Precision measurement of the mass and lifetime of the $\Xi_b^0$ baryon

Using a proton-proton collision data sample corresponding to an integrated luminosity of 3 fb$^{-1}$ collected by LHCb at center-of-mass energies of 7 and 8 TeV, about 3800 $\Xi_b^0\to\Xi_c^+\pi^-$, $\Xi_c^+\to pK^-\pi^+$ signal decays are reconstructed. From this sample, the first measurement of the $\Xi_b^0$ baryon lifetime is made, relative to that of the $\Lambda_b^0$ baryon. The mass differences $M(\Xi_b^0)-M(\Lambda_b^0)$ and $M(\Xi_c^+)-M(\Lambda_c^+)$ are also measured with precision more than four times better than the current world averages. The resulting values are $\frac{\tau_{\Xi_b^0}}{\tau_{\Lambda_b^0}} = 1.006\pm0.018\pm0.010$, $M(\Xi_b^0) - M(\Lambda_b^0) = 172.44\pm0.39\pm0.17 MeV/c^2$, $M(\Xi_c^+) - M(\Lambda_c^+) = 181.51\pm0.14\pm0.10 MeV/c^2$, where the first uncertainty is statistical and the second is systematic. The relative rate of $\Xi_b^0$ to $\Lambda_b^0$ baryon production is measured to be $\frac{f_{\Xi_b^0}}{f_{\Lambda_b^0}}\frac{{\cal{B}}(\Xi_b^0\to\Xi_c^+\pi^-)}{{\cal{B}}(\Lambda_b^0\to\Lambda_c^+\pi^-)}\frac{{\cal{B}}(\Xi_c^+\to pK^-\pi^+)}{{\cal{B}}(\Lambda_c^+\to pK^-\pi^+)} = (1.88\pm0.04\pm0.03)\times10^{-2}$, where the first factor is the ratio of fragmentation fractions, $b\to\Xi_b^0$ relative to $b\to\Lambda_b^0$. Relative production rates as functions of transverse momentum and pseudorapidity are also presented.

where the first uncertainty is statistical and the second is systematic.The relative rate of Ξ 0 b to Λ 0 b baryon production is measured to be where the first factor is the ratio of fragmentation fractions, b → Ξ 0 b relative to b → Λ 0 b .Relative production rates as functions of transverse momentum and pseudorapidity are also presented.
b P.N.Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia c Università di Bari, Bari, Italy d Università di Bologna, Bologna, Italy e Università di Cagliari, Cagliari, Italy f Università di Ferrara, Ferrara, Italy g Università di Firenze, Firenze, Italy h Università di Urbino, Urbino, Italy i Università di Modena e Reggio Emilia, Modena, Italy j Università di Genova, Genova, Italy k Università di Milano Bicocca, Milano, Italy l Università di Roma Tor Vergata, Roma, Italy m Università di Roma La Sapienza, Roma, Italy n Università della Basilicata, Potenza, Italy o AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland p LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain q Hanoi University of Science, Hanoi, Viet Nam r Università di Padova, Padova, Italy s Università di Pisa, Pisa, Italy t Scuola Normale Superiore, Pisa, Italy u Università degli Studi di Milano, Milano, Italy vii Over the last two decades great progress has been made in understanding the nature of hadrons containing beauty quarks.A number of theoretical tools have been developed to describe their decays.One of them, the heavy quark expansion (HQE) [1][2][3][4][5][6][7][8], expresses the decay widths as an expansion in powers of Λ QCD /m b , where Λ QCD is the energy scale at which the strong coupling constant becomes large, and m b is the b-quark mass.At leading order in the HQE, all weakly decaying b hadrons (excluding those containing charm quarks) have the same lifetime, and differences enter only at order (Λ QCD /m b ) 2 .In the baryon sector, one expects for the lifetimes τ (Ξ 0 b ) ≈ τ (Λ 0 b ) [8] and τ (Ξ 0 b )/τ (Ξ − b ) = 0.95 ± 0.06 [9,10].Precise measurements of the Ξ 0 b and Ξ − b lifetimes would put bounds on the magnitude of the higher order terms in the HQE.A number of approaches exist to predict the b-baryon masses [11][12][13][14][15][16][17][18][19].As predictions for the masses span a large range, more precise mass measurements will help to refine these models.
