10 σ is obtained. The Ξ b (6227) 0 peak parameters are

Production ratio R(Ξ
The relative production rate is obtained from where N (Ξ b (6227) 0 ) and N (Ξ − b ) are the signal yields and rel is the relative efficiency between the Ξ b (6227) 0 and Ξ − b selections. As the Ξ − b selection is common to both samples, the relative efficiency is predominantly due to the efficiency of reconstructing and selecting the π + meson. About 80% of the signal is from the 13 TeV data set, and therefore R(Ξ − b π + ) is measured using only that subset of the data. In addition, the acceptance requirement p T < 30 GeV and 2 < η < 5 is applied to the reconstructed Ξ b (6227) 0 candidates. To obtain N (Ξ b (6227) 0 ) and N (Ξ − b ), an alternative fit with only the 13 TeV data is performed, with the resulting Ξ b (6227) 0 and Ξ − b signal yields shown in Table 1. The Ξ − b signal yield is obtained by integrating the Ξ − b → Ξ 0 c π − , Ξ 0 c K − , and Ξ 0 c π − signal shapes over the same mass interval (5737 < M (Ξ 0 c π − ) < 5847 MeV) that is used in the Ξ b (6227) 0 selection. The Ξ 0 c K − , and Ξ 0 c π − components are included in the Ξ − b yield because simulation shows that these misidentified Ξ − b decays also produce a narrow structure in the δM π spectrum with approximately the same resolution as the Ξ 0 c π − signal. The relative signal efficiency is obtained from the tuned simulation, from which the value rel = (40.0 ± 0.5)% is obtained, where the uncertainty is due to the finite simulated sample sizes. Much of the efficiency loss is due to the p T > 700 MeV requirement; with a less stringent requirement of p T > 200 MeV, the relative efficiency is 75%. The efficiency includes a correction factor of 0.978 ± 0.021, which accounts for a slightly lower tracking efficiency in data than in simulation, as determined from an inclusive J/ψ → µ + µ − calibration sample [59], weighted to match the kinematics of the π + meson from the Ξ b (6227) 0 decay.
With the signal yields in Table 1 and the above value of rel , it is found that where the uncertainty is statistical only.

Fit to the
The spectra of mass differences, Fig. 4 for the As with the Ξ b (6227) 0 signal fit, an unbinned extended maximum-likelihood fit is performed. The wrong-sign spectra are not considered in the fit, since the δM K background shape for the wrong-sign is visibly different from that of the right-sign. As for the Ξ b (6227) 0 fit, the signal shape is described by a P -wave relativistic Breit-Wigner function with a Blatt-Weisskopf barrier factor convolved with a resolution function. The mass resolution is described by the sum of two Gaussian functions with a common mean of zero and widths that are fixed to the values obtained from simulation. The weighted-average width is about 1.4 MeV, which is small compared to the expected natural width of the signal peak. The background shape is given by the same functional form as Eq. (3), with the replacement δM π → δM K and δM 0 is fixed to the kaon mass [50]; the parameters A and C are freely varied in the fit.
The fit projections are superimposed to the data distributions in Fig. 4. The measured Ξ b (6227) − peak parameters are [60] is used to obtain m(Ξ b (6227) − ), with signal yields given in Table 2. It is notable that the sample size is only about 57% as large. This enhancement is expected due to the higher average p T of the kaon from the

Ξ − b mass measurement
The large Ξ − b and Λ 0 b samples allow for a significant improvement in the uncertainty on the Ξ − b mass. Only the H b → H c π − decays are used for this measurement. The lowest total uncertainty is achieved by measuring the mass difference, and m fit (Λ 0 b ) are the peak mass values from fits to the invariant-mass spectra. In m diff , the largest systematic uncertainty, the momentum scale calibration, is greatly reduced. The Ξ − b mass is then obtained from m(Ξ − b ) = m diff + m(Λ 0 b ). All of the previously discussed selection requirements are applied to the samples. Additionally, to render the Cabibbo-suppressed H b → H c K − contribution negligible, a tighter PID requirement is applied to the pion coming directly from the H b decay. This is done to avoid the systematic uncertainty associated with the shape and yield of a H b → H c K − contribution in the mass fit. The efficiency of this additional selection is 89% for both the Λ 0 b and Ξ − b signal decays. The binned likelihood fits described previously are applied to the subset of data for this measurement, with the H b → H c K − background shape removed. Separate fits are performed on the Run 1 (7 and 8 TeV), Run 2 (13 TeV) and the full data set. The invariant-mass spectra for Ξ − b and Λ 0 b candidates and the fits to the full data sample are shown in Fig. 5, along with the full fit and the individual fit components. The numerical results of the mass fits for each running period and the combined data set are given in Table 3. The different values of m fit (Λ 0 b ) for Run 1 and Run 2 are a result of the momentum scale uncertainty, which is greatly reduced in m diff . The values of m diff are statistically compatible between the two running periods.
The Ξ − b mass is found to be where the uncertainty is statistical only.
, for each center-of-mass energy and for the full data sample. For the last row, the known Λ 0 b mass [60] is used. Uncertainties are statistical only.

