Abstract
We analyze the behavior of cumulants of conserved charges in a subvolume of a thermal system with exact global conservation laws by extending a recently developed subensemble acceptance method (SAM) [1] to multiple conserved charges. Explicit expressions for all diagonal and off-diagonal cumulants up to sixth order that relate them to the grand canonical susceptibilities are obtained. The derivation is presented for an arbitrary equation of state with an arbitrary number of different conserved charges. The global conservation effects cancel out in any ratio of two second order cumulants, in any ratio of two third order cumulants, as well as in a ratio of strongly intensive measures Σ and ∆ involving any two conserved charges, making all these quantities particularly suitable for theory-to-experiment comparisons in heavy-ion collisions. We also show that the same cancellation occurs in correlators of a conserved charge, like the electric charge, with any non-conserved quantity such as net proton or net kaon number. The main results of the SAM are illustrated in the framework of the hadron resonance gas model. We also elucidate how net-proton and net-Λ fluctuations are affected by conservation of electric charge and strangeness in addition to baryon number.
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V. Vovchenko, O. Savchuk, R.V. Poberezhnyuk, M.I. Gorenstein and V. Koch, Connecting fluctuation measurements in heavy-ion collisions with the grand-canonical susceptibilities, arXiv:2003.13905 [INSPIRE].
A. Bazavov et al., The QCD Equation of State to \( \mathcal{O}\left({\mu}_B^6\right) \) from Lattice QCD, Phys. Rev. D 95 (2017) 054504 [arXiv:1701.04325] [INSPIRE].
S. Borsányi et al., Higher order fluctuations and correlations of conserved charges from lattice QCD, JHEP 10 (2018) 205 [arXiv:1805.04445] [INSPIRE].
A. Bzdak, S. Esumi, V. Koch, J. Liao, M. Stephanov and N. Xu, Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan, Phys. Rept. 853 (2020) 1 [arXiv:1906.00936] [INSPIRE].
M.A. Stephanov, K. Rajagopal and E.V. Shuryak, Signatures of the tricritical point in QCD, Phys. Rev. Lett. 81 (1998) 4816 [hep-ph/9806219] [INSPIRE].
M.A. Stephanov, K. Rajagopal and E.V. Shuryak, Event-by-event fluctuations in heavy ion collisions and the QCD critical point, Phys. Rev. D 60 (1999) 114028 [hep-ph/9903292] [INSPIRE].
M. Gazdzicki and P. Seyboth, Search for Critical Behaviour of Strongly Interacting Matter at the CERN Super Proton Synchrotron, Acta Phys. Polon. B 47 (2016) 1201 [arXiv:1506.08141] [INSPIRE].
V. Koch, A. Majumder and J. Randrup, Baryon-strangeness correlations: A diagnostic of strongly interacting matter, Phys. Rev. Lett. 95 (2005) 182301 [nucl-th/0505052] [INSPIRE].
NA49 collaboration, Energy Dependence of Multiplicity Fluctuations in Heavy Ion Collisions at the CERN SPS, Phys. Rev. C 78 (2008) 034914 [arXiv:0712.3216] [INSPIRE].
STAR collaboration, Collision Energy Dependence of Moments of Net-Kaon Multiplicity Distributions at RHIC, Phys. Lett. B 785 (2018) 551 [arXiv:1709.00773] [INSPIRE].
ALICE collaboration, Global baryon number conservation encoded in net-proton fluctuations measured in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 2.76 TeV, Phys. Lett. B 807 (2020) 135564 [arXiv:1910.14396] [INSPIRE].
STAR collaboration, Beam energy dependence of net-Λ fluctuations measured by the STAR experiment at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C 102 (2020) 024903 [arXiv:2001.06419] [INSPIRE].
T. Anticic et al., Phase-space dependence of particle-ratio fluctuations in Pb + Pb collisions from 20 A to 158 A GeV beam energy, Phys. Rev. C 89 (2014) 054902 [arXiv:1310.3428] [INSPIRE].
NA49 collaboration, Measurement of event-by-event transverse momentum and multiplicity fluctuations using strongly intensive measures ∆[PT , N ] and Σ[PT , N ] in nucleus-nucleus collisions at the CERN Super Proton Synchrotron, Phys. Rev. C 92 (2015) 044905 [arXiv:1509.04633] [INSPIRE].