Hadron collider experiments have collected large samples of b-baryon decays, which have enabled increasingly precise measurements of their masses and lifetimes [20][21][22][23][24][25].These advances include 1% precision on the lifetime of the Λ 0 b baryon [20] and 0.3 MeV/c 2 uncertainty on its mass [22].Progress has also been made on improving the precision on the masses of the 26,30] and Ω − b [26,30] baryons.The strangebeauty baryon measurements are still limited by small sample sizes owing to their low production rates, and either low detection efficiency or small branching fractions.
In this Letter, we present the first measurement of the Ξ 0 b lifetime and report the most precise measurement of its mass, using a sample of about 3800 decay is used for normalization, as it has the same final state, and is kinematically very similar.The ratio of Ξ 0 b to Λ 0 b baryon production rates, and its dependence on pseudorapidity, η, and transverse momentum, p T , are also presented.We also use the Ξ + c → pK − π + and Λ + c → pK − π + signals to make the most precise measurement of the Ξ + c mass to date.In what follows, we use X b (X c ) to refer to either a Ξ 0 b (Ξ + c ) or Λ 0 b (Λ + c ) baryon.The measurements use proton-proton (pp) collision data samples collected by the LHCb experiment corresponding to an integrated luminosity of 3 fb −1 , of which 1 fb −1 was recorded at a center-of-mass energy of 7 TeV and 2 fb −1 at 8 TeV.The LHCb detector [31] 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 highprecision tracking system that provides a momentum measurement with precision of about 0.5% from 2−100 GeV/c and impact parameter (IP) resolution of 20 µm for particles with large p T .Ring-imaging Cherenkov detectors [32] are used to distinguish charged hadrons.Photon, electron and hadron candidates are identified using a calorimeter system, followed by a set of detectors to identify muons [33].
The trigger [34] 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 [34,35].About 57% of the recorded X b events are triggered at the hardware level by one or more of the final state particles in the signal X b decay.The remaining 43% are triggered only on other activity in the event.We refer to these two classes of events as triggered on signal (TOS) and triggered independently of signal (TIS).The software trigger requires a two-, three-or four-track secondary vertex with a large sum of the transverse momentum of the particles and a significant displacement from the primary pp interaction vertices (PVs).At least one particle should have p T > 1.7 GeV/c and χ 2 IP with respect to any primary interaction greater than 16, where χ 2 IP is defined as the difference in χ 2 of a given PV fitted with and without the considered particle included.The signal candidates are required to pass a multivariate software trigger selection algorithm [35].
Proton-proton collisions are simulated using Pythia [36] with a specific LHCb configuration [37].Decays of hadronic particles are described by EvtGen [38], in which final state radiation is generated using Photos [39].The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [40] as described in Ref. [41].
Candidate X b decays are reconstructed by combining in a kinematic fit selected X c → pK − π + candidates with a π − candidate (referred to as the bachelor).Each X b candidate is associated to the PV with the smallest χ 2 IP .The X c daughters are required to have p T > 100 MeV/c, and the bachelor pion is required to have p T >500 MeV/c.To improve the signal purity, all four final state particles are required to be significantly displaced from the PV and pass particle identification (PID) requirements.The PID requirements on the X c daughter particles have an efficiency of 74%, while reducing the combinatorial background by a factor of four.The PID requirements on the bachelor pion are 98% efficient, and remove about 60% of the cross-feed from , and D + → K − π + π + decays is removed by requiring either the mass under these alternate decay hypotheses to be inconsistent with the known D ( * )+ (s) masses [42], or that the candidate satisfy more stringent PID requirements.The efficiency of these vetoes is about 98% and they reject 28% of the background.The X c candidate is required to be within 20 MeV/c 2 of the nominal X c mass [42].
