Measurement of the $\Lambda$ hyperon lifetime

TL;DR

This paper presents a highly precise measurement of the $\\Lambda$ hyperon lifetime and tests CPT invariance by comparing it with the anti-hyperon, using data from Pb-Pb collisions at 5.02 TeV with the ALICE detector.

Contribution

The study provides the most precise measurement to date of the $\\Lambda$ hyperon lifetime and the first precise test of CPT invariance in this context.

Findings

Measured $\\Lambda$ lifetime: 261.07 ps with small uncertainties.

Found no significant difference between $\\Lambda$ and $\\overline{\Lambda}$ lifetimes.

Results agree with world averages and improve precision by a factor of three.

Abstract

A new, more precise measurement of the $\Lambda$ hyperon lifetime is performed using a large data sample of Pb$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV with ALICE. The $\Lambda$ and $\overline{\Lambda}$ hyperons are reconstructed at midrapidity using their two-body weak decay channel $\Lambda \rightarrow \mathrm{p} + \pi^{-}$ and $\overline{\Lambda} \rightarrow \overline{\mathrm{p}} + \pi^{+}$. The measured value of the $\Lambda$ lifetime is $\tau_{\Lambda} = [261.07 \pm 0.37 \ ( \rm stat.) \pm 0.72 \ (\rm syst.) ]\ \rm ps$. The relative difference between the lifetime of $\Lambda$ and $\overline{\Lambda}$, which represents an important test of CPT invariance in the strangeness sector, is also measured. The obtained value $(\tau_{\Lambda}-\tau_{\overline{\Lambda}})/\tau_{\Lambda} = 0.0013 \pm 0.0028 \ (\mathrm{stat.}) \pm 0.0021 \ (\mathrm{syst.})$ is consistent with zero within the uncertainties. Both measurements of the $\Lambda$ hyperon lifetime and of the relative difference between $\tau_{\Lambda}$ and $\tau_{\overline{\Lambda}}$ are in agreement with the corresponding world averages of the Particle Data Group and about a factor of three more precise.

Tables

Table 1. Table 1: Number of events used for the analysis.

Centrality		Number of events ($\times {10}^6$)
0–10$\%$		70.97
10–30$\%$		18.43
30–50$\%$		61.43
50–90$\%$		36.86

Table 2. Table 2: Raw counts of Λ Λ \Lambda and Λ ¯ ¯ Λ \overline{\Lambda} for different centralities.

Centrality	$\Lambda$ ($\times {10}^6$)	$\overline{\Lambda }$ ($\times {10}^6$)
0–10$\%$	312.6	296.4
10–30$\%$	49.7	47.2
30–50$\%$	41.2	35.9
50–90$\%$	4.2	3.6

Table 3. Table 3: Summary of the systematic uncertainties on the Λ Λ \Lambda and Λ ¯ ¯ Λ \overline{\Lambda} lifetime measurements. All values are in ps.

Source	$\Lambda$	$\overline{\Lambda }$	$\Lambda$ + $\overline{\Lambda }$
Track and $V^0$ selections	0.55	0.69	0.65
Signal extraction	0.03	0.03	0.02
Efficiency and feed-down corrections	0.30	0.33	0.30
Total	0.63	0.77	0.72

Table 4. Table 4: Invariant-mass intervals used for the signal extraction systematic uncertainty.

	Left extreme	Right extreme
Background fit range	$[M_0-14\sigma ,M_0-11\sigma ]$	$[M_0+20\sigma ,M_0+32\sigma ]$
Signal integration range	$[M_0-13\sigma ,M_0-7\sigma ]$	$[M_0+5\sigma ,M_0+11\sigma ]$

Equations

$$L_{\mathrm{proper}}=L_{\mathrm{lab}}/\beta \gamma =M_{\Lambda }\frac{L_{\mathrm{lab}}}{p},$$

$${\left[\frac{\mathrm{d}{N}_{\Lambda }}{\mathrm{d}{L}_{\mathrm{proper}}}\right]}_{\mathrm{corr}}=\frac{1}{ϵ(L_{\mathrm{proper}})}\times f_{\mathrm{prim}}(L_{\mathrm{proper}})\times {\left[\frac{\mathrm{d}{N}_{\Lambda }}{\mathrm{d}{L}_{\mathrm{proper}}}\right]}_{\mathrm{raw}},$$

$$ϵ(L_{\mathrm{proper}})=\frac{{\left[\frac{\mathrm{d}{N}_{\Lambda }}{\mathrm{d}{L}_{\mathrm{proper}}}\right]}_{\mathrm{rec}}}{{\left[\frac{\mathrm{d}{N}_{\Lambda }}{\mathrm{d}{L}_{\mathrm{proper}}}\right]}_{\mathrm{gen}}}.$$

$$f_{\mathrm{prim}}(L_{\mathrm{proper}})=1-\frac{\mathrm{d}{N}_{{\Lambda }_{\sec }}/\mathrm{d}{L}_{\mathrm{proper}}}{\mathrm{d}{N}_{{\Lambda }_{\mathrm{all}}}/\mathrm{d}{L}_{\mathrm{proper}}}.$$

$$k_i=\frac{N_{\mathrm{events}}^{0-10\%}/w_{0-10\%}}{N_{\mathrm{events}}^i/w_i}{w}_i,$$

$${\tau }_{\Lambda }=[261.20\pm 0.49(stat.)\pm 0.63(syst.)]\mathrm{ps},$$

$${\tau }_{\overline{\Lambda }}=[260.86\pm 0.55(stat.)\pm 0.77(syst.)]\mathrm{ps},$$

$${\tau }_{\Lambda +\overline{\Lambda }}=[261.07\pm 0.37(stat.)\pm 0.72(syst.)]ps.$$

$$\left[\frac{\tau_{\overline{\Lambda}}}{\tau_{\Lambda}}\right]_{\rm upper}=\frac{\tau_{\overline{\Lambda}}+\Delta\tau_{\overline{\Lambda}}(\rm corrections)}{\tau_{\Lambda}+\Delta\tau_{\Lambda}(\rm corrections)},\$$

$${\left[\frac{{\tau }_{\overline{\Lambda }}}{{\tau }_{\Lambda }}\right]}_{\mathrm{lower}}=\frac{{\tau }_{\overline{\Lambda }}-\Delta {\tau }_{\overline{\Lambda }}(\mathrm{corrections})}{{\tau }_{\Lambda }-\Delta {\tau }_{\Lambda }(\mathrm{corrections})},$$

$$({\tau }_{\Lambda }-{\tau }_{\overline{\Lambda }})/{\tau }_{\Lambda }=0.0013\pm 0.0028(stat.)\pm 0.0021(syst.),$$

Full text

\PHyear2023 \PHnumber020 \PHdate17 February

\ShortTitleMeasurement of the $\Lambda$ hyperon lifetime

\CollaborationALICE Collaboration††thanks: See Appendix A for the list of collaboration members \ShortAuthorALICE Collaboration

A new, more precise measurement of the $\Lambda$ hyperon lifetime is performed using a large data sample of Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ $=$ 5.02 TeV with ALICE. The $\Lambda$ and $\overline{\Lambda}$ hyperons are reconstructed at midrapidity using their two-body weak decay channel $\Lambda\rightarrow\mathrm{p}+\pi^{-}$ and $\overline{\Lambda}\rightarrow\overline{\mathrm{p}}+\pi^{+}$. The measured value of the $\Lambda$ lifetime is $\tau_{\Lambda}=[261.07\pm 0.37\ (\rm stat.)\pm 0.72\ (\rm syst.)]\ \rm ps$. The relative difference between the lifetime of $\Lambda$ and $\overline{\Lambda}$, which represents an important test of CPT invariance in the strangeness sector, is also measured. The obtained value $(\tau_{\Lambda}-\tau_{\overline{\Lambda}})/\tau_{\Lambda}=0.0013\pm 0.0028\ (\mathrm{stat.})\pm 0.0021\ (\mathrm{syst.})$ is consistent with zero within the uncertainties. Both measurements of the $\Lambda$ hyperon lifetime and of the relative difference between $\tau_{\Lambda}$ and $\tau_{\overline{\Lambda}}$ are in agreement with the corresponding world averages of the Particle Data Group and about a factor of three more precise.