Systematic uncertainties
Several sources of systematic uncertainty affect the measurements reported in this paper, and are summarized in Table 4.

Ξ b (6227) 0 mass and natural width
To estimate the systematic effect of the background shape, three variations on the nominal fit are considered, including removing the wrong-sign data from the fit, varying the upper range of the mass fit by ±100 MeV, and varying the δM 0 parameter in the background shape, which was fixed in the nominal fit, by ±10 MeV. The maximum values among these variations, 0.1 MeV for δm peak π and 1.4 MeV for Γ(Ξ b (6227) 0 ), are assigned as systematic uncertainty due to the background shape.
For the signal model, several alternative fits are investigated. Varying the barrier radius between 1 GeV −1 and 5 GeV −1 , and changing the relativistic Breit-Wigner function to model either an S-or D-wave decay, do not change the peak parameters significantly. The peak parameters are found to depend slightly on the assumed mass resolution. Varying the mass resolution by ±10% leads to a change in the peak mass and width of 0.1 MeV. A 0.1 MeV uncertainty is assigned to δm peak π and the Ξ b (6227) 0 width from the signal model. The momentum scale calibration uncertainty, known to a precision of ±0.03% [61], largely cancels in the mass difference. To investigate the effect on δm peak π , the simulation is evaluated with the momentum scale shifted up and then down by this amount, leading to an uncertainty of 0.2 MeV. The energy loss uncertainty is estimated to be less than 0.1 MeV based upon the studies presented in Ref. [62]. A 0.1 MeV uncertainty is assigned.
In computing the uncertainty on m(Ξ b (6227) 0 ), the momentum scale and energy loss are taken to be 100% correlated between δm peak π and m(Ξ − b ). The total systematic uncertainty is 0.3 MeV for δm peak π , and 0.5 MeV and 1.4 MeV for the Ξ b (6227) 0 mass and width, respectively.

Ξ b (6227) − mass and natural width
Several variations to the nominal fit are performed to assess the background shape uncertainty. The variations include changing both the lower (by +20 MeV) and upper mass limits (by ±50 MeV) in the fit. The largest changes in the peak parameters, 0.4 MeV in δm peak K and 1.4 MeV in Γ(Ξ b (6227) − ), are assigned as systematic uncertainties. There is a small excess of events in the δm peak K spectrum in the data near 520 MeV. In an alternative fit, a second peak is included in the fit model for both mass spectra. The second peak is found to be statistically insignificant, however, its inclusion changes the Ξ b (6227) − mass by 0.1 MeV and its width by 0.

Production ratio R(Ξ
In the measurement of R(Ξ − b π + ), the sources of uncertainty include the signal and background shapes in the Ξ − b and Ξ b (6227) 0 mass fits, and the relative efficiency estimate. For the Ξ − b mass fit, the signal yield is evaluated with an alternative signal model comprised of the sum of two Gaussian functions, where the means need not be the same and the widths are allowed to vary in the fit. The yield in this alternative fit changes by 2%, which is taken as a systematic error. The uncertainty due to the background shape is studied by changing to a Chebyshev polynomial, which leads to a 1.4% change in the yield. The upper end of the mass fit is reduced from 5950 MeV to 5900 MeV, and the 0.4% change in signal yield is assigned as systematic uncertainty. These two contributions are added in quadrature, resulting in an uncertainty of 1.5% due to the Ξ − b background shape. Variations in the Ξ b (6227) 0 background shape are also considered for the uncertainty on R(Ξ − b π + ). The same set of variations that were performed for the Ξ b (6227) 0 mass and width are considered. Adding the changes in yield in quadrature leads to a 5.6% uncertainty due to the Ξ b (6227) 0 background shape. Several variations in the signal model are considered, and the only non-negligible change in signal yield occurs when a non-relativistic Breit-Wigner function is used in place of the relativistic Breit-Wigner shape. The 0.7% change in the signal yield is assigned as an uncertainty to the Ξ b (6227) 0 yield.
The relative efficiency depends on the extent to which the simulation properly models the (p T , η) spectrum of Ξ − b and the Ξ b (6227) 0 production spectra. The large Ξ − b sample allows for a precise tuning of the κ parameters, so that the p T and η spectrum in simulation is well matched to that of the data. Due to the low signal yields in the Ξ b (6227) 0 sample, it is estimated that the κ parameters have an uncertainty of ±0.005 units. A larger shift than 0.005 units leaves the simulation in clear disagreement with the background-subtracted data. Varying the κ T parameter by this amount leads to an 8% change in rel . This change is due almost entirely to the p T > 700 MeV requirement on the π + meson in the Ξ b (6227) 0 decay. A ±0.005 unit variation in κ z is also investigated, but leads to a negligible change in the relative efficiency. The π + tracking efficiency correction has an uncertainty of 2.1%, which includes a 1.5% contribution from the calibration using J/ψ → µ + µ − decays and 1.4% due to the difference in material interactions between muons and pions [59]. The finite simulated sample sizes lead to an additional systematic uncertainty of 1.2%.

