Measurement of the lifetimes of promptly produced $\Omega^{0}_{c}$ and $\Xi^{0}_{c}$ baryons

A measurement of the lifetimes of the $\Omega^{0}_{c}$ and $\Xi^{0}_{c}$ baryons is reported using proton-proton collision data at a centre-of-mass energy of $13\text{ TeV}$, corresponding to an integrated luminosity of $5.4\text{ fb}^{-1}$ collected by the LHCb experiment. The $\Omega^{0}_{c}$ and $\Xi^{0}_{c}$ baryons are produced directly from proton interactions and reconstructed in the $pK^{-}K^{-}\pi^{+}$ final state. The $\Omega^{0}_{c}$ lifetime is measured to be $276.5\pm13.4\pm4.4\pm0.7\text{ fs}$, and the $\Xi^{0}_{c}$ lifetime is measured to be $148.0\pm2.3\pm2.2\pm0.2\text{ fs}$, where the first uncertainty is statistical, the second systematic, and the third due to the uncertainty on the $D^{0}$ lifetime. These results confirm previous LHCb measurements based on semileptonic beauty-hadron decays, which disagree with earlier results of a four times shorter $\Omega^{0}_{c}$ lifetime, and provide the single most precise measurement of the $\Omega^{0}_{c}$ lifetime.


Introduction
the Ω 0 c decay-vertex fit; the transverse momentum, pseudorapidity and the direction angle of the Ω 0 c candidate; the transverse momenta as well as the minimal transverse momentum of the four final-state particles; and the natural logarithm of the sum and minimum χ 2 IP of the four final-state particles.A requirement on the BDT response is chosen which selects approximately 99% of Ω 0 c signal decays while rejecting about 60% of the background.The same requirement is also applied to the Ξ 0 c signal decays.The number of signal candidates for the Ω 0 c , Ξ 0 c , and D 0 decay modes are determined using the [2645, 2745] MeV/c 2 , [2421, 2521] MeV/c 2 , and [1835,1915] MeV/c 2 invariant-mass regions, respectively.
Specific trigger requirements are applied to candidates to ensure a precise estimation of the selection efficiency as a function of decay time.In the offline selection, trigger signals are associated with reconstructed particles.Selection requirements can therefore be made on the trigger selection itself and if the decision was due to the signal candidate.At the hardware stage, at least one of the final-state tracks is required to deposit large transverse energy in the hadronic calorimeter.At the software stage, at least one of the final-state tracks is required to pass a MatrixNet classifier [36], which is trained to select displaced tracks [37].

Prompt yield determination
Charmed hadron candidates are split into intervals of their decay time, which is calculated using the PV, its decay vertex, and its measured momentum.The signal yields are then determined in each interval.The interval boundaries of the Ω 0 c sample are chosen to have a similar yield of Ω 0 c signals in each interval, and correspond to [0.45, 0.52, 0.57, 0.63, 0.69, 0.75, 0.81, 0.90, 1.05, 2.00] ps.For the Ξ 0 c sample, the same boundaries are used except the last interval, which, for computational simplicity, is not included as the yield is consistent with zero.The same boundaries are used for the D 0 control mode as for the signal modes.Two variables are used to discriminate signal decays from different background contributions.One is the invariant mass of the charmed hadron, which is used to distinguish decays from combinatorial background due to the random combinations of tracks.The other is the logarithm of the χ 2 IP of the charmed hadron, log 10 χ 2 IP , which is used to separate prompt candidates from those produced in decays of beauty hadrons.The log 10 χ 2 IP distribution for signal decays has smaller mean values than for those originating from beauty-hadron decays due to the lifetime of the ancestor beauty hadron.
Example distributions of invariant mass and log 10 χ 2 IP , in reduced mass regions around the peak, are presented in Fig. 1; the decay-time interval of [0.69, 0.75] ps for data collected in 2018 is shown.To obtain the Ω 0 c , Ξ 0 c , and D 0 signal yields in each decay-time interval, two-dimensional unbinned extended maximum likelihood fits are performed to the invariant-mass and log 10 χ 2 IP distributions.For each mode, the fits are performed simultaneously in all decay-time intervals and the three data-taking periods, 2016, 2017, and 2018.The invariant-mass distribution of the signal candidates is described with the sum of a Gaussian function and a double-sided Crystal Ball function [38] with a shared mean.The fit parameters are fixed to values obtained from simulation except for the mass peak and the effective resolution, which are obtained directly from data, but shared among the different decay-time intervals.The invariant-mass distribution of the combinatorial background contribution is described by a linear function with a slope left free to vary in the fit.The log 10 χ 2 IP distributions of both the signal and background components are described by a Bukin function [39].For signal components, parameters of the Bukin function are fixed to values obtained from simulation except for the peak position that depends on the decay time.Here, an offset parameter is added to account for the disagreement between data and simulation.The offset parameter is free to vary and shared between decay-time intervals and data-taking periods in the fit.The parameters of the Bukin function of the combinatorial background contribution are fixed to values obtained from fits to the data samples in the sideband region as defined in the BDT training.The two-dimensional model used for signal, secondary decays, and background components is the product of the models for the invariant-mass and for the log 10 χ 2 IP distributions.Fit projections to the invariant-mass and log 10 χ 2 IP distribution are shown in Fig 1.

Decay time fit
The lifetimes of the Ω 0 c and Ξ 0 c baryons are determined from a binned χ 2 fit comparing the signal yields in data with those from the simulation, where the lifetime is known.The latter is corrected using the control mode, as follows where: N sig i,j (N con i,j ) is the signal yield in data for the signal (control) mode in decay-time interval i and for the data-taking period j; M i,j is the effective yield predicted from simulation; C j is a normalisation factor to account for the difference in size between the data and the simulated samples; and σ is the uncertainty of the relevant quantity.The difference in lifetime between data and simulated samples is accounted for by where τ sim = 250 fs is the signal mode lifetime in simulation and τ con = τ con sim is the known D 0 lifetime [35], but is allowed to vary for estimating the systematic uncertainty.The resulting lifetime is τ Ω 0 c = 276.5 ± 13.4 fs with χ 2 /ndf = 22/23 and τ Ξ 0 c = 148.0± 2.3 fs with χ 2 /ndf = 30/20, where the uncertainty is due to the limited size of the data and simulation samples.The result of the χ 2 fit to data is illustrated in Fig. 2, which shows the signal yield N sig for selected candidates as a function of decay time, divided by the width of the corresponding decay-time interval, where the fit results are superimposed.
Several cross-checks are performed to ensure the robustness of the results.The χ 2 fit is performed to data of the D 0 → K + K − π + π − control mode for each data-taking period to validate the analysis procedure.The obtained lifetimes are consistent between data-taking periods and with the known D 0 lifetime [35].The data samples are split into sub-samples according to data-taking periods and magnetic polarities of the LHCb dipole magnet, and the lifetimes are measured for each sub-sample.The resulting lifetimes are in good agreement with each other and with the default results.The measurement is repeated with two alternative boundaries of decay-time intervals and the obtained lifetimes are consistent with the default results within their statistical uncertainties.To ensure that the result is independent of the input lifetime used in simulation, the simulated signal decays are weighted to have alternative effective lifetimes within seven times the statistical uncertainty around the default lifetime.The χ 2 fit is then repeated.The difference of the obtained lifetimes with regard to the default fit is negligible.

Systematic uncertainties
Sources of systematic uncertainty are investigated and summarised in Table 1, including those due to the fit model, the limited size of the calibration samples, differences between data and simulation, and the uncertainty due to the choice of the D 0 control mode.The systematic uncertainty due to the modelling of log 10 χ 2 IP is studied with the D 0 control mode.The following alternative models were tried and their impact on the signal yields studied.First, the effect due to fixed parameters in the Bukin function is studied by removing these constraints one at a time in the fit to the invariant-mass and log 10 χ 2 IP distributions.Second, the uncertainty due to the choice of a single offset parameter for the peak positions of the Bukin functions across different decay-time intervals is studied by allowing independent offsets in each decay-time interval.Third, an alternative model for the log 10 χ 2 IP distribution of the combinatorial background is obtained with the sPlot technique [40] using the invariant mass as the discriminating variable.Half of the largest difference between the signal yields from the alternative model fits is taken as the systematic uncertainty.The obtained systematic uncertainties on the signal yields are propagated to the measured lifetime using pseudoexperiments.In each pseudoexperiment, the yields of the signal and control modes are varied according to a Gaussian distribution whose mean is the value obtained with the default fit model and standard deviation the systematic uncertainty obtained with alternative models in the corresponding decay-time interval, and the lifetime is fit.The standard deviation of the distribution for the fitted lifetime is taken as the systematic uncertainty.
The selection efficiency of the hardware trigger is estimated in data using Λ + c candidates from semileptonic Λ 0 b decays [41].The uncertainty due to the limited size of the calibration sample is estimated using pseudoexperiments, where the efficiency determined from the calibration sample is varied according to its uncertainty.The standard deviation of the distribution of the fitted lifetime is taken as the systematic uncertainty.The kinematic distributions of the simulated signal decays, including the transverse momentum and rapidity of the charmed hadron and the transverse momentum of final-state tracks, are weighted according to the distributions observed in data for each mode.The impact of the limited size of the data samples, which is more pronounced for the Ω 0 c mode, is studied with pseudoexperiments following the same procedure as described above.
Decay-time resolution in data is known to be different from simulation, although it cannot be accurately determined for the signal modes due to their limited yields in data.Nonetheless, the impact of this difference on the measured charm-hadron lifetimes largely cancels due to taking the ratio with the D 0 control mode.The residual effect is studied using pseudoexperiments and assigned as a systematic uncertainty.For these pseudoexperiments the D 0 control mode is generated with both a 30% larger and smaller decay-time resolution in the pseudo-data compared to pseudo-simulation, and the lifetime is fit.The difference between the input lifetime and the mean value of the distribution of the fitted lifetimes is taken as the systematic uncertainty.
The χ 2 IP variables of the final-state tracks in simulation are scaled to account for differences between data and simulation for the data-taking periods of 2017 and 2018.The scaling factor is obtained by comparing data distributions in the control mode.The uncertainty on the scaling factor is determined to be 2%, based on χ 2 comparisons of data distributions with alternate scaling factors.The difference between the default fitted lifetime and the lifetime determined with a scaling factor varied by 2% is taken as the systematic uncertainty.
The measurement of the distance between the PV and the charmed-hadron decay vertex depends on the relative longitudinal positions of the vertex locator modules of the LHCb detector with respect to the beam axis.The uncertainty on the positions of the modules is estimated using survey measurements and the track based alignment [42,43], where the latter has the larger contribution.Its uncertainty does not cancel in the decay-time ratio and is taken as a relative systematic uncertainty of the measured lifetime.
The D 0 signal decays are reconstructed in a self-conjugate final state and D 0 -D 0 mixing is not considered in the χ 2 fit of the lifetime.The impact of D 0 mixing is estimated using pseudoexperiments in which the D 0 decay-time distribution is generated with mixing terms and the default χ 2 fit is performed to obtain the lifetime.The obtained difference between the input and resultant lifetime is assigned as a systematic uncertainty.The known value of 410.1 fs [35] is assigned as D 0 lifetime in the default decay-time fit.The uncertainty on the D 0 lifetime, 1.5 fs [35], is propagated to the measured lifetime using pseudoexperiments.In each pseudoexperiment, the D 0 lifetime is varied according to its uncertainty.The standard deviation of the distribution for the fitted lifetime is taken as the systematic uncertainty.

Conclusion
In summary, a measurement of the lifetimes of the Ω 0 c and Ξ 0 c baryons is reported with Ω 0 c and Ξ 0 c baryons produced directly in proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb −1 collected by the LHCb experiment.The Ω 0 c lifetime is measured to be τ Ω 0 c = 276.5 ± 13.4 ± 4.4 ± 0.7 fs, and the Ξ 0 c lifetime is measured to be where the first uncertainty is statistical, the second systematic, and the third due to the uncertainty of the D 0 lifetime.This result is consistent with the previous LHCb measurements of the Ω 0 c and Ξ 0 c lifetimes, obtained from semileptonic beauty-hadron decays [1,2], and confirms the charmed-hadron lifetime hierarchy of τ Ξ + c > τ Ω 0 c > τ Λ + c > τ Ξ 0 c .The precision of the Ω 0 c lifetime is improved by a factor of two compared to that of the previous result [1].
This result is independent of previous LHCb measurements [1,2] due to the choice of independent data sample and analysis technique.Combining this measurement with previous LHCb measurements [1,2], given that both the statistical uncertainties and the dominant systematic uncertainties are uncorrelated, results in the weighted average lifetimes of τ Ω 0 c = 274.5 ± 12.4 fs, τ Ξ 0 c = 152.0± 2.0 fs.The uncertainty includes both the statistical and systematic uncertainties.

Figure 1 :
Figure 1: (Color online) Distributions of (a) invariant mass and (b) log 10 χ 2 IP in the reduced mass region of [2683, 2707] MeV/c 2 for the Ω 0 c data sample, (c) invariant mass and (d) log 10 χ 2 IP in the reduced mass region of [2461, 2481] MeV/c 2 for the Ξ 0 c data sample, (e) invariant mass and (f) log 10 χ IP in the reduced mass region of [1853, 1877] MeV/c 2 for the D 0 data sample, along with the fit results.The sample is collected in 2018 in the decay-time interval of [0.69, 0.75] ps.The contributions of the signal, the secondary decays, and the combinatorial background are shown in red (solid), green (dashed), and gray (dash-dotted), respectively.

Figure 2 :
Figure 2: (Color online) Decay-time distributions for the (a) Ω 0 c mode and the (b) Ξ 0 c mode with the χ 2 fit superimposed.The uncertainty on the data distribution is statistical only.

Table 1 :
Systematic uncertainties for the Ω 0 c and Ξ 0 c lifetimes.
82National Research University Higher School of Economics, Moscow, Russia, associated to42  83National University of Science and Technology "MISIS", Moscow, Russia, associated to41  84National Research Tomsk Polytechnic University, Tomsk, Russia, associated to 41 85 DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45 86 University of Michigan, Ann Arbor, United States, associated to 68 a Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil b Hangzhou Institute for Advanced Study, UCAS, Hangzhou, China 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 Genova, Genova, Italy i Università degli Studi di Milano, Milano, Italy j Università di Milano Bicocca, Milano, Italy k Università di Modena e Reggio Emilia, Modena, Italy l Università di Padova, Padova, Italy m Scuola Normale Superiore, Pisa, Italy n Università di Pisa, Pisa, Italy o Università della Basilicata, Potenza, Italy p Università di Roma Tor Vergata, Roma, Italy q Università di Siena, Siena, Italy r Università di Urbino, Urbino, Italy s MSU -Iligan Institute of Technology (MSU-IIT), Iligan, Philippines t AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland u P.N.Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia v Novosibirsk State University, Novosibirsk, Russia w Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden x Hanoi University of Science, Hanoi, Vietnam