Measurement of Charm Baryon Lifetimes at Belle II

Outstanding vertexing performance and low-background environment are key enablers of a systematic Belle II program targeted at measurements of charm baryon lifetimes. Recent results from measurements of the Λc+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda _{c}^{+}$$\end{document} and Ωc0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega _{c}^{0}$$\end{document} baryon lifetimes are presented. The former result is the most precise to date.

Such a setup provides effective constraint on the D meson production vertex.Belle II has collected a sample of 428 fb −1 of integrated luminosity.The analyses presented here use only a fraction of the available data.
The Belle II detector [15] is located around the interaction point.As shown in Fig. 1, the innermost detector is the VerteX Detector (VXD), which comprises of the PiXel detector (PXD) and the silicon vertex detector (SVD).The PXD is made up of two layers of DEpleted p-channel field effect transistors (DEPFETs).The first layer of the PXD is at 1.4 cm from the interaction point.It is followed by four layers of the SVD.The first layer of the SVD is at a distance of 3.9 cm from the interaction point, while the fourth layer is situated at a 13.5 cm.Each layer of the SVD is made up of double sided silicon strip detectors (DSSDs).The VXD is surrounded by the Central Drift Chamber (CDC).It is a large volume drift chamber containing a gaseous mixture of 50% He -50% C 2 H 6 .It reconstructs particle trajectories of low momentum particles, precisely measures their momenta and provides particle identification (PID) using d E/dx in its volume.The CDC is enclosed by the time-of-propagation (TOP) counter, which is a Cherenkov detector and is used for PID in the barrel region.In the forward endcap region, aerogel ring imaging cherenkov (ARICH) is used for PID.Further we have a electromagnetic calorimeter (ECL), which is made up of thallium doped cesium iodide CsI(Tl) crystals.It is used to detect photons and to separate electrons from hadrons (in particular pions).The K L and muon detector (KLM) is the outermost sub detector.It is made up of an alternating sandwich of iron plates and active detector material.