STAR collaboration, Collision-energy dependence of second-order off-diagonal and diagonal cumulants of net-charge, net-proton, and net-kaon multiplicity distributions in Au + Au collisions, Phys. Rev. C 100 (2019) 014902 [arXiv:1903.05370] [INSPIRE].
STAR collaboration, Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC, Phys. Rev. Lett. 112 (2014) 032302 [arXiv:1309.5681] [INSPIRE].
STAR collaboration, Beam energy dependence of moments of the net-charge multiplicity distributions in Au+Au collisions at RHIC, Phys. Rev. Lett. 113 (2014) 092301 [arXiv:1402.1558] [INSPIRE].
STAR collaboration, Net-proton number fluctuations and the Quantum Chromodynamics critical point, arXiv:2001.02852 [INSPIRE].
HADES collaboration, Proton number fluctuations in \( \sqrt{s_{NN}} \) = 2.4 GeV Au+Au collisions studied with HADES, Phys. Rev. C 102 (2020) 024914 [arXiv:2002.08701] [INSPIRE].
M. Kitazawa and M. Asakawa, Revealing baryon number fluctuations from proton number fluctuations in relativistic heavy ion collisions, Phys. Rev. C 85 (2012) 021901 [arXiv:1107.2755] [INSPIRE].
M. Kitazawa and M. Asakawa, Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions, Phys. Rev. C 86 (2012) 024904 [Erratum ibid. 86 (2012) 069902] [arXiv:1205.3292] [INSPIRE].
M.I. Gorenstein and M. Gazdzicki, Strongly Intensive Quantities, Phys. Rev. C 84 (2011) 014904 [arXiv:1101.4865] [INSPIRE].
V. Skokov, B. Friman and K. Redlich, Volume Fluctuations and Higher Order Cumulants of the Net Baryon Number, Phys. Rev. C 88 (2013) 034911 [arXiv:1205.4756] [INSPIRE].
F. Karsch and K. Redlich, Probing freeze-out conditions in heavy ion collisions with moments of charge fluctuations, Phys. Lett. B 695 (2011) 136 [arXiv:1007.2581] [INSPIRE].
A. Bazavov et al., Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics, Phys. Rev. Lett. 109 (2012) 192302 [arXiv:1208.1220] [INSPIRE].
S. Borsányi, Z. Fodor, S.D. Katz, S. Krieg, C. Ratti and K.K. Szabo, Freeze-out parameters from electric charge and baryon number fluctuations: is there consistency?, Phys. Rev. Lett. 113 (2014) 052301 [arXiv:1403.4576] [INSPIRE].
P. Alba et al., Freeze-out conditions from net-proton and net-charge fluctuations at RHIC, Phys. Lett. B 738 (2014) 305 [arXiv:1403.4903] [INSPIRE].
K. Fukushima, Hadron resonance gas and mean-field nuclear matter for baryon number fluctuations, Phys. Rev. C 91 (2015) 044910 [arXiv:1409.0698] [INSPIRE].
M. Albright, J. Kapusta and C. Young, Baryon Number Fluctuations from a Crossover Equation of State Compared to Heavy-Ion Collision Measurements in the Beam Energy Range \( \sqrt{s_{NN}} \) = 7.7 to 200 GeV, Phys. Rev. C 92 (2015) 044904 [arXiv:1506.03408] [INSPIRE].
W.-j. Fu, J.M. Pawlowski, F. Rennecke and B.-J. Schaefer, Baryon number fluctuations at finite temperature and density, Phys. Rev. D 94 (2016) 116020 [arXiv:1608.04302] [INSPIRE].
G.A. Almasi, B. Friman and K. Redlich, Baryon number fluctuations in chiral effective models and their phenomenological implications, Phys. Rev. D 96 (2017) 014027 [arXiv:1703.05947] [INSPIRE].
V. Vovchenko, L. Jiang, M.I. Gorenstein and H. Stoecker, Critical point of nuclear matter and beam energy dependence of net proton number fluctuations, Phys. Rev. C 98 (2018) 024910 [arXiv:1711.07260] [INSPIRE].
