Correcting event-by-event fluctuations in heavy-ion collisions for exact global conservation laws with the generalized subensemble acceptance method

Abstract

We introduce the subensemble acceptance method 2.0 (SAM-2.0) -a procedure to correct cumulants of a random number distribution inside a subsystem for the effect of exact global conservation of a conserved quantity to which this number is correlated, with applications to measurements of event-by-event fluctuations in heavy-ion collisions. The method expresses the corrected cumulants in terms of the cumulants inside and outside the subsystem that are not subject to the exact conservation. The derivation assumes that all probability distributions associated with the cumulants are peaked at the mean values but are otherwise of arbitrary shape. The formalism reduces to the original SAM [1] when applied to a coordinate space subvolume of a uniform thermal system. As the new method is restricted neither to the uniform systems nor to the coordinate space, it is applicable to fluctuations measured in heavy-ion collisions at various collision energies in different momentum space acceptances. The SAM-2.0 thus brings the experimental measurements and theoretical calculations of event-by-event fluctuations closer together, as the latter are typically performed without the account of exact global conservation.

Proton number cumulants and correlation functions in Au-Au collisions at $\sqrt{s_{\rm NN}} = 7.7-200$ GeV from hydrodynamics

“…We shall correct the cumulants for the baryon number conservation via the recently developed method of Ref. [40] afterwards. We further assume that the dynamical correlation length ξ that defines the range of correlations is smaller than any other relevant scale, such that one can assume ξ → 0.…”

“…[36]). For this purpose we use a recently developed subensemble acceptance method 2.0 (SAM-2.0) [40], which allows one to perform a correction of cumulants of accepted protons for the effect of exact global baryon conservation analytically. As a result, we are able to calculate cumulants of (anti)proton number distribution emerging from hydrodynamics to high orders without the need to generate large numbers of Monte Carlo events.…”

Conservation laws in a novel hybrid approach

“…Note that, in contrast to e.g. [14,15], the herein presented results correspond to global and on average conservation of E, B, and Q. To emphasize the importance of a well matching equation of state underlying the creation of the hydrodynamic freezeout hypersurface, the SMASH-vHLLE-hybrid is applied in two setups utilizing (i) the unmodified equation of state and (ii) the improved equation of state of the SMASH hadron resonance gas.…”

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.…”

“…To address these limitations, an extended formalism -SAM-2.0 -was recently formulated in Ref. [36]. The SAM-2.0 allows one to study the effects of exact conservation of charge 𝐵 on cumulants of a non-conserved quantity 𝑝 correlated to 𝐵, in arbitrary acceptance.…”