1 Introduction

The $\Lambda$ is the lightest hyperon, with strangeness $S=-1$, isospin $I=0$, and quark content $\mathrm{uds}$. Its lifetime has been measured in past experiments starting from 1963 using its weak decay channels $\Lambda\rightarrow\mathrm{p}+\pi^{-}$ and $\overline{\Lambda}\rightarrow\overline{\mathrm{p}}+\pi^{+}$. The world average reported in the Review of Particle Physics of the Particle Data Group (PDG) [1] is $\tau_{\Lambda}=263.2\pm 2.0$ ps. This is the result of averaging the measurements performed in 1973 by Poulard et al. [2] and 1975 by Clayton et al. [3] using $\Lambda$ produced in interactions of low-energy charged kaon beams with a fixed target, and the measurement of Zech et al. [4] in 1977 using a neutral hyperon beam. These results are based on data samples containing a maximum of fifty-three thousand events. The relative difference between the lifetimes of $\Lambda$ and $\overline{\Lambda}$ reported in the PDG is $(\tau_{\Lambda}-\tau_{\overline{\Lambda}})/\tau_{\Lambda}=-0.001\pm 0.009$, resulting from the average of two measurements, one performed in 1967 by Badier et al. [5] and another one in 1996 by Barnes et al. [6], using $\Lambda$ and $\overline{\Lambda}$ produced in low-energy $\mathrm{p}+\mathrm{\overline{p}}\rightarrow\Lambda+\overline{\Lambda}$ reactions. The excellent tracking and particle-identification capabilities of ALICE over a broad momentum range and the large amount of data collected during Run 2 of the LHC are exploited to improve the current precision on the measurement of the $\Lambda$ lifetime and on the relative difference between the lifetimes of $\Lambda$ and $\overline{\Lambda}$. The latter provides a fundamental test of CPT invariance in the strangeness sector.

This measurement is also a fundamental reference for the studies of the properties of hypernuclear states created in heavy-ion collisions and for future precision studies of other hyperon properties. The analysis presented here is performed in Pb–Pb collisions at a center-of-mass energy $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV using the same data sample employed for the measurements of the (anti)hypertriton lifetime and $\Lambda$ separation energy [7]. The latter measurements are fundamental to infer the internal structure of this hypernucleus as well as the properties of hyperon–nucleon interaction in the low-density limit, as described in [8].

2 Experimental apparatus

ALICE is one of the four large experiments at the LHC and it is dedicated to the study of heavy-ion collisions at ultrarelativistic energies. A detailed description of the ALICE apparatus and its performance can be found in Refs. [9] and [10]. In the following, only the subdetector systems used for the analysis presented in this paper are described.

Trajectories of charged particles are reconstructed in the ALICE central barrel with the Inner Tracking System (ITS) [11] and the Time Projection Chamber (TPC) [12]. These are located within a large solenoidal magnet, providing a highly homogeneous magnetic field of 0.5 T parallel to the beam axis. The ITS consists of six cylindrical layers of silicon detectors, concentric and coaxial to the beam pipe, with a total pseudorapidity coverage $|\eta|<0.9$ with respect to the nominal interaction point. Three different technologies are used for this detector: the two innermost layers consist of silicon pixel detectors (SPD), the two central layers of silicon drift detectors (SDD), and the two outermost layers of double-sided silicon strip detectors (SSD). This detector is used in the determination of primary and secondary vertices, and in the track reconstruction.

The TPC is the largest detector in the ALICE central barrel, with a pseudorapidity coverage $|\eta|<0.9$. It is used for charged-particle track reconstruction, momentum measurement, and particle identification (PID) via the measurement of the specific energy loss ($\mathrm{d}E/\mathrm{d}x$) of particles in the TPC gas. This detector provides up to 159 spacial points per track for charged-particle reconstruction. The resolution in the measurement of the distance-of-closest approach of primary tracks to the primary collision vertex, projected on the transverse plane, ranges from about 200 $\mu$m at 0.2 GeV$/\textit{c}$ to about 10 $\mu$m at 10 GeV$/\textit{c}$ [10]. The transverse-momentum ($p_{\mathrm{T}}$) resolution ranges from about 1$\%$ at 1 GeV$/\textit{c}$ to about 10$\%$ at 50 GeV$/\textit{c}$ in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV [13]. The $\textrm{d}E/\textrm{d}x$ resolution depends on the event multiplicity and is about 5–6.5$\%$ for minimum-ionizing particles crossing the full volume of the TPC [10].

The PID is complemented by the Time-Of-Flight (TOF) system [14]. This detector is made of Multi-gap Resistive Plate Chambers (MRPC) and is located at a radial distance of 3.7 m from the nominal interaction point. The TOF detector measures the arrival time of particles relative to the event collision time provided by the TOF detector itself or by the T0 detectors, two arrays of Cherenkov counters located at forward and backward rapidities [15]. The TOF detector is used in this analysis for pile-up rejection, mostly from out-of-bunch collisions, by requiring that at least one of the $\Lambda$ ($\overline{\Lambda}$) charged decay-daughter tracks has an associated hit in the TOF detector.

Collision events are triggered by two plastic scintillator arrays, V0A and V0C [16], located on both sides of the interaction point, covering the pseudorapidity regions 2.8 $<\eta<$ 5.1 and $-3.7<\eta<-1.7$, respectively. Each array consists of four concentric rings, each ring comprising eight cells with the same azimuthal coverage. The V0A and V0C scintillators are used to determine the collision centrality from the measured signals produced by charged particles [17, 18]. The centrality is defined in terms of percentiles of the total hadronic cross section.

