Cumulants of multiple conserved charges and global conservation laws
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Springer
Received: July 17, 2020 Accepted: September 7, 2020 Published: October 14, 2020
Volodymyr Vovchenko,a Roman V. Poberezhnyukb,c and Volker Kocha a
Nuclear Science Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, U.S.A. b Bogolyubov Institute for Theoretical Physics, Metrolohichna St. 14-b, 03143 Kyiv, Ukraine c Frankfurt Institute for Advanced Studies, Giersch Science Center, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main, Germany
E-mail: [email protected], [email protected], [email protected] 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. Keywords: Heavy Ion Phenomenology, QCD Phenomenology ArXiv ePrint: 2007.03850
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)089
JHEP10(2020)089
Cumulants of multiple conserved charges and global conservation laws
Contents 1 Introduction
1 3 3 4 6 7 8 10 10 10 12 12 14 15 17
3 Application to the hadron resonance gas model 3.1 HRG model setup 3.2 Second order cumulants of conserved charges 3.3 Third order cumulants of conserved charges 3.4 Fourth order cumulants of conserved charges 3.5 Off-diagonal cumulants involving non-conserved quantities 3.6 Net-proton and net-Λ fluctuations
18 18 19 19 21 22 25
4 Discussion and conclusions
29
A Evaluation of the higher-order cumulants
32
B Deriving QCD cumulants from the general expressions
33
1
Introduction
Fluctuations and correlations of conserved charges in statistical systems carry rich information on intrinsic properties of matter. These quantities play a central role in studies of the QCD phase diagram, both in first-principle lattice QCD simulations [2, 3] and in heavy-ion collision experiments [4]. Event-by-event fluctuations of different quantities are used in the search of the QCD critical point [5–7].
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