Multiplicity fluctuations in a hadron gas with exact conservation laws

Abstract

The study of fluctuations of particle multiplicities in relativistic heavy-ion reactions has drawn much attention in recent years, because they have been proposed as a probe for underlying dynamics and possible formation of quark-gluon plasma. Thus, it is of uttermost importance to describe the baseline of statistical fluctuations in the hadron gas phase in a correct way. We have performed a comprehensive study of multiplicity distributions in the full ideal hadron-resonance gas in different ensembles, namely grand-canonical, canonical and microcanonical, using two different methods: asymptotic expansions and full Monte Carlo simulations. The method based on asymptotic expansion allows a quick numerical calculation of dispersions in the hadron gas with three conserved charges at primary hadron level, while the Monte-Carlo simulation is suitable to study the effect of resonance decays. Even though mean multiplicities converge to the same values, major differences in fluctuations for these ensembles persist in the thermodynamic limit, as pointed out in recent studies. We observe that this difference is ultimately related to the non-additivity of the variances in the ensembles with exact conservation of extensive quantities.

Multiplicity fluctuations in limited segments of momentum space in statistical models

“…For large system volume the main contribution to the integral (16) comes from a small region around the origin [15]. Thus we proceed by Taylor expansion of the integrant of (16) around φ j = 0.…”

“…Provided the signal survives the subsequent evolution and hadronization of the system (see also [12]). Therefore, in order to asses the discriminating power of proposed measures, for a recent review see [13], one should firstly study properties of equilibrated sources [6,14,15,16] and quantify 'baseline' (or thermal/statistical) fluctuations. Apart from being an important tool in an effort to study a possible critical behavior, the study of fluctuations within the statistical model constitutes also a further test of its validity.…”

Statistical ensembles with finite bath: A description for an event generator

“…The approximation (19) gives then a reliable description of Z Q l g around the equilibrium value Q l g = V g κ l 1 , provided V g is sufficiently large. The charge vector, Eq.…”

“…For λ → 1, we effectively approach a "sample-reject" procedure, as (for instance) used in Refs. [19,20], and…”

“…Sample and reject procedures, suitable for relativistic systems, become rapidly inefficient with large system size. However, they have the advantage of being very successful for small system sizes [19,20].…”