3 Data analysis

3.1 Event selection

The data used for this analysis were collected in 2018 during the LHC Pb–Pb run at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV. A minimum bias (MB) event trigger and two centrality triggers were used. The MB trigger, fully efficient in the centrality interval 0–90$\%$, requires coincident signals in the V0 detectors, synchronous with the bunch crossing time defined by the LHC clock. The two centrality triggers, fully efficient in the centrality classes 0–10$\%$ and 30–50$\%$, are based on the signal amplitude measured by the V0 scintillators, which is proportional to the charged-particle multiplicity of the event. The analysis is performed in four centrality classes: 0–10$\%$, 10–30$\%$, 30–50$\%$, and 50–90$\%$. The events in the centrality classes 0–10$\%$ and 30–50$\%$ are selected using both the MB and centrality triggers, while the MB event trigger alone is used for the other centrality classes. In order to keep the conditions of the detectors as uniform as possible and reject background collisions, the coordinate of the primary vertex along the beam axis is required to be within 10 cm from the nominal interaction point. Events with multiple vertices identified with the SPD are tagged as pile-up and removed from the analysis [10]. In addition, events with pile-up occurring during the drift time of the TPC are rejected based on the correlation between the number of SDD and SSD clusters and the total number of clusters in the TPC, as described in Ref. [19]. To further suppress the pile-up contribution, mostly from out-of-bunch collisions, the $\Lambda$ daughter tracks are required to have an associated hit in the TOF detector. This requirement is applied only for the centrality classes 30–50$\%$ and 50–90$\%$. For the most central events, the matching of daughter tracks with a TOF hit does not have a significant impact on the fraction of $\Lambda$ ($\overline{\Lambda}$) from events with out-of-bunch pile-up, which is found to be between 0.02$\%$ and 0.07$\%$. The total number of events selected for each centrality class is reported in Table 1.

3.2 Selection of $\Lambda$ candidates

The two-body decay channels $\Lambda\rightarrow\mathrm{p}+\pi^{-}$ and $\overline{\Lambda}\rightarrow\overline{\mathrm{p}}+\pi^{+}$ are used in this measurement. These have a branching ratio BR of $(63.9\pm 0.5)\%$ [1]. The $\Lambda$ ($\overline{\Lambda}$) candidates are reconstructed using the standard ALICE weak decay finder. This algorithm searches for weak decay topologies, called $\mathrm{V}^{0}$, by reconstructing oppositely-charged particle tracks originating from a displaced vertex as described in Refs. [20, 21]. In the case of a decay vertex located inside the ITS volume, at least one hit in any of the ITS layers is used in the reconstruction of the charged tracks originating from the $\mathrm{V}^{0}$ decay. The reconstructed tracks, selected in the pseudorapidity region $|\eta|<0.8$, are required to fulfil a set of quality criteria such as having a number of TPC crossed rows larger than 80, a number of TPC clusters used for the $\textrm{d}E/\textrm{d}x$ calculation larger than 60 to ensure a good $\textrm{d}E/\textrm{d}x$ resolution, a fraction of TPC crossed rows and findable clusters larger than 70$\%$, and a good track fit $\chi^{2}/N^{\rm TPC}_{\rm cls}<2.5$, where $N^{\rm TPC}_{\rm cls}$ is the number of TPC clusters.

To reduce the combinatorial background, a set of topological selections are applied, i.e. the distance of closest approach (DCA) between the $\mathrm{V}^{0}$ daughter tracks is required to be less than 1 cm, the DCA between the $\mathrm{V}^{0}$ and the primary collision vertex less than 0.5 cm, the radial distance between primary and secondary vertices larger than 3 cm, and $\mathrm{cos}(\theta_{\rm p})>0.995$, where $\theta_{\rm p}$ is the angle between the vector connecting the primary and secondary vertices and the total $\mathrm{V}^{0}$ momentum ($\vec{p}_{\mathrm{V}^{0}}=\vec{p}_{\rm p}+\vec{p}_{\pi}$). The selection criteria applied for this measurement are similar to those already used in previous measurements [21, 22, 23].

The particle identification is based on the energy loss per unit of track length measured by the TPC. Protons and pions are identified by requiring that their measured $\textrm{d}E/\textrm{d}x$ is within 3$\sigma_{\mathrm{d}E/\mathrm{d}x}$ from the expected average calculated using the Bethe–Bloch, where $\sigma_{\mathrm{d}E/\mathrm{d}x}$ is the $\textrm{d}E/\textrm{d}x$ resolution. Proton and pion candidates are selected in the transverse-momentum intervals $0.2<p^{\pi}_{\rm T}<2\ \mathrm{GeV}/c$ and $0.2<p^{\rm p}_{\rm T}<10\ \mathrm{GeV}/c$, respectively.

3.3 Signal extraction

The $\Lambda$ and $\overline{\Lambda}$ lifetimes are extracted from a fit to their proper decay length distributions using the exponential function $\mathrm{exp}\left(-L_{\rm proper}/\langle L_{\rm proper}\rangle\right)$. The proper decay length is calculated for every $\Lambda$ ($\overline{\Lambda}$) as

[TABLE]

where $L_{\rm lab}$ is the decay length measured in the laboratory system as the distance between primary and secondary vertices, $M_{\Lambda}$ is the $\Lambda$ mass taken from the PDG ($M_{\Lambda}=1115.683\ \mathrm{MeV}/c^{2}$) [1], and $p$ is the total momentum of the $\Lambda$ ($\overline{\Lambda}$) measured at the decay point. The number of signal counts in each $L_{\rm proper}$ interval is obtained using the following procedure, which is illustrated in Fig. 1:

Location of the peak region: the invariant mass of the decay daughters is calculated and the region around the maximum of the invariant-mass distribution is fitted using a Gaussian function. The peak region is defined as $[M_{0}-8\sigma,M_{0}+10\sigma]$, where $M_{0}$ is the mean and $\sigma$ is the standard deviation of the Gaussian fit. The choice of such a wide signal region is motivated by the fact that the peak has two long tails and is slightly asymmetric, especially for low values of $L_{\rm proper}$. This asymmetry is an effect of residual imperfections in tracking and energy loss corrections, which affect candidates with invariant masses above and below the expected mass differently. 2. 2.

Fit of the background: the background on the side bands of the peak is fitted using a continuous function to extrapolate the expected background inside the peak region. Since the background shape changes with $L_{\rm proper}$, a third-order polynomial function is used to fit the background at low $L_{\rm proper}$ while the sum of a power-law and a linear function is used at high $L_{\rm proper}$ values. These functions have the minimum number of parameters that guarantees a data-to-fit ratio consistent with unity within statistical uncertainties in the sidebands. 3. 3.

Signal extraction: the signal is extracted in each $L_{\rm proper}$ interval by subtracting the estimated background from the invariant mass distribution and counting the entries inside the peak region.

The total number of $\Lambda$ and $\overline{\Lambda}$ raw counts within the peak region are reported in Table 2 for each centrality interval.

3.4 Efficiency and secondary $\Lambda$ corrections

The raw $L_{\rm proper}$ spectrum of $\Lambda$ ($\overline{\Lambda}$) is corrected for the reconstruction efficiency, the feed-down contribution from higher-mass baryons and secondary $\Lambda$ ($\overline{\Lambda}$) originating from interactions of particles with the detector material as

[TABLE]

where $\epsilon(L_{\rm proper})$ is the efficiency of primary $\Lambda$ ($\overline{\Lambda}$) and $f_{\rm prim}(L_{\rm proper})$ is the fraction of primary $\Lambda$ ($\overline{\Lambda}$). The dominant feed-down contributions are given by the weak decays of $\Xi^{\pm}$, $\Xi^{0}$, and $\Omega^{\pm}$: [1]

• $\bullet$

$\Xi^{0}(\overline{\Xi}^{0})\rightarrow\Lambda(\overline{\Lambda})+\pi^{0}$    BR $=$ $(99.524\pm 0.012)\%$,

• $\bullet$

$\Xi^{\pm}\rightarrow\Lambda+\pi^{\pm}$    BR $=$ $(99.887\pm 0.035)\%$,

• $\bullet$

$\Omega^{\pm}\rightarrow\Lambda+K^{\pm}$    BR $=$ $(67.8\pm 0.7)\%$,

• $\bullet$

$\Omega^{\pm}\rightarrow\Xi^{0}+\pi^{\pm}\ \mathrm{and}\ \Omega^{\pm}\rightarrow\Xi^{\pm}+\pi^{0}$    BR $=$ $(32.2\pm 0.8)\%$.