R. Bellwied et al., Off-diagonal correlators of conserved charges from lattice QCD and how to relate them to experiment, Phys. Rev. D 101 (2020) 034506 [arXiv:1910.14592] [INSPIRE].
V. Koch, Hadronic Fluctuations and Correlations, in Relativistic Heavy Ion Physics, R. Stock, ed., pp. 626–652 (2010), DOI [arXiv:0810.2520] [INSPIRE].
M. Bleicher, S. Jeon and V. Koch, Event-by-event fluctuations of the charged particle ratio from nonequilibrium transport theory, Phys. Rev. C 62 (2000) 061902 [hep-ph/0006201] [INSPIRE].
V.V. Begun, M. Gazdzicki, M.I. Gorenstein, M. Hauer, V.P. Konchakovski and B. Lungwitz, Multiplicity fluctuations in relativistic nuclear collisions: Statistical model versus experimental data, Phys. Rev. C 76 (2007) 024902 [nucl-th/0611075] [INSPIRE].
A. Bzdak, V. Koch and V. Skokov, Baryon number conservation and the cumulants of the net proton distribution, Phys. Rev. C 87 (2013) 014901 [arXiv:1203.4529] [INSPIRE].
P. Braun-Munzinger, A. Rustamov and J. Stachel, Bridging the gap between event-by-event fluctuation measurements and theory predictions in relativistic nuclear collisions, Nucl. Phys. A 960 (2017) 114 [arXiv:1612.00702] [INSPIRE].
R. Rogly, G. Giacalone and J.-Y. Ollitrault, Isolating dynamical net-charge fluctuations, Phys. Rev. C 99 (2019) 034902 [arXiv:1809.00648] [INSPIRE].
O. Savchuk, R.V. Poberezhnyuk, V. Vovchenko and M.I. Gorenstein, Binomial acceptance corrections for particle number distributions in high-energy reactions, Phys. Rev. C 101 (2020) 024917 [arXiv:1911.03426] [INSPIRE].
M. Barej and A. Bzdak, Factorial cumulants from global baryon number conservation, arXiv:2006.02836 [INSPIRE].
P. Braun-Munzinger, B. Friman, K. Redlich, A. Rustamov and J. Stachel, Relativistic nuclear collisions: Establishing the non-critical baseline for fluctuation measurements, arXiv:2007.02463 [INSPIRE].
R.V. Poberezhnyuk et al., Critical point fluctuations: Finite size and global charge conservation effects, Phys. Rev. C 102 (2020) 024908 [arXiv:2004.14358] [INSPIRE].
S. Borsányi, Z. Fodor, S.D. Katz, S. Krieg, C. Ratti and K. Szabo, Fluctuations of conserved charges at finite temperature from lattice QCD, JHEP 01 (2012) 138 [arXiv:1112.4416] [INSPIRE].
HotQCD collaboration, Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model, Phys. Rev. D 86 (2012) 034509 [arXiv:1203.0784] [INSPIRE].
K. Huang, Statistical Mechanics. John Wiley and Sons, (2000).
https://github.com/vlvovch/SAM, (accessed 07 July 2020).
A. Bzdak and V. Koch, Rapidity dependence of proton cumulants and correlation functions, Phys. Rev. C 96 (2017) 054905 [arXiv:1707.02640] [INSPIRE].
M. Gazdzicki, M.I. Gorenstein and M. Mackowiak-Pawlowska, Normalization of strongly intensive quantities, Phys. Rev. C 88 (2013) 024907 [arXiv:1303.0871] [INSPIRE].
R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl. 3 (1965) 147 [INSPIRE].
J. Letessier and J. Rafelski, Hadron production and phase changes in relativistic heavy ion collisions, Eur. Phys. J. A 35 (2008) 221 [nucl-th/0504028] [INSPIRE].
F. Becattini, An Introduction to the Statistical Hadronization Model, in International School on Quark-Gluon Plasma and Heavy Ion Collisions: past, present, future, Villa Gualino, Torino, Italy, December 8–14, 2008, arXiv:0901.3643 [INSPIRE].
