Lorenzo Ferroni

Statistical hadronization and hadronic microcanonical ensemble I

Abstract.We present a full treatment of the microcanonical ensemble of the ideal hadron-resonance gas starting from a quantum-mechanical formulation which is appropriate for the statistical model of hadronization. By using a suitable transition operator for hadronization we are able to recover the results of the statistical theory, particularly the expressions of the rates of different channels. Explicit formulae are obtained for the phase space volume or density of states of the ideal relativistic gas in quantum statistics as a cluster decomposition, generalizing previous ones in the literature. The problem of the computation of averages in the hadron gas microcanonical ensemble and the comparison with canonical ones will be the main subject of a forthcoming second paper.

The microcanonical ensemble of the ideal relativistic quantum gas

We derive the microcanonical partition function of the ideal relativistic quantum gas of spinless bosons in a quantum field framework as an expansion over fixed multiplicities. Our calculation generalizes well known expressions in the literature in that it does not introduce any large-volume approximation and it is valid at any volume. We discuss the issues concerned with the definition of the microcanonical ensemble for a free quantum field at volumes comparable with the Compton wavelength and provide a consistent prescription for calculating the microcanonical partition function that is finite at finite volume and yielding the correct thermodynamic limit. Besides an immaterial overall factor, the expression obtained turns out to be the same as in the non-relativistic multi-particle approach. This work is an introduction to the derivation of the most general expression of the microcanonical partition function fixing the maximal set of observables of the Poincaré group.

Multiplicity fluctuations in a hadron gas with exact conservation laws

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 performed a comprehensive study of multiplicity distributions in the full ideal hadron-resonance gas in different ensembles, namely grand canonical, canonical, and microcanonical, by 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 the primary hadron level, while the Monte Carlo simulation is suitable for studying 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 nonadditivity of the variances in the ensembles with exact conservation of extensive quantities.

Threshold effects in relativistic gases

Particle multiplicities and ratios in the micro-canonical ensemble of relativistic gases near production thresholds are studied. It is shown that the ratio of heavy to light particle multiplicity may be enhanced in comparison to its thermodynamic limit.

A test of statistical hadronization with exclusive rates

We studied the statistical hadronization model in its full microcanonical formulation enforcing the maximal set of conservation laws: energy-momentum, angular momentum, parity, C-parity, isospin and abelian charges. The microcanonical weight (proportional to the probability) of an asymptotic channel, has been calculated in a field theory framework in order to account for relativistic effects due to the finite cluster’s volume. A purposely devised Monte-Carlo method which allows to calculate efficiently the channel weight has been set up. A preliminary comparison of the model with measured exclusive rates in low energy ( √ s = 2.1 GeV and 2.4 GeV) e+e− collisions and with branching ratios of some heavy resonance is shown.

Fluctuations in the statistical ensembles

In this paper, we address multiplicity fluctuations of the ideal hadron-resonance gas in different ensembles: grand-canonical, canonical and microcanonical. Two different calculation methods are used: 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. This difference is ultimately related to the non-additivity of the variances in the ensembles with exact conservation of extensive quantities.

Statistical model and microcanonical ensemble

The study of the microcanonical ensemble of hadron-resonance gas is needed to probe the statistical model of hadronization and to settle some long-standing issues about its scope and meaning. We present a formulation of the microcanonical ensemble suitable for relativistic systems and numerical Monte Carlo techniques purposely developed for the multi-species hadron-resonance system.