To further improve the signal-to-background ratio, a boosted decision tree (BDT) [43,44] algorithm using eight input variables is employed.Three variables from the X b candidate are used, χ 2 IP , the vertex fit χ 2 vtx , and the χ 2 VS , which is the increase in χ 2 of the PV fit when the X b is forced to have zero lifetime relative to the nominal fit.For the X c baryon, we use the χ 2 IP , and amongst its daughters, we take the minimum p T , the smallest χ 2 IP , and the largest distance between any pair of daughter particles.Lastly, the χ 2 IP of the bachelor π − is used.The BDT is trained using simulated signal decays to represent the signal and candidates from the high X b mass region (beyond the fit region) to describe the background distributions.A selection is applied that provides 97% signal efficiency while rejecting about 50% of the combinatorial background with respect to all previously applied selections.
For each X b candidate, the mass is recomputed using vertex constraints to improve the momentum resolution; X c mass constraints are not used since the Ξ + c mass is not known to sufficient precision.The resulting X b mass spectra are simultaneously fitted to the sum of a signal component and three background contributions.The X b signal shape is parameterized as the sum of two Crystal Ball (CB) functions [45], with a common mean.The shape parameters are freely varied in the fit to data.The Λ 0 b and Ξ 0 b signal shape parameters are common except for their means and widths.The Ξ 0 b widths are fixed to be 0.6% larger than those for the Λ 0 b , based on simulation.The main background sources are misidentified X b → X c K − decays, partially reconstructed X b → X c ρ − and Λ 0 b → Σ + c π − decays, and combinatorial background.The X b → X c K − background shape is obtained from simulated decays that are weighted according to PID misidentification rates obtained from D * + → D 0 (K − π + )π + calibration data.The X b → X c K − yield is fixed to be 3.1% of the X b → X c π − signal yield, which is the product of the misidentification rate of 42% and the ratio of branching fractions, [27].The assumed equality of this ratio for Ξ 0 b and Λ 0 b is considered as a source of systematic uncertainty.The partially reconstructed backgrounds are modeled empirically using an ARGUS [46] function, convolved with a Gaussian shape; all of its shape parameters are freely varied in the fit.The combinatorial background shape is described using an exponential function with a freely varied shape parameter.
The results of the simultaneous binned extended maximum likelihood fits are shown in Fig. 1.Peaking backgrounds from charmless final states are investigated using the X c sidebands and are found to be negligible.We observe (180.5 ± 0.5) The data are also used to make the first determination of the relative lifetime τ (Ξ 0 b )/τ (Λ 0 b ).This is performed by fitting the efficiency-corrected ratio of yields, N cor (Ξ 0 b )/N cor (Λ 0 b ), as a function of decay time to an exponential function, e βt .The ) is readily obtained.The data are binned in 0.5 ps bins from 0 − 6 ps, and 1 ps bins from 7 to 9 ps.The same fit as described above for the full sample is used to fit the mass spectra in each time bin.The signal and partially-reconstructed background shapes are fixed to the values from the fit to the full data sample, since they do not change with decay time, but the combinatorial background shape is freely varied in each time bin fit.
The measured yield ratio in each time bin is corrected by the relative efficiency, (Λ 0 b )/ (Ξ 0 b ), as obtained from simulated decays.This ratio is consistent with a constant value of about 0.93, except for the 0.0 − 0.5 ps bin, which has a value of about 0.7.This lower value is expected due to the differing lifetimes, τ (Ξ + c ) ≈ 0.45 ps τ (Λ + c ) ≈ 0.2 ps, and the χ 2 IP requirements in the trigger and offline selections.The 7% overall lower efficiency for the Λ 0 b mode is due to the larger momenta of the daughters in the Ξ 0 b decay.The efficiency-corrected yield ratio is shown in Fig. 2, along with the fit to an exponential function.The points are placed at the weighted average time value within each bin, assuming an exponential distribution with lifetime equal to τ (Λ 0 b ).The bias due to this assumption is negligible.From the fit, we find β = (0.40 ± 1.21) × 10 −2 ps −1 .Using the measured Λ 0 b lifetime from LHCb of 1.468 ± 0.009 ± 0.008 ps [20], we obtain  b → Ξ + c π − decays is exploited to measure the Ξ + c mass.Signal X b candidates within 50 MeV/c 2 of their respective peak values are selected, and a simultaneous fit to the Λ + c and Ξ + c mass spectra is performed.For this measurement, we remove the 20 MeV/c 2 restriction on the X c mass.The sum of two CB functions is used to describe the signal and an exponential shape describes the background.The signal shape parameters are common, except for their means and widths.The larger Ξ + c resolution is due to the greater energy release in the decay.The mass distributions and the results of the fit are shown in Fig. 4. The fitted mass difference is ∆M Xc ≡ M (Ξ + c ) − M (Λ + c ) = 181.51± 0.14 (stat) MeV/c 2 .The results presented are all ratio or difference measurements, reducing their sensitivity to most potential biases.A summary of the systematic uncertainties is given in Table 1.Unless otherwise noted, systematic uncertainties are assigned by taking the difference between the nominal result and the result after a particular variation.In all measurements, possible dependencies on the signal and background models are investigated by exploring alternative shapes and fit ranges (for mass differences).Uncertainties are combined by summing all sources of uncertainty in quadrature.
For the mass difference measurements, common and separate variations in the fraction of X b → X c K − by ±1% (absolute) are used to assign the cross-feed uncertainty.Shifts in the momentum scale of ±0.03% [48] are applied coherently to both signal and normalization mode to determine the momentum scale uncertainty.Validation of the procedure on simulated decays shows no biases on the results.The uncertainty due to the limited size of those simulated samples are taken as a systematic error.
For the relative lifetime measurement, the relative acceptance uncertainty is dominated by a potential bias in the first time bin.The uncertainty is assessed by dropping this bin from the fit.Potential bias due to the BDT's usage of χ 2 IP information is examined by correcting the data using simulated efficiencies with a tighter BDT requirement.The smaller lifetime of the Λ 0 b baryon assumed in the simulation (1.426 ps) has a negligible impact on the measured lifetime ratio.Lastly, the finite size of the simulated samples is also taken into account.
For the relative production rate, the signal and background shape uncertainties, and the X b → X c K − cross-feed uncertainties are treated in the same way as above.For the relative acceptance we include contributions from (i) the geometric acceptance by comparing Pythia 6 and Pythia 8; (ii) the X c Dalitz structure, by reweighting the efficiencies according to the distributions seen in data, and (iii) the lower efficiency in the 0 − 0.5 ps bin by requiring τ (X b ) > 0.5 ps.The uncertainty in the relative trigger efficiency is estimated by taking the difference in the average trigger efficiency, when using the different TOS/TIS fractions in data and simulation.A correction and an uncertainty due to the 20 MeV/c 2 mass range on X c is obtained using the results of the X c mass fits.The results for the 7 TeV and 8 TeV data differ by about 1% and are statistically compatible with each other.In summary, a 3 fb −1 pp collision data set is used to make the first measurement of the Ξ 0 b lifetime.The relative and absolute lifetimes are  .The mass and mass difference are consistent with, and about five times more precise than the value recently obtained in Ref. [27].
We also measure the mass difference M (Ξ + where M (Λ + c ) = 2286.46± 0.14 MeV/c 2 [42] is used.These values are consistent with and at least three times more precise than other measurements [29,42].

Figure 2 :
Figure 2: Efficiency-corrected yield ratio of Ξ 0 b → Ξ + c π − relative to Λ 0 b → Λ + c π − decays in bins of decay time.A fit using an exponential function is shown.The uncertainties are statistical only.

Figure 3 :
Figure 3: Efficiency-corrected yield ratio of Ξ 0 b → Ξ + c π − relative to Λ 0 b → Λ + c π − decays as functions of (left) p T and (right) pseudorapidity, η.The points are positioned along the horizontal axis at the weighted average value within each bin.The uncertainties are statistical only.

Figure 4 :
Figure 4: Distributions of the pK − π + invariant mass for (left) Λ + c and (right) Ξ + c candidates along with the projections of the fit.