Measurement of Λ + c Lifetime
To measure the decay time of Λ + c , promptly produced Λ + c candidates originating from e + e − −→ cc events are considered.The lifetime is measured using a 2D fit to t and σ t , where t is the decay-time and σ t is the uncertainty on t.The decay-time is calculated using the formula Here, L is the displacement of the Λ + c decay vertex from the e + e − interaction point (IP), projected along the direction of its momentum (p) and m is the world average mass of the Λ + c [16].The position and size of the interaction region are determined using e + e − −→ μ + μ − events.For the Λ + c , the VXD provides a decay length resolution of 87 fs for an average decay length of 96 µm resolution.Candidate Λ + c −→ pK − π + (charge conjugation is always implied, unless stated otherwise) are reconstructed using one negatively and two positively charged particle tracks.The particle identification (PID) information is combined from all sub-detectors, excluding the VXD.PID efficiency study is carried out using Λ 0 −→ pπ − and D * + tagged D 0 −→ K − π + decays.The Λ + c coming from B decays are suppressed by requiring the center of mass momentum ( p cms ) of Λ + c to be greater −→ Λ + c π −/0 can bias the measurement as their production vertices are shifted away from the IP.Such events are removed by applying a veto on the invariant mass of 0/+ c .However, 61% of these decays still remain and are accounted for as systematic.The selection criteria and the fit strategy are optimized and validated using Monte Carlo (MC) and no input therefrom is used to fit the collision data.A binned least-squares fit to M(pK − π + ) is performed in which the signal peak is modelled using the sum of a Gaussian and a Johnson's S U function that have a common mode.Figure 2 shows the M(pK − π + ) distribution with the fit projections overlaid.The total signal yield is measured to be 116000 with 7.5% background in the signal region.
Λ + c lifetime is then extracted using an unbinned maximum likelihood fit to candidates in the signal region only.The signal PDF is modelled using an exponential in t, convolved with a Gaussian resolution function dependent on t and a PDF in σ t .The PDF of σ t is a histogram template that is formed from signal candidates subtracted by the distribution of sideband candidates after scaling according to the size of the signal and background regions.The background PDF is an empirical model of the sideband data.It is modelled using the sum of two exponential functions, convolved with a Gaussian resolution function.A simultaneous fit to events in signal and background region is performed to better constrain the background, as shown in Fig. 3.
The systematic uncertainties in the measurement of Λ + c lifetime are shown in Table 1.The major source of uncertainty is the contamination arising from 0/+ c −→ Λ + c π −/0 decays.The correlations between t and σ t as we consider a simple Gaussian as the resolution function.The impact of these correlations are included as a systematic.The background in the sidebands is assumed to accurately model the background in the signal region in simulation as well as in data.However, there are some data-MC differences, which is accounted for as a systematic.Imperfections in detector alignment can bias the lifetime measurements due to which it is included as a systematic.The momentum scaling factor for charged particles is taken to be, 0.99971 and the uncertainty in it, results in an additional systematic uncertainty on the measurement.
The Λ + c life time measured by other experiments are tabulated in Table 2.The most precise measurement of Λ + c life time is provided by Belle II [17].
3.2 Measurement of Ω 0 c Lifetime 207 fb −1 of collision data is used for the measurement of Ω 0 c lifetime and the decay in consideration is This decay chain has two secondary vertices.The Λ 0 is reconstructed using two charged tracks, one of which must be a proton.The decay vertex of the Λ 0 must at least be 0.35 cm from the IP.The Λ 0 are then combined with  a K − with transverse momentum greater than 0.15 GeV, thereby forming the Ω − .The Ω − thus reconstructed is combined with a positively charged track from the IP, whose momentum is at least 0.5 GeV.Ω 0 c coming from B decays are eliminated by requiring its scaled momentum to exceed 0.6 GeV/c.Scaled momentum is defined as p cms / s/4 − m(Ω − π + ) 2 , where p cms is the center of mass momentum of Ω 0 c , s is the squared centre of mass energy and m(ω − π + ) is the reconstructed mass of Ω 0 c .Candidate Ω 0 c −→ Ω − π + thus reconstructed are used to perform an unbinned maximum likelihood fit to m(ω − π + ).The signal peak is modelled using a Gaussian and the background is modelled using a linear function as shown in Fig. 4. The total signal yield is 132 with 33% background contamination in the signal region and signal purity (66 ± 3.3)%.
To extract the Ω 0 c lifetime, an unbinned maximum likelihood fit to (t, σ t ) is performed for candidates in the signal region only.The signal PDF is modelled using an exponential in t, convolved with a Gaussian resolution function dependent on t and a PDF in σ t .The background template is obtained from the sideband data.A simultaneous fit to events in signal and background region is performed to better constrain the background, as shown in Fig. 5.
The major source of systematic uncertainty in this measurement is the background model.This is because the sideband data differs from the background in the signal region.The corresponding systematic uncertainty is estimated using the differences in data-MC.Simulation shows that the resolution function has tails that are inconsistent with a Gaussian model and as these inconsistencies are accounted for as a systematic.The small data sample used for the analysis results in a fit bias for the measurement, which results in an additional systematic uncertainty.The uncertainties are tabulated in Table 3.The measured lifetime of Ω 0 c is 243 ± 48 (stat.)± 11(syst.)fs [11].It is consistent with the LHCb average of 274.5 ± 12.4 fs [18], and also inconsistent at 3.4 standard deviations with the pre-LHCb world average of 69 ± 12 fs [19].Measurements of Ω 0 c lifetime is given in Table 4.

Summary and Conclusion
SuperKEKB has achieved the world record for instantaneous luminosity of 4.7×10 34 cm −2 s −1 and Belle II has already collected over 428 fb −1 of data.Belle II has produced world's most precise Λ + c lifetime measurement, which is consistent with current world averages.It has also independently confirmed that Ω 0 c is not the shortest lived, weakly decaying singly charmed baryon.It shows the excellent vertexing capabilities of the Belle II VXD and has set a benchmark for mesurements using complex topologies.The persistent efforts of the members of the collaboration from all over the world have ensured smooth functioning of Belle II and SuperKEKB, even through the COVID-19 pandemic.

Fig. 1 A
Fig. 1 A Schematic Diagram of Belle II Detector [15]

Fig. 3
Fig. 3 Distributions for decay-time (left) and decay-time uncertainty (right) of Λ + c for candidates populating the signal region (top) and sidebands (bottom), with fit projections are overlaid

Table 1
Systematic uncertainties on the Λ +

Table 3
Systematic uncertainties on the Ω 0