These corrections are calculated using Monte Carlo (MC) simulations. Collision events between lead ions are simulated using the HIJING event generator [24] and the passage of particles through the experimental apparatus is simulated using GEANT3 [25] as transport code. Considering that the $p_{\rm T}$ distributions of particles and their relative abundances in MC simulations are different from data, centrality and $p_{\rm T}$-dependent corrections are applied in MC simulations using weights. These are defined, for different centrality classes, as the ratio of the $p_{\rm T}$ spectrum measured by ALICE and the $p_{\rm T}$ spectrum generated by HIJING.

The ALICE measurements of the $p_{\rm T}$ spectra of $\Lambda$, $\Xi^{\pm}$, and $\Omega^{\pm}$ [21, 26] in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $=$ 2.76 TeV, scaled by the ratio of the proton $p_{\rm T}$ spectra measured at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV [27] and $\sqrt{s_{\mathrm{NN}}}$ $=$ 2.76 TeV [28], are used to calculate the weights for different centralities. Based on isospin symmetry, the $p_{\rm T}$ spectra of $\Xi^{0}$ are assumed to be identical to those of $\Xi^{\pm}$. Centrality dependent factors, given by the ratios $(\Xi/\Lambda)_{\rm data}/(\Xi/\Lambda)_{\rm MC}$ and $(\Omega/\Lambda)_{\rm data}/(\Omega/\Lambda)_{\rm MC}$, are also included to reproduce the centrality dependence of the particle ratios observed in data. The efficiency is calculated as the ratio between reconstructed and generated primary $\Lambda$ in the simulation

[TABLE]

The efficiencies of $\Lambda$ and $\overline{\Lambda}$ for central Pb–Pb collisions (0–10$\%$) as a function of $L_{\rm proper}$ are shown in Fig. 2 (left). The correction for secondary $\Lambda$ ($\overline{\Lambda}$) from material and weak decays is applied by scaling the raw $L_{\rm proper}$ spectrum by the fraction of primary $\Lambda$ ($\overline{\Lambda}$) given by

[TABLE]

The fraction of secondary $\Lambda$ and $\overline{\Lambda}$ for central Pb–Pb (0–10$\%$) is shown as a function of $L_{\rm proper}$ in the right panel of Fig. 2. The individual contributions from material and weak decays are shown in addition to the total fraction for illustration. The observed trend of the fraction of secondary $\Lambda$ ($\overline{\Lambda}$) from weak decays with $L_{\rm proper}$ is due to an interplay between the efficiency and decay time of the $\Lambda$ ($\overline{\Lambda}$) mother particle. For secondary $\Lambda$ ($\overline{\Lambda}$) from material, it is due to a combined effect of efficiency and the radial distance at which the secondary $\Lambda$ ($\overline{\Lambda}$) is produced.

4 Systematic uncertainties

The dominant sources of systematic uncertainties on the $\Lambda$ and $\overline{\Lambda}$ lifetime measurements are related to the track and $\mathrm{V}^{0}$ selections, signal extraction, efficiency and feed-down corrections. These are summarized in Table 3. The methods used to estimate the systematic uncertainties from these sources are illustrated in the following. In addition, effects of the material budget uncertainty, the uncertainty on the hadronic interaction of $\Lambda$, $\overline{\Lambda}$, and their decay daughters, and potential effects of residual pile-up —which are found to be negligible —are also discussed.

4.1 Systematic uncertainty from track and $\mathrm{V}^{0}$ selection

The systematic uncertainty due to the track and $\mathrm{V}^{0}$ selection criteria is estimated by repeating the full analysis chain using one hundred different analysis parameters, where the single-track, topological, and particle-identification selection criteria are varied, such that they produce a maximum variation of $\pm 10\%$ in the raw signal yield, similarly to the approach used in Refs. [21, 22, 23]. The systematic uncertainty from the track and $\mathrm{V}^{0}$ selection is calculated by fitting the distribution of lifetime values obtained from different selection criteria using a Gaussian function and taking the $\sigma$ of the Gaussian fit as an uncertainty. The obtained uncertainties are 0.55 ps for $\tau_{\Lambda}$, 0.69 ps for $\tau_{\overline{\Lambda}}$, and 0.65 ps for $\tau_{\Lambda+\overline{\Lambda}}$. This contribution is the dominant source of systematic uncertainty.

4.2 Signal extraction uncertainty

The systematic uncertainty from the signal extraction includes two contributions: the choice of the background fit range and the integration range used for the raw yield extraction. For both contributions, one hundred different intervals are randomly generated, with a uniform probability distribution between two extremes, and the signal extraction procedure is repeated for each of these intervals. The limits used are specified in Table 4.

The standard deviation of the distribution of raw yields in each $L_{\rm proper}$ interval is taken as the systematic uncertainty. These two contributions are independent and added in quadrature. The stability of the results was tested against different choices of the fit functions used to model the background. In particular, linear and second-order polynomials were also tried at low $L_{\rm proper}$, while an exponential (power-law) for the left and second-order polynomial (exponential) for the right side of the background were also used at high $L_{\rm proper}$. The use of alternative fit functions to model the background resulted in negligible changes in the extracted yield. For this reason, this contribution to the signal extraction uncertainty is considered negligible. The uncertainty on the lifetime is calculated by replacing the statistical uncertainties on the corrected $L_{\rm proper}$ spectrum with the signal extraction uncertainties, which are bin-by-bin uncorrelated, and taking the uncertainty from the exponential fit as the systematic uncertainty. This contribution is found to be $(\Delta\tau)^{\rm syst}_{\rm signal}=0.03$ ps for both $\tau_{\Lambda}$ and $\tau_{\overline{\Lambda}}$, and 0.02 ps for $\tau_{\Lambda+\overline{\Lambda}}$.

4.3 Systematic uncertainty from efficiency and feed-down corrections

The systematic uncertainty related to the efficiency and feed-down corrections is estimated by varying: (i) the $p_{\rm T}$-dependent weights used to adjust the input $p_{\rm T}$ distributions of $\Lambda$, $\Xi$, and $\Omega$ in the simulations, (ii) the $\Lambda$, $\Xi$, and $\Omega$ lifetimes by the PDG uncertainties [1] and (iii) the $\Lambda/\Xi$ and $\Lambda/\Omega$ ratios by the measured uncertainties. The $\Omega$ is found to give a negligible contribution to the systematic uncertainties. To vary the lifetimes implemented in the simulations, which are taken from the PDG [1], $L_{\rm proper}$-dependent weights are used. These are obtained as the ratio between the $L_{\rm proper}$ spectrum with modified lifetime and the default spectrum. To estimate the total contribution of these sources, a set of five hundred different efficiency and feed-down corrections is generated. Each of them is obtained using a different set of weights where the $p_{\rm T}$ spectra of $\Lambda$, $\Xi$, and $\Omega$, their lifetimes and particle ratios are varied by a fraction of their uncertainty. Such a fraction is extracted randomly from a Gaussian distribution centered at zero and with a width equal to 1. When modifying the $p_{\rm T}$ spectra measured in data to recalculate the weights, the correlated and uncorrelated uncertainties with $p_{\rm T}$ are treated differently:

$p_{\rm T}$-correlated uncertainties: all data points of the $p_{\rm T}$ spectrum are shifted coherently upward and downward by a fraction of their systematic uncertainty in each $p_{\rm T}$ interval. 2. 2.

