Hadronic fluctuations at the QCD phase transition

S Ejiri,F Karsch,K Redlich

doi:10.1016/j.physletb.2005.11.083

Abstract

We discuss the properties of hadronic fluctuations, i.e., fluctuations of net quark and isospin numbers as well as electