Date

Multiplicity dependence of light-flavor hadron production in pp collisions at $\sqrt{s}$ = 7 TeV

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
Phys.Rev.C 99 (2019) 024906, 2019.
Inspire Record 1684320 DOI 10.17182/hepdata.84282

Comprehensive results on the production of unidentified charged particles, $\pi^{\pm}$, $\rm{K}^{\pm}$, $\rm{K}^{0}_{S}$, $\rm{K}$*(892)$^{0}$, $\rm{p}$, $\overline{\rm{p}}$, $\phi$(1020), $\Lambda$, $\overline{\Lambda}$, $\Xi^{-}$, $\overline{\Xi}^{+}$, $\Omega^{-}$ and $\overline{\Omega}^{+}$ hadrons in proton-proton (pp) collisions at $\sqrt{s}$ = 7 TeV at midrapidity ($|y| < 0.5$) as a function of charged-particle multiplicity density are presented. In order to avoid auto-correlation biases, the actual transverse momentum ($p_{\rm{T}}$) spectra of the particles under study and the event activity are measured in different rapidity windows. In the highest multiplicity class, the charged-particle density reaches about 3.5 times the value measured in inelastic collisions. While the yield of protons normalized to pions remains approximately constant as a function of multiplicity, the corresponding ratios of strange hadrons to pions show a significant enhancement that increases with increasing strangeness content. Furthermore, all identified particle to pion ratios are shown to depend solely on charged-particle multiplicity density, regardless of system type and collision energy. The evolution of the spectral shapes with multiplicity and hadron mass shows patterns that are similar to those observed in p-Pb and Pb-Pb collisions at LHC energies. The obtained $p_{\rm{T}}$ distributions and yields are compared to expectations from QCD-based pp event generators as well as to predictions from thermal and hydrodynamic models. These comparisons indicate that traces of a collective, equilibrated system are already present in high-multiplicity pp collisions.

106 data tables

Transverse momentum spectra of charged particles in V0M I multiplicity class

Transverse momentum spectra of charged particles in V0M II multiplicity class

Transverse momentum spectra of charged particles in V0M III multiplicity class

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Medium modification of the shape of small-radius jets in central Pb-Pb collisions at $\sqrt{s_{\mathrm {NN}}} = 2.76\,\rm{TeV}$

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
JHEP 10 (2018) 139, 2018.
Inspire Record 1682990 DOI 10.17182/hepdata.85738

We present the measurement of a new set of jet shape observables for track-based jets in central Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 2.76$ TeV. The set of jet shapes includes the first radial moment or angularity, $g$; the momentum dispersion, $p_{\rm T}D$; and the difference between the leading and sub-leading constituent track transverse momentum, $LeSub$. These observables provide complementary information on the jet fragmentation and can constrain different aspects of the theoretical description of jet-medium interactions. The jet shapes were measured for a small resolution parameter $R = 0.2$ and were fully corrected to particle level. The observed jet shape modifications indicate that in-medium fragmentation is harder and more collimated than vacuum fragmentation as obtained by PYTHIA calculations, which were validated with the measurements of the jet shapes in proton-proton collisions at $\sqrt{s} = 7$ TeV. The comparison of the measured distributions to templates for quark and gluon-initiated jets indicates that in-medium fragmentation resembles that of quark jets in vacuum. We further argue that the observed modifications are not consistent with a totally coherent energy loss picture where the jet loses energy as a single colour charge, suggesting that the medium resolves the jet structure at the angular scales probed by our measurements ($R=0.2$). Furthermore, we observe that small-$R$ jets can help to isolate purely energy loss effects from other effects that contribute to the modifications of the jet shower in medium such as the correlated background or medium response.

18 data tables

Fully corrected $g$ distributions in pp collisions at $\sqrt{s} = 7$\,TeV for $R = 0.2$ in the range of jet $p_{\mathrm{T,jet}}^{\rm ch}$ of $40$--$60$\,GeV$/c$. The results are compared to PYTHIA.

Ratio of fully corrected $g$ distributions pp collisions at $\sqrt{s} = 7$\,TeV for $R = 0.2$ in the range of jet $p_{\mathrm{T,jet}}^{\rm ch}$ of $40$--$60$\,GeV$/c$ and PYTHIA 8 Tune 4C simulations. The systematic uncertainty of $g$ is propagated to the ratio.

Ratio of fully corrected $g$ distributions pp collisions at $\sqrt{s} = 7$\,TeV for $R = 0.2$ in the range of jet $p_{\mathrm{T,jet}}^{\rm ch}$ of $40$--$60$\,GeV$/c$ and PYTHIA Perugia 11 simulations. The systematic uncertainty of $g$ is propagated to the ratio.

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Measurement of dielectron production in central Pb-Pb collisions at $\sqrt{{\textit{s}}_{\mathrm{NN}}}$ = 2.76 TeV

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
Phys.Rev.C 99 (2019) 024002, 2019.
Inspire Record 1680638 DOI 10.17182/hepdata.86551

The first measurement of dielectron ($\mathrm{e}^{+}\mathrm{e}^{-}$) production in central (0$-$10$\%$) Pb-Pb collisions at $\mathbf{\sqrt{{\textit{s}}_{\mathrm{NN}}}}$ = 2.76 TeV at the LHC is presented. The dielectron invariant-mass spectrum is compared to the expected contributions from hadron decays in the invariant-mass range $0 < m_{\mathrm{ee}}<3.5\ \mathrm{GeV}/\textit{c}^{2}$. The ratio of data and the cocktail of hadronic contributions without vacuum $\rho^{0}$ is measured in the invariant-mass range $0.15 < m_{\mathrm{ee}}<0.7\ \mathrm{GeV}/\textit{c}^{2}$, where an excess of dielectrons is observed in other experiments, and its value is $1.40 \pm 0.28\ (\mathrm{stat.}) \pm 0.08\ (\mathrm{syst.}) \pm 0.27\ (\mathrm{cocktail})$. The dielectron spectrum measured in the invariant mass range $0 < m_{\mathrm{ee}}<1\ \mathrm{GeV}/\textit{c}^{2}$ is consistent with the predictions from two theoretical model calculations that include thermal dielectron production from both partonic and hadronic phases with in-medium broadened $\rho^{0}$ meson. The fraction of direct virtual photons over inclusive virtual photons is extracted for dielectron pairs with invariant mass $0.1 < m_{\mathrm{ee}}<0.3\ \mathrm{GeV}/\textit{c}^{2}$, and in the transverse-momentum intervals $1<p_{\mathrm{T}, \mathrm{ee}}<2\ \mathrm{GeV}/\textit{c}$ and $2<p_{\mathrm{T}, \mathrm{ee}}<4\ \mathrm{GeV}/\textit{c}$. The measured fraction of virtual direct photons is consistent with the measurement of real direct photons by ALICE and with the expectations from previous dielectron measurements at RHIC within the experimental uncertainties.

7 data tables

Dielectron invariant-mass spectrum measured in central Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV. The statistical and systematic uncertainties of the data are represented by vertical bars and boxes.

Data-to-cocktail ratio. Statistical uncertainties are represented by vertical bars and systematic uncertainties by boxes.

Dielectron invariant-mass spectrum divided by the hadronic cocktail without the contribution from the vacuum $\rho^{0}$. The statistical and systematic uncertainties of data are represented by vertical bars and boxes.

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p-p, p-$\Lambda$ and $\Lambda$-$\Lambda$ correlations studied via femtoscopy in pp reactions at $\sqrt{s}$ = 7 TeV

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
Phys.Rev.C 99 (2019) 024001, 2019.
Inspire Record 1675759 DOI 10.17182/hepdata.89305

We report on the first femtoscopic measurement of baryon pairs, such as p-p, p-$\Lambda$ and $\Lambda$-$\Lambda$, measured by ALICE at the Large Hadron Collider (LHC) in proton-proton collisions at $\sqrt{s}$ = 7 TeV. This study demonstrates the feasibility of such measurements in pp collisions at ultrarelativistic energies. The femtoscopy method is employed to constrain the hyperon-nucleon and hyperon-hyperon interactions, which are still rather poorly understood. A new method to evaluate the influence of residual correlations induced by the decays of resonances and experimental impurities is hereby presented. The p-p, p-$\Lambda$ and $\Lambda$-$\Lambda$ correlation functions were fitted simultaneously with the help of a new tool developed specifically for the femtoscopy analysis in small colliding systems 'Correlation Analysis Tool using the Schr\"odinger Equation' (CATS). Within the assumption that in pp collisions the three particle pairs originate from a common source, its radius is found to be equal to $r_{0} = 1.144\pm0.019$ (stat) $^{+0.069}_{-0.012}$ (syst) fm. The sensitivity of the measured p-$\Lambda$ correlation is tested against different scattering parameters which are defined by the interaction among the two particles, but the statistics is not sufficient yet to discriminate among different models. The measurement of the $\Lambda$-$\Lambda$ correlation function constrains the phase space spanned by the effective range and scattering length of the strong interaction. Discrepancies between the measured scattering parameters and the resulting correlation functions at LHC and RHIC energies are discussed in the context of various models.

4 data tables

The p$-$p $\oplus$ $\overline{\mathrm{p}}-\overline{\mathrm{p}}$ correlation function.

The p$-\Lambda$ $\oplus$ $\overline{\mathrm{p}}-\overline{\Lambda}$ correlation function.

The $\Lambda-\Lambda$ $\oplus$ $\overline{\Lambda}-\overline{\Lambda}$ correlation function.

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Analysis of the apparent nuclear modification in peripheral Pb-Pb collisions at 5.02 TeV

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
Phys.Lett.B 793 (2019) 420-432, 2019.
Inspire Record 1672944 DOI 10.17182/hepdata.89396

Charged-particle spectra at midrapidity are measured in Pb-Pb collisions at the centre-of-mass energy per nucleon-nucleon pair $\sqrt{s_{\rm NN}}$ = 5.02 TeV and presented in centrality classes ranging from most central (0-5%) to most peripheral (95-100%) collisions. Possible medium effects are quantified using the nuclear modification factor ($R_{\rm AA}$) by comparing the measured spectra with those from proton-proton collisions, scaled by the number of independent nucleon-nucleon collisions obtained from a Glauber model. At large transverse momenta ($8<p_{\rm T}<20$ GeV/$c$), the average $R_{\rm AA}$ is found to increase from about $0.15$ in 0-5% central to a maximum value of about $0.8$ in 75-85% peripheral collisions, beyond which it falls off strongly to below $0.2$ for the most peripheral collisions. Furthermore, $R_{\rm AA}$ initially exhibits a positive slope as a function of $p_{\rm T}$ in the $8$-$20$ GeV/$c$ interval, while for collisions beyond the 80% class the slope is negative. To reduce uncertainties related to event selection and normalization, we also provide the ratio of $R_{\rm AA}$ in adjacent centrality intervals. Our results in peripheral collisions are consistent with a PYTHIA-based model without nuclear modification, demonstrating that biases caused by the event selection and collision geometry can lead to the apparent suppression in peripheral collisions. This explains the unintuitive observation that $R_{\rm AA}$ is below unity in peripheral Pb-Pb, but equal to unity in minimum-bias p-Pb collisions despite similar charged-particle multiplicities.

45 data tables

Nuclear modification factor RAA versus pT for charged particles at midrapidity in 0-5% central Pb-Pb collisions at 5.02 TeV

Nuclear modification factor RAA versus pT for charged particles at midrapidity in 5-10% central Pb-Pb collisions at 5.02 TeV

Nuclear modification factor RAA versus pT for charged particles at midrapidity in 10-15% central Pb-Pb collisions at 5.02 TeV

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Version 2
Centrality and pseudorapidity dependence of the charged-particle multiplicity density in Xe-Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
Phys.Lett.B 790 (2019) 35-48, 2019.
Inspire Record 1672756 DOI 10.17182/hepdata.88397

In this Letter, the ALICE Collaboration presents the first measurements of the charged-particle multiplicity density, $\rm{d}N_{\rm{ch}}/\rm{d}\eta$, and total charged-particle multiplicity, $N_{\rm{ch}}^{\rm{tot}}$, in Xe-Xe collisions at a centre-of-mass energy per nucleon--nucleon pair of $\sqrt{s_{\rm NN}}$ = 5.44 TeV. The measurements are performed as a function of collision centrality over a wide pseudorapidity range of $-3.5 < \eta < 5$. The values of $\rm{d}N_{\rm{ch}}/\rm{d}\eta$ at mid-rapidity and $N_{\rm{ch}}^{\rm{tot}}$ for central collisions, normalised to the number of nucleons participating in the collision ($N_{\rm{part}}$) as a function of $\sqrt{s_{\rm NN}}$, follow the trends established in previous heavy-ion measurements. The same quantities are also found to increase as a function of $N_{\rm{part}}$, and up to the 10% most central collisions the trends are the same as the ones observed in Pb-Pb at a similar energy. For more central collisions, the Xe-Xe scaled multiplicities exceed those in Pb-Pb for a similar $N_{\rm{part}}$. The results are compared to phenomenological models and theoretical calculations based on different mechanisms for particle production in nuclear collisions. All considered models describe the data reasonably well within 20%.

6 data tables

Charged-particle pseudorapidity density for 12 centrality classes over a broad $\eta$ range in Xe--Xe collisions at $\sqrt{s_{_{\mathrm{NN}}}} = 5.44\,\mathrm{TeV}$. Statistical errors are generally insignificant.

Values of $2/\langle N_\mathrm{part} \rangle \langle \mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\rangle$ and $2/\langle N_\mathrm{part} \rangle N^\mathrm{tot}_\mathrm{ch}$ in Xe--Xe collisions at $\sqrt{s_{_{\mathrm{NN}}}} = 5.44\,\mathrm{TeV}$ for the top 5$\%$ central collisions.

Values of $2/\langle N_\mathrm{part} \rangle \langle \mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\rangle$ and $2/\langle N_\mathrm{part} \rangle N^\mathrm{tot}_\mathrm{ch}$ as a function of $\langle N_\mathrm{part} \rangle$ in Xe--Xe collisions at $\sqrt{s_{_{\mathrm{NN}}}} = 5.44\,\mathrm{TeV}$.

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Inclusive J/$\psi$ production at forward and backward rapidity in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 8.16 TeV

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
JHEP 07 (2018) 160, 2018.
Inspire Record 1672807 DOI 10.17182/hepdata.83702

Inclusive J/$\psi$ production is studied in p-Pb interactions at a centre-of-mass energy per nucleon-nucleon collision $\sqrt{s_{\rm NN}}=8.16$ TeV, using the ALICE detector at the CERN LHC. The J/$\psi$ meson is reconstructed, via its decay to a muon pair, in the centre-of-mass rapidity intervals $2.03<y_{\rm {cms}}<3.53$ and $-4.46<y_{\rm {cms}}<-2.96$, where positive and negative $y_{\rm {cms}}$ refer to the p-going and Pb-going direction, respectively. The transverse momentum coverage is $p_{\rm T}<20$ GeV/$c$. In this paper, $y_{\rm cms}$- and $p_{\rm T}$-differential cross sections for inclusive J/$\psi$ production are presented, and the corresponding nuclear modification factors $R_{\rm pPb}$ are shown. Forward results show a suppression of the J/$\psi$ yield with respect to pp collisions, concentrated in the region $p_{\rm T}\lesssim 5$ GeV/$c$. At backward rapidity no significant suppression is observed. The results are compared to previous measurements by ALICE in p-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and to theoretical calculations. Finally, the ratios $R_{\rm FB}$ between forward- and backward-$y_{\rm {cms}}$ $R_{\rm pPb}$ values are shown and discussed.

8 data tables

The y-differential inclusive JPsi cross section obtained in p-Pb and Pb-p collisions. The first uncertainty is statistical, the second one is the uncorrelated systematic uncertainty, while the third one is the global uncertainty common to p-Pb and Pb-p results.

The pt-differential inclusive JPsi cross section obtained in Pb-p collisions. The first uncertainty is statistical, the second one is the uncorrelated systematic uncertainty, while the third one is the global uncertainty common to p-Pb and Pb-p results.

The pt-differential inclusive JPsi nuclear modification factor obtained in p-Pb. The first uncertainty is statistical, the second one is the uncorrelated systematic uncertainty, while the third one is the global uncertainty common to p-Pb and Pb-p results.

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Dielectron production in proton-proton collisions at $\sqrt{s}$ = 7 TeV

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
JHEP 09 (2018) 064, 2018.
Inspire Record 1672792 DOI 10.17182/hepdata.83913

The first measurement of e$^+$e$^-$ pair production at mid-rapidity ($|\eta_{{\rm e}}|$ $<$ 0.8) in pp collisions at $\sqrt{s} = 7$ TeV with ALICE at the LHC is presented. The dielectron production is studied as a function of the invariant mass ($m_{\rm ee}$ $<$ 3.3 GeV/$c^{2}$), the pair transverse momentum ($p_{\rm T,ee}$ $<$ 8 GeV/$c$), and the pair transverse impact parameter (DCA$_{{\rm ee}}$), i.e., the average distance of closest approach of the reconstructed electron and positron tracks to the collision vertex, normalised to its resolution. The results are compared with the expectations from a cocktail of known hadronic sources and are well described when PYTHIA is used to generate the heavy-flavour contributions. In the low-mass region (0.14 $<$ $m_{\rm ee}$ $<$ 1.1 GeV/$c^{2}$), prompt and non-prompt e$^+$e$^-$ sources can be separated via the DCA$_{\rm ee}$. In the intermediate-mass region (1.1 $<$ $m_{\rm ee}$ $<$ 2.7 GeV/$c^{2}$), a double-differential fit to the data in $m_{\rm ee}$ and $p_{\rm T,ee}$ and a fit of the DCA$_{\rm ee}$ distribution allow the total ${\rm c\overline c}$ and ${\rm b\overline b}$ cross sections to be extracted. Two different event generators, PYTHIA and POWHEG, can reproduce the shape of the two-dimensional $m_{\rm ee}$ and $p_{\rm T,ee}$ spectra, as well as the shape of the DCA$_{\rm ee}$ distribution, reasonably well. However, differences in the ${\rm c\overline c}$ and ${\rm b\overline b}$ cross sections are observed when using the generators to extrapolate to full phase space. Finally, the ratio of inclusive to decay photons is studied via the measurement of virtual direct photons in the transverse-momentum range 1 $<$ $p_{\rm T}$ $<$ 8 GeV/$c$. This is found to be unity within the statistical and systematic uncertainties and consistent with expectations from next-to-leading order perturbative quantum chromodynamic calculations.

11 data tables

Inclusive $e^+e^-$ cross section in pp collisions at $\sqrt{s}$ = 7 TeV in the ALICE acceptance as a function of $m_{\rm ee}$.

Inclusive $e^+e^-$ cross section in pp collisions at $\sqrt{s}$ = 7 TeV in the ALICE acceptance as a function of $p_{\rm T,ee}$ for $m_{\rm ee}$ < 0.14 GeV/$c^{2}$.