$p_{\rm T}$-uncorrelated uncertainties: the data points are moved independently by a fraction of their uncorrelated uncertainty in each $p_{\rm T}$ interval.

These five hundred different efficiencies and fractions of secondary $\Lambda$ ($\overline{\Lambda}$) are then used to correct the raw-$L_{\rm proper}$ spectrum measured in data. The lifetime is extracted for each corrected spectrum and the standard deviation of the distribution of lifetimes is taken as an estimate of the systematic uncertainty from efficiency and feed-down corrections. The obtained uncertainties are 0.30 ps for $\tau_{\Lambda}$, 0.33 ps for $\tau_{\overline{\Lambda}}$, and 0.30 ps for $\tau_{\Lambda+\overline{\Lambda}}$.

4.4 Inelastic interaction with the detector materials

The default efficiency is based on GEANT3 transport package. The effect of (anti)matter absorption was studied by comparing the default efficiency with that obtained using a MC production based on GEANT4 [29], which contains slightly different parametrizations of the inelastic cross sections of (anti)matter particles. The GEANT3 and GEANT4-based efficiencies are consistent within uncertainties. The $\Lambda$ and $\overline{\Lambda}$ lifetimes are found to be consistent within uncertainties, and therefore, no systematic uncertainty is assigned due to this effect.

4.5 Material budget

The ALICE detector material is known with a precision of 4.5$\%$ [10]. The effect of the limited knowledge of the material budget, which could affect the efficiency and the fraction of secondary $\Lambda$ ($\overline{\Lambda}$) from material and its dependence on $L_{\rm proper}$, is studied by comparing the efficiency and corrections for secondary $\Lambda$ ($\overline{\Lambda}$) using MC productions with increased and decreased material density by 4.5$\%$. The difference in the mean lifetime is found to not be statistically significant and therefore this contribution is neglected.

4.6 Pile-up effects

Simultaneous collisions with displaced vertices (pile-up) could, in principle, create a bias in the measurement of the $\Lambda$ ($\overline{\Lambda}$) decay length due to the wrong $\mathrm{V}^{0}$–vertex association. The tight selection on the $\mathrm{cos}(\theta_{\rm p})$ allows the matching between a reconstructed $\mathrm{V}^{0}$ and the wrong vertex only for close vertices. This happens with very low probability and is found to give a negligible bias in the decay length measurement. To further cross-check potential pile-up effects, the analysis is repeated removing all pile-up rejections. The $\Lambda$ ($\overline{\Lambda}$) lifetimes, in this case, are found to be consistent with the value using default pile-up rejection within the statistical uncertainties. It is concluded that the pile-up effects combined with rather strong topological selections used in this analysis give a negligible effect on the $\Lambda$ ($\overline{\Lambda}$) lifetime.

5 Results

The $L_{\rm proper}$ spectra of $\Lambda$ and $\overline{\Lambda}$ measured in each centrality interval are corrected for the corresponding efficiency, feed-down from higher mass baryons, and the fraction of secondary $\Lambda$ ($\overline{\Lambda}$) from the material. The use of centrality triggers in the data used in this analysis leads to a non-uniform centrality distribution. In order to restore the correct relative contribution from different centralities, the $L_{\rm proper}$ spectra measured in the centrality intervals 10–30$\%$, 30–50$\%$, and 50–90$\%$ are scaled by a factor

[TABLE]

where $N_{\rm events}^{i}$ and $w_{i}$ are the number of events and the centrality bin width of the $i$-th centrality interval and $N_{\rm events}^{0-10\%}$ and $w_{0-10\%}=10$ are those related to the reference centrality interval 0–10$\%$. The obtained spectrum is normalized to unity and fitted with an exponential function in the $L_{\rm proper}$ interval [3,30] cm to extract the mean lifetime. The fit results for $\Lambda$, $\overline{\Lambda}$ and their sum are shown in Fig. 3, which also contains the data-to-fit ratios in the bottom panels. The data-to-fit ratio in each interval is obtained as the ratio between the interval content and the weighted average of the fit function within the interval, with weight given by the exponential function. In this figure, only statistical uncertainties in each $L_{\rm proper}$ interval and on the mean lifetime are shown. The systematic uncertainties are calculated using the procedure described in Sec. 4 and are reported only for the final result of the lifetime in the 0–90$\%$ centrality class. The fit is stable when changing fit range ($L^{\rm min}_{\rm proper}$ $=$ 1,2,3,4,5,…, 10 cm) and binning (width $=$ 0.5,1,2 cm) leading to results that are consistent within the statistical uncertainties.

The measured lifetimes of $\Lambda$ and $\overline{\Lambda}$ with statistical and systematic uncertainties, are

[TABLE]

The lifetimes extracted in different centrality intervals are consistent within their statistical uncertainties, as shown in Fig. 4. As a cross-check, the lifetime is also calculated as the weighted average of the results in different centrality intervals, with weights given by the inverse of the statistical uncertainties squared. The result is fully consistent with that extracted from the $L_{\rm proper}$ distribution obtained using Eq. 5.

The present measurement is compared with previous results in Fig. 5. The STAR measurement is taken from Ref. [30]. For this comparison, statistical and systematic uncertainties are added in quadrature.

Assuming CPT invariance, the lifetimes of the $\Lambda$ and $\overline{\Lambda}$ are expected to be consistent within uncertainties. To test CPT invariance, the relative difference $(\tau_{\Lambda}-\tau_{\overline{\Lambda}})/\tau_{\Lambda}$ is measured. Statistical uncertainties on $\tau_{\Lambda}$ and $\tau_{\overline{\Lambda}}$ and the systematic uncertainties originating from the signal extraction are uncorrelated and propagated independently. On the other hand, the systematic uncertainties on the efficiency and feed-down corrections as well as those on the track and $\mathrm{V}^{0}$ selections of $\Lambda$ and $\overline{\Lambda}$ are partially correlated. The systematic uncertainty on the relative difference $(\tau_{\Lambda}-\tau_{\overline{\Lambda}})/\tau_{\Lambda}$ from the former contribution is considered as half of the interval with the following extremes

[TABLE]

[TABLE]

and is found to be $1.1\times 10^{-4}$. To take into account the correlation between the uncertainties from the track and $\mathrm{V}^{0}$ selections, the relative difference $(\tau_{\Lambda}-\tau_{\overline{\Lambda}})/\tau_{\Lambda}$ is calculated for each of the different analysis settings used. The uncertainty is given by the standard deviation of the distribution of $(\tau_{\Lambda}-\tau_{\overline{\Lambda}})/\tau_{\Lambda}$ values and is found to be 0.0021, which is the largest contribution to the total systematic uncertainty. The measured value of the relative difference between the $\Lambda$ and $\overline{\Lambda}$ lifetimes is

[TABLE]

while that reported in the PDG is $(\tau_{\Lambda}-\tau_{\overline{\Lambda}})/\tau_{\Lambda}=-0.001\pm 0.009$ [1]. The present measurement is consistent with zero with an overall improvement of the absolute precision with respect to the PDG by approximately a factor of three.

6 Summary

Unprecedentedly precise measurements of the $\Lambda$ ($\overline{\Lambda}$) lifetime and of the relative difference between the lifetimes of $\Lambda$ and $\overline{\Lambda}$ are presented. The latter represents an important test of the CPT symmetry in the strangeness sector. The confidence range of the $\Lambda$ ($\overline{\Lambda}$) lifetime is reduced by approximately a factor of three with respect to the PDG average.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA), Thailand Science Research and Innovation (TSRI) and National Science, Research and Innovation Fund (NSRF), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: European Research Council, Strong 2020 - Horizon 2020, Marie Skłodowska Curie (grant nos. 950692, 824093, 896850), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland; Programa de Apoyos para la Superación del Personal Académico, UNAM, Mexico;

Appendix A The ALICE Collaboration

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M. Kowalski  107, V. Kozhuharov  36, I. Králik  59, A. Kravčáková  37, L. Krcal  32,38, L. Kreis97, M. Krivda  100,59, F. Krizek  86, K. Krizkova Gajdosova  32, M. Kroesen  94, M. Krüger  63, D.M. Krupova  35, E. Kryshen  140, V. Kučera  32, C. Kuhn  127, P.G. Kuijer  84, T. Kumaoka123, D. Kumar132, L. Kumar  90, N. Kumar90, S. Kumar  31, S. Kundu  32, P. Kurashvili  79, A. Kurepin  140, A.B. Kurepin  140, A. Kuryakin  140, S. Kushpil  86, J. Kvapil  100, M.J. Kweon  57, J.Y. Kwon  57, Y. Kwon  138, S.L. La Pointe  38, P. La Rocca  26, A. Lakrathok105, M. Lamanna  32, R. Langoy  119, P. Larionov  32, E. Laudi  32, L. Lautner  32,95, R. Lavicka  102, T. Lazareva  140, R. Lea  131,54, H. Lee  104, G. Legras  135, J. Lehrbach  38, T.M. Lelek2, R.C. Lemmon  85, I. León Monzón  109, M.M. Lesch  95, E.D. Lesser  18, P. Lévai  136, X. Li10, X.L. Li6, J. Lien  119, R. Lietava  100, I. Likmeta  114, B. Lim  24, S.H. Lim  16, V. Lindenstruth  38, A. Lindner45, C. Lippmann  97, A. Liu  18, D.H. Liu  6, J. Liu  117, I.M. Lofnes  20, C. Loizides  87, S. Lokos  107, J. Lomker  58, P. Loncar  33, J.A. Lopez  94, X. Lopez  125, E. López Torres  7, P. Lu  97,118, J.R. Luhder  135, M. Lunardon  27, G. Luparello  56, Y.G. Ma  39, A. Maevskaya140, M. Mager  32, A. Maire  127, M.V. Makariev  36, M. Malaev  140, G. Malfattore  25, N.M. Malik  91, Q.W. Malik19, S.K. Malik  91, L. Malinina  VI,141, D. Mal’Kevich  140, D. Mallick  80, N. Mallick  47, G. Mandaglio  30,52, S.K. Mandal  79, V. Manko  140, F. Manso  125, V. Manzari  49, Y. Mao  6, G.V. Margagliotti  23, A. Margotti  50, A. Marín  97, C. Markert  108, P. Martinengo  32, J.L. Martinez114, M.I. Martínez  44, G. Martínez García  103, S. Masciocchi  97, M. Masera  24, A. Masoni  51, L. Massacrier  72, A. Mastroserio  129,49, O. Matonoha  75, P.F.T. Matuoka110, A. Matyja  107, C. Mayer  107, A.L. Mazuecos  32, F. Mazzaschi  24, M. Mazzilli  32, J.E. Mdhluli  121, A.F. Mechler63, Y. Melikyan  43,140, A. Menchaca-Rocha  66, E. Meninno  102,28, A.S. Menon  114, M. Meres  12, S. Mhlanga113,67, Y. Miake123, L. Micheletti  55, L.C. Migliorin126, D.L. Mihaylov  95, K. Mikhaylov  141,140, A.N. Mishra  136, D. Miśkowiec  97, A. Modak  4, A.P. Mohanty  58, B. Mohanty80, M. Mohisin Khan  IV,15, M.A. Molander  43, Z. Moravcova  83, C. Mordasini  95, D.A. Moreira De Godoy  135, I. Morozov  140, A. Morsch  32, T. Mrnjavac  32, V. Muccifora  48, S. Muhuri  132, J.D. Mulligan  74, A. Mulliri22, M.G. Munhoz  110, R.H. Munzer  63, H. Murakami  122, S. Murray  113, L. Musa  32, J. Musinsky  59, J.W. Myrcha  133, B. Naik  121, A.I. Nambrath  18, B.K. Nandi  46, R. Nania  50, E. Nappi  49, A.F. Nassirpour  17,75, A. Nath  94, C. Nattrass  120, M.N. Naydenov  36, A. Neagu19, A. Negru124, L. Nellen  64, S.V. Nesbo34, G. Neskovic  38, D. Nesterov  140, B.S. Nielsen  83, E.G. Nielsen  83, S. Nikolaev  140, S. Nikulin  140, V. Nikulin  140, F. Noferini  50, S. Noh  11, P. Nomokonov  141, J. Norman  117, N. Novitzky  123, P. Nowakowski  133, A. Nyanin  140, J. Nystrand  20, M. Ogino  76, A. Ohlson  75, V.A. Okorokov  140, J. Oleniacz  133, A.C. Oliveira Da Silva  120, M.H. Oliver  137, A. Onnerstad  115, C. Oppedisano  55, A. Ortiz Velasquez  64, J. Otwinowski  107, M. Oya92, K. Oyama  76, Y. Pachmayer  94, S. Padhan  46, D. Pagano  131,54, G. Paić  64, A. Palasciano  49, S. Panebianco  128, H. Park  123, H. Park  104, J. Park  57, J.E. Parkkila  32, R.N. Patra91, B. Paul  22, H. Pei  6, T. Peitzmann  58, X. Peng  6, M. Pennisi  24, L.G. Pereira  65, D. Peresunko  140, G.M. Perez  7, S. Perrin  128, Y. Pestov140, V. Petráček  35, V. Petrov  140, M. Petrovici  45, R.P. Pezzi  103,65, S. Piano  56, M. Pikna  12, P. Pillot  103, O. Pinazza  50,32, L. Pinsky114, C. Pinto  95, S. Pisano  48, M. Płoskoń  74, M. Planinic89, F. Pliquett63, M.G. Poghosyan  87, B. Polichtchouk  140, S. Politano  29, N. Poljak  89, A. Pop  45, S. Porteboeuf-Houssais  125, V. Pozdniakov  141, I.Y. Pozos  44, K.K. Pradhan  47, S.K. Prasad  4, S. Prasad  47, R. Preghenella  50, F. Prino  55, C.A. Pruneau  134, I. Pshenichnov  140, M. Puccio  32, S. Pucillo  24, Z. Pugelova106, S. Qiu  84, L. Quaglia  24, R.E. Quishpe114, S. Ragoni  14, A. Rakotozafindrabe  