Ξ − b mass
The systematic uncertainty in m diff is studied by performing alternative fits to the data, and assigning the change in m diff with respect to the nominal value as a systematic uncertainty. The background shape uncertainty is estimated by using a Chebychev polynomial instead of the exponential background shape (0.05 MeV), reducing the upper limit of the fit range by 50 MeV (0.06 MeV), and fitting with a finer binning (0.02 MeV). The total background shape uncertainty is taken as the quadrature sum, which is 0.08 MeV. The signal shape uncertainty is assigned by changing the way the tail parameters are treated in the signal function. For the Ξ − b mass fit, they are changed from fixed values to floating values, and for the Λ 0 b , they are changed from floating values to fixed values based on the simulation. These variations lead to a change in m diff of 0.10 MeV, which is assigned as the signal shape uncertainty. The momentum scale and energy loss uncertainties are unchanged from the previous result [63], and are 0.08 MeV and 0.06 MeV, respectively. Adding these uncertainties in quadrature, the total uncertainty on m diff is 0.16 MeV.
In combining m diff = 177.71 ± 0.24 ± 0.16 MeV with m(Λ 0 b ) [60] to obtain m(Ξ − b ), the momentum scale and energy loss portion of the systematic uncertainties are taken to be 100% correlated. The remainder of the uncertainties are taken to be uncorrelated. The resulting systematic uncertainty on m(Ξ − b ) is 0.29 MeV.

Summary
Using pp collision data at √ s = 7, 8 and 13 TeV, corresponding to an integrated luminosity of 8.5 fb −1 , a new Ξ 0 b baryon, referred to as Ξ b (6227) 0 , is reported with a statistical significance of 10 σ. The mass difference, mass and natural width of the peak are measured to be where the first uncertainty is statistical and the second is experimental systematic. The relative production rate of the Ξ b (6227) 0 state at √ s = 13 TeV is measured through its decay to Ξ − b π + to be This is consistent with the values of R(Ξ 0 b π − ) found in Ref. [23] for the Ξ b (6227) − state. The value of R(Ξ − b π + ) can also be compared to the corresponding value found for the lower-mass Ξ b (5945) 0 state of 0.28 ± 0.03 ± 0.01 [7]. Additional unobserved decay modes, Table 4: Summary of systematic uncertainties on quantities related to the Ξ b (6227) 0 (δm peak π , Γ(Ξ b (6227) 0 ), R(Ξ − b π + )), the Ξ b (6227) − (δm peak K , Γ(Ξ b (6227) − ), and the Ξ − b mass (m diff ) measurements. The statistical uncertainties are also reported for comparison. such as Ξ b (5945) 0 → Ξ 0 b π 0 and Ξ b (6227) 0 → (Ξ 0 b π 0 , Λ 0 b K 0 ), would clearly contribute to the total production rate of these excited states, but are yet to be observed.
The result obtained here represents the single most precise determination of the Ξ − b mass. It is consistent with previous measurements and is about a factor of 1.6 times more precise than the current world average [50], and it supersedes the measurement reported in Ref. [63].
With the current data sample, it cannot be excluded that there are two or more narrower, closely spaced states contained within the peaks referred to as Ξ b (6227) − and Ξ b (6227) 0 . With larger data samples in the future, it should be possible to probe whether these peaks are comprised of narrower states.