A. Andronic, P. Braun-Munzinger, K. Redlich and J. Stachel, Decoding the phase structure of QCD via particle production at high energy, Nature 561 (2018) 321 [arXiv:1710.09425] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
V. Vovchenko and H. Stoecker, Thermal-FIST: A package for heavy-ion collisions and hadronic equation of state, Comput. Phys. Commun. 244 (2019) 295 [arXiv:1901.05249] [INSPIRE].
STAR collaboration, Bulk Properties of the Medium Produced in Relativistic Heavy-Ion Collisions from the Beam Energy Scan Program, Phys. Rev. C 96 (2017) 044904 [arXiv:1701.07065] [INSPIRE].
J. Cleymans, H. Oeschler, K. Redlich and S. Wheaton, Comparison of chemical freeze-out criteria in heavy-ion collisions, Phys. Rev. C 73 (2006) 034905 [hep-ph/0511094] [INSPIRE].
V. Vovchenko, V.V. Begun and M.I. Gorenstein, Hadron multiplicities and chemical freeze-out conditions in proton-proton and nucleus-nucleus collisions, Phys. Rev. C 93 (2016) 064906 [arXiv:1512.08025] [INSPIRE].
F. Becattini and L. Ferroni, Statistical hadronization and hadronic microcanonical ensemble. 2., Eur. Phys. J. C 38 (2004) 225 [Erratum ibid. 66 (2010) 341] [hep-ph/0407117] [INSPIRE].
V. Vovchenko, M.I. Gorenstein and H. Stoecker, Monte Carlo approach to the excluded-volume hadron resonance gas in grand canonical and canonical ensembles, Phys. Rev. C 98 (2018) 064909 [arXiv:1805.01402] [INSPIRE].
M. Asakawa, S. Ejiri and M. Kitazawa, Third moments of conserved charges as probes of QCD phase structure, Phys. Rev. Lett. 103 (2009) 262301 [arXiv:0904.2089] [INSPIRE].
V.V. Begun, M.I. Gorenstein, M. Hauer, V.P. Konchakovski and O.S. Zozulya, Multiplicity Fluctuations in Hadron-Resonance Gas, Phys. Rev. C 74 (2006) 044903 [nucl-th/0606036] [INSPIRE].
E. Sangaline, Strongly Intensive Cumulants: Fluctuation Measures for Systems With Incompletely Constrained Volumes, arXiv:1505.00261 [INSPIRE].
P. Castorina and H. Satz, Causality Constraints on Hadron Production In High Energy Collisions, Int. J. Mod. Phys. E 23 (2014) 1450019 [arXiv:1310.6932] [INSPIRE].
V. Vovchenko, B. Dönigus and H. Stoecker, Multiplicity dependence of light nuclei production at LHC energies in the canonical statistical model, Phys. Lett. B 785 (2018) 171 [arXiv:1808.05245] [INSPIRE].
D. Oliinychenko and V. Koch, Microcanonical Particlization with Local Conservation Laws, Phys. Rev. Lett. 123 (2019) 182302 [arXiv:1902.09775] [INSPIRE].
C.A. Pruneau, Role of baryon number conservation in measurements of fluctuations, Phys. Rev. C 100 (2019) 034905 [arXiv:1903.04591] [INSPIRE].
V. Vovchenko, B. Dönigus and H. Stoecker, Canonical statistical model analysis of p-p, p -Pb, and Pb-Pb collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. C 100 (2019) 054906 [arXiv:1906.03145] [INSPIRE].
P. Braun-Munzinger, A. Rustamov and J. Stachel, The role of the local conservation laws in fluctuations of conserved charges, arXiv:1907.03032 [INSPIRE].
D. Oliinychenko, S. Shi and V. Koch, Effects of local event-by-event conservation laws in ultrarelativistic heavy-ion collisions at particlization, Phys. Rev. C 102 (2020) 034904 [arXiv:2001.08176] [INSPIRE].
I. Altsybeev, Higher-order cumulants of net-charge distributions from local charge conservation, arXiv:2002.11398 [INSPIRE].
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Vovchenko, V., Poberezhnyuk, R.V. & Koch, V. Cumulants of multiple conserved charges and global conservation laws. J. High Energ. Phys. 2020, 89 (2020). https://doi.org/10.1007/JHEP10(2020)089
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DOI: https://doi.org/10.1007/JHEP10(2020)089