128, L. Ramello  130,55, F. Rami  127, S.A.R. Ramirez  44, T.A. Rancien73, M. Rasa  26, S.S. Räsänen  43, R. Rath  50, M.P. Rauch  20, I. Ravasenga  84, K.F. Read  87,120, C. Reckziegel  112, A.R. Redelbach  38, K. Redlich  V,79, C.A. Reetz  97, A. Rehman20, F. Reidt  32, H.A. Reme-Ness  34, Z. Rescakova37, K. Reygers  94, A. Riabov  140, V. Riabov  140, R. Ricci  28, M. Richter  19, A.A. Riedel  95, W. Riegler  32, C. Ristea  62, M. Rodríguez Cahuantzi  44, K. Røed  19, R. Rogalev  140, E. Rogochaya  141, T.S. Rogoschinski  63, D. Rohr  32, D. Röhrich  20, P.F. Rojas44, S. Rojas Torres  35, P.S. Rokita  133, G. Romanenko  141, F. Ronchetti  48, A. Rosano  30,52, E.D. Rosas64, K. Roslon  133, A. Rossi  53, A. Roy  47, S. Roy  46, N. Rubini  25, O.V. Rueda  114, D. Ruggiano  133, R. Rui  23, B. Rumyantsev141, P.G. Russek  2, R. Russo  84, A. Rustamov  81, E. Ryabinkin  140, Y. Ryabov  140, A. Rybicki  107, H. Rytkonen  115, W. Rzesa  133, O.A.M. Saarimaki  43, R. Sadek  103, S. Sadhu  31, S. Sadovsky  140, J. Saetre  20, K. Šafařík  35, S.K. Saha  4, S. Saha  80, B. Sahoo  46, B. Sahoo  47, R. Sahoo  47, S. Sahoo60, D. Sahu  47, P.K. Sahu  60, J. Saini  132, K. Sajdakova37, S. Sakai  123, M.P. Salvan  97, S. Sambyal  91, I. Sanna  32,95, T.B. Saramela110, D. Sarkar  134, N. Sarkar132, P. Sarma  41, V. Sarritzu  22, V.M. Sarti  95, M.H.P. Sas  137, J. Schambach  87, H.S. Scheid  63, C. Schiaua  45, R. Schicker  94, A. Schmah94, C. Schmidt  97, H.R. Schmidt93, M.O. Schmidt  32, M. Schmidt93, N.V. Schmidt  87, A.R. Schmier  120, R. Schotter  127, A. Schröter  38, J. Schukraft  32, K. Schwarz97, K. Schweda  97, G. Scioli  25, E. Scomparin  55, J.E. Seger  14, Y. Sekiguchi122, D. Sekihata  122, I. Selyuzhenkov  97,140, S. Senyukov  127, J.J. Seo  57, D. Serebryakov  140, L. Šerkšnytė  95, A. Sevcenco  62, T.J. Shaba  67, A. Shabetai  103, R. Shahoyan32, A. Shangaraev  140, A. Sharma90, B. Sharma  91, D. Sharma  46, H. Sharma  107, M. Sharma  91, S. Sharma  76, S. Sharma  91, U. Sharma  91, A. Shatat  72, O. Sheibani114, K. Shigaki  92, M. Shimomura77, J. Shin11, S. Shirinkin  140, Q. Shou  39, Y. Sibiriak  140, S. Siddhanta  51, T. Siemiarczuk  79, T.F. Silva  110, D. Silvermyr  75, T. Simantathammakul105, R. Simeonov  36, B. Singh91, B. Singh  95, R. Singh  80, R. Singh  91, R. Singh  47, S. Singh  15, V.K. Singh  132, V. Singhal  132, T. Sinha  99, B. Sitar  12, M. Sitta  130,55, T.B. Skaali19, G. Skorodumovs  94, M. Slupecki  43, N. Smirnov  137, R.J.M. Snellings  58, E.H. Solheim  19, J. Song  114, A. Songmoolnak105, F. Soramel  27, A.B. Soto-hernandez  88, R. Spijkers  84, I. Sputowska  107, J. Staa  75, J. Stachel  94, I. Stan  62, P.J. Steffanic  120, S.F. Stiefelmaier  94, D. Stocco  103, I. Storehaug  19, P. Stratmann  135, S. Strazzi  25, C.P. Stylianidis84, A.A.P. Suaide  110, C. Suire  72, M. Sukhanov  140, M. Suljic  32, R. Sultanov  140, V. Sumberia  91, S. Sumowidagdo  82, S. Swain60, I. Szarka  12, M. Szymkowski  133, S.F. Taghavi  95, G. Taillepied  97, J. Takahashi  111, G.J. Tambave  20, S. Tang  125,6, Z. Tang  118, J.D. Tapia Takaki  116, N. Tapus124, L.A. Tarasovicova  135, M.G. Tarzila  45, G.F. Tassielli  31, A. Tauro  32, G. Tejeda Muñoz  44, A. Telesca  32, L. Terlizzi  24, C. Terrevoli  114, S. Thakur  4, D. Thomas  108, A. Tikhonov  140, A.R. Timmins  114, M. Tkacik106, T. Tkacik  106, A. Toia  63, R. Tokumoto92, N. Topilskaya  140, M. Toppi  48, F. Torales-Acosta18, T. Tork  72, A.G. Torres Ramos  31, A. Trifiró  30,52, A.S. Triolo  32,30,52, S. Tripathy  50, T. Tripathy  46, S. Trogolo  32, V. Trubnikov  3, W.H. Trzaska  115, T.P. Trzcinski  133, A. Tumkin  140, R. Turrisi  53, T.S. Tveter  19, K. Ullaland  20, B. Ulukutlu  95, A. Uras  126, M. Urioni  54,131, G.L. Usai  22, M. Vala37, N. Valle  21, L.V.R. van Doremalen58, M. van Leeuwen  84, C.A. van Veen  94, R.J.G. van Weelden  84, P. Vande Vyvre  32, D. Varga  136, Z. Varga  136, M. Vasileiou  78, A. Vasiliev  140, O. Vázquez Doce  48, V. Vechernin  140, E. Vercellin  24, S. Vergara Limón44, L. Vermunt  97, R. Vértesi  136, M. Verweij  58, L. Vickovic33, Z. Vilakazi121, O. Villalobos Baillie  100, A. Villani  23, G. Vino  49, A. Vinogradov  140, T. Virgili  28, M.M.O. Virta  115, V. Vislavicius75, A. Vodopyanov  141, B. Volkel  32, M.A. Völkl  94, K. Voloshin140, S.A. Voloshin  134, G. Volpe  31, B. von Haller  32, I. Vorobyev  95, N. Vozniuk  140, J. Vrláková  37, C. Wang  39, D. Wang39, Y. Wang  39, A. Wegrzynek  32, F.T. Weiglhofer38, S.C. Wenzel  32, J.P. Wessels  135, S.L. Weyhmiller  137, J. Wiechula  63, J. Wikne  19, G. Wilk  79, J. Wilkinson  97, G.A. Willems  135, B. Windelband  94, M. Winn  128, J.R. Wright  108, W. Wu39, Y. Wu  118, R. Xu  6, A. Yadav  42, A.K. Yadav  132, S. Yalcin  71, Y. Yamaguchi  92, S. Yang20, S. Yano  92, Z. Yin  6, I.-K. Yoo  16, J.H. Yoon  57, S. Yuan20, A. Yuncu  94, V. Zaccolo  23, C. Zampolli  32, F. Zanone  94, N. Zardoshti  32, A. Zarochentsev  140, P. Závada  61, N. Zaviyalov140, M. Zhalov  140, B. Zhang  6, L. Zhang  39, S. Zhang  39, X. Zhang  6, Y. Zhang118, Z. Zhang  6, M. Zhao  10, V. Zherebchevskii  140, Y. Zhi10, D. Zhou  6, Y. Zhou  83, J. Zhu  97,6, Y. Zhu6, S.C. Zugravel  55, N. Zurlo  131,54

Affiliation Notes

I Deceased

II Also at: Max-Planck-Institut für Physik, Munich, Germany

III Also at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy

IV Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India

V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

VI Also at: An institution covered by a cooperation agreement with CERN

Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia

2 AGH University of Science and Technology, Cracow, Poland

3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine

4 Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India

5 California Polytechnic State University, San Luis Obispo, California, United States

6 Central China Normal University, Wuhan, China

7 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba

8 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico

9 Chicago State University, Chicago, Illinois, United States

10 China Institute of Atomic Energy, Beijing, China

11 Chungbuk National University, Cheongju, Republic of Korea

12 Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovak Republic

13 COMSATS University Islamabad, Islamabad, Pakistan

14 Creighton University, Omaha, Nebraska, United States

15 Department of Physics, Aligarh Muslim University, Aligarh, India

16 Department of Physics, Pusan National University, Pusan, Republic of Korea

17 Department of Physics, Sejong University, Seoul, Republic of Korea

18 Department of Physics, University of California, Berkeley, California, United States

19 Department of Physics, University of Oslo, Oslo, Norway

20 Department of Physics and Technology, University of Bergen, Bergen, Norway

21 Dipartimento di Fisica, Università di Pavia, Pavia, Italy

22 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

23 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

24 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

25 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy

26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy

27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy

28 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy

29 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

30 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy

31 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy

32 European Organization for Nuclear Research (CERN), Geneva, Switzerland

33 Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia

34 Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway

35 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic

36 Faculty of Physics, Sofia University, Sofia, Bulgaria

37 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic

38 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

39 Fudan University, Shanghai, China

40 Gangneung-Wonju National University, Gangneung, Republic of Korea

41 Gauhati University, Department of Physics, Guwahati, India

42 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany

43 Helsinki Institute of Physics (HIP), Helsinki, Finland

44 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

45 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania

46 Indian Institute of Technology Bombay (IIT), Mumbai, India

47 Indian Institute of Technology Indore, Indore, India

48 INFN, Laboratori Nazionali di Frascati, Frascati, Italy

49 INFN, Sezione di Bari, Bari, Italy

50 INFN, Sezione di Bologna, Bologna, Italy

51 INFN, Sezione di Cagliari, Cagliari, Italy

52 INFN, Sezione di Catania, Catania, Italy

53 INFN, Sezione di Padova, Padova, Italy

54 INFN, Sezione di Pavia, Pavia, Italy

55 INFN, Sezione di Torino, Turin, Italy

56 INFN, Sezione di Trieste, Trieste, Italy

57 Inha University, Incheon, Republic of Korea

58 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands

59 Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic

60 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

61 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

62 Institute of Space Science (ISS), Bucharest, Romania

63 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

64 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico

65 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil

66 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico

67 iThemba LABS, National Research Foundation, Somerset West, South Africa

68 Jeonbuk National University, Jeonju, Republic of Korea

69 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany

70 Korea Institute of Science and Technology Information, Daejeon, Republic of Korea

71 KTO Karatay University, Konya, Turkey

72 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France

73 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

74 Lawrence Berkeley National Laboratory, Berkeley, California, United States

75 Lund University Department of Physics, Division of Particle Physics, Lund, Sweden

76 Nagasaki Institute of Applied Science, Nagasaki, Japan

77 Nara Women’s University (NWU), Nara, Japan

78 National and Kapodistrian University of Athens, School of Science, Department of Physics , Athens, Greece

79 National Centre for Nuclear Research, Warsaw, Poland

80 National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India

81 National Nuclear Research Center, Baku, Azerbaijan

82 National Research and Innovation Agency - BRIN, Jakarta, Indonesia

83 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

84 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

85 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom

86 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež, Czech Republic

87 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

88 Ohio State University, Columbus, Ohio, United States

89 Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia

90 Physics Department, Panjab University, Chandigarh, India

91 Physics Department, University of Jammu, Jammu, India

92 Physics Program and International Institute for Sustainability with Knotted Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan

93 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany

94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

95 Physik Department, Technische Universität München, Munich, Germany

96 Politecnico di Bari and Sezione INFN, Bari, Italy

97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

98 Saga University, Saga, Japan

99 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India

100 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom

101 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru

102 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

103 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France

104 Sungkyunkwan University, Suwon City, Republic of Korea

105 Suranaree University of Technology, Nakhon Ratchasima, Thailand

106 Technical University of Košice, Košice, Slovak Republic

107 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland

108 The University of Texas at Austin, Austin, Texas, United States

109 Universidad Autónoma de Sinaloa, Culiacán, Mexico

110 Universidade de São Paulo (USP), São Paulo, Brazil

111 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

112 Universidade Federal do ABC, Santo Andre, Brazil

113 University of Cape Town, Cape Town, South Africa

114 University of Houston, Houston, Texas, United States

115 University of Jyväskylä, Jyväskylä, Finland

116 University of Kansas, Lawrence, Kansas, United States

117 University of Liverpool, Liverpool, United Kingdom

118 University of Science and Technology of China, Hefei, China

119 University of South-Eastern Norway, Kongsberg, Norway

120 University of Tennessee, Knoxville, Tennessee, United States

121 University of the Witwatersrand, Johannesburg, South Africa

122 University of Tokyo, Tokyo, Japan

123 University of Tsukuba, Tsukuba, Japan

124 University Politehnica of Bucharest, Bucharest, Romania

125 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

126 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, Lyon, France

127 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France

128 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Saclay, France

129 Università degli Studi di Foggia, Foggia, Italy

130 Università del Piemonte Orientale, Vercelli, Italy

131 Università di Brescia, Brescia, Italy

132 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India

133 Warsaw University of Technology, Warsaw, Poland

134 Wayne State University, Detroit, Michigan, United States

135 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany

136 Wigner Research Centre for Physics, Budapest, Hungary

137 Yale University, New Haven, Connecticut, United States

138 Yonsei University, Seoul, Republic of Korea

139 Zentrum für Technologie und Transfer (ZTT), Worms, Germany

140 Affiliated with an institute covered by a cooperation agreement with CERN

141 Affiliated with an international laboratory covered by a cooperation agreement with CERN.