Cumulants of multiple conserved charges and global conservation laws

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.

Non-equilibrium cumulants within model A near the QCD critical point

“…In order to quantitatively describe the experimental observed cumulants of net proton multiplicities, more sophisticated and realistic dynamical modeling are required from the theoretical side [56,57]. Besides, a number of effects play their role, including the subject of the proper equation of state [58][59][60], of the unknown parameters of the Ising-to-QCD mapping [61], of the critical transport coefficients [62][63][64][65], of the finite size, finite size scaling and global charge conservation in the vicinity of a CP [66][67][68][69][70], of the non-critical baseline for the cumulants of net-proton number fluctuations [71], and of the nonuniform temperature/chemical potential effects [72]. In addition, further connections between the criticality and the experimental observables have been established through theoretical efforts [73][74][75][76][77][78].…”

Cumulants: It's More Than You Think

“…Moreover, experiments measure not baryon number cumulants, as used in our model, but proton number cumulants. Effects due to baryon number conservation may also be important [28,29].…”

Phenomenological developments for event-by-event fluctuations of conserved charges

“…The subensemble acceptance method (SAM) has been developed recently [33][34][35][36] to perform a correction on the cumulants for exact global conservation laws. Although this topic has been studied before in the framework of ideal gas of particles and antiparticles [37,38], the main feature of the SAM is that it is model-independent and has no assumptions about the underlying equation of state.…”

“…However, the estimates based on the HRG model presented in Ref. [35] indicate that, at least for the kurtosis, this effect is small in heavy-ion collisions.…”

“…In Ref. [35] the SAM has been extended to the case of multiple exactly conserved charges, as appropriate for baryon, electric charge and strangeness in heavy-ion collisions. In this case one can express the joint 𝐵𝑄𝑆 cumulants inside the subsystem in terms of the fraction 𝛼 and the grandcanonical mixed susceptibilities 𝜒 𝐵𝑄𝑆 𝑙𝑚𝑛 .…”