Inclusive $e^+e^-$ cross section in pp collisions at $\sqrt{s}$ = 7 TeV in the ALICE acceptance as a function of $\rm DCA_{ee}$ for 0.08 < $m_{\rm ee}$ < 0.14 GeV/$c^{2}$.

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Direct photon elliptic flow in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
Phys.Lett.B 789 (2019) 308-322, 2019.
Inspire Record 1672789 DOI 10.17182/hepdata.88050

The elliptic flow of inclusive and direct photons was measured at mid-rapidity in two centrality classes 0-20% and 20-40% in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV by ALICE. Photons were detected with the highly segmented electromagnetic calorimeter PHOS and via conversions in the detector material with the $e^{+}e^{-}$ pairs reconstructed in the central tracking system. The results of the two methods were combined and the direct photon elliptic flow was extracted in the transverse momentum range $0.9 < p_{\rm T} < 6.2$ GeV/$c$. A comparison to RHIC data shows a similar magnitude of the measured direct-photon elliptic flow. Hydrodynamic and transport model calculations are systematically lower than the data, but are found to be compatible.

8 data tables

Ratio V2{GAMMA,INCLUSIVE,PCM}/V2{GAMMA,INCLUSIVE,COMBINED} as function of $p_\text{T}$, collision centrality 0-20%, for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV.

Ratio V2{GAMMA,INCLUSIVE,PHOS}/V2{GAMMA,INCLUSIVE,COMBINED} as function of $p_\text{T}$, collision centrality 20-40%, for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV.

V2{GAMMA,DECAY} as function of $p_\text{T}$, collision centrality 0-20%, for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV.

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Suppression of $\Lambda(1520)$ resonance production in central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

The ALICE collaboration Acharya, Shreyasi ; Torales - Acosta, Fernando ; Adamova, Dagmar ; et al.
Phys.Rev.C 99 (2019) 024905, 2019.
Inspire Record 1672806 DOI 10.17182/hepdata.84284

The production yield of the $\Lambda(1520)$ baryon resonance is measured at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV with the ALICE detector at the LHC. The measurement is performed in the $\Lambda(1520)\rightarrow {\rm pK}^{-}$ (and charge conjugate) hadronic decay channel as a function of the transverse momentum ($p_{\rm T}$) and collision centrality. The $p_{\rm T}$-integrated production rate of $\Lambda(1520)$ relative to $\Lambda$ in central collisions is suppressed by about a factor of 2 with respect to peripheral collisions. This is the first observation of the suppression of a baryonic resonance at LHC and the first evidence of $\Lambda(1520)$ suppression in heavy-ion collisions. The measured $\Lambda(1520)/\Lambda$ ratio in central collisions is smaller than the value predicted by the statistical hadronisation model calculations. The shape of the measured $p_{\rm T}$ distribution and the centrality dependence of the suppression are reproduced by the EPOS3 Monte Carlo event generator. The measurement adds further support to the formation of a dense hadronic phase in the final stages of the evolution of the fireball created in heavy-ion collisions, lasting long enough to cause a significant reduction in the observable yield of short-lived resonances.

5 data tables

$p_{\rm T}$-differential yields of $\Lambda$(1520) (sum of particle and anti-particle states) at midrapidity in the 0-20% centrality class. The uncertainty 'syst,uncorrelated' indicates the systematic uncertainty after removing the contributions common to all centrality classes

$p_{\rm T}$-differential yields of $\Lambda$(1520) (sum of particle and anti-particle states) at midrapidity in the 20-50% centrality class. The uncertainty 'syst,uncorrelated' indicates the systematic uncertainty after removing the contributions common to all centrality classes

$p_{\rm T}$-differential yields of $\Lambda$(1520) (sum of particle and anti-particle states) at midrapidity in the 50-80% centrality class. The uncertainty 'syst,uncorrelated' indicates the systematic uncertainty after removing the contributions common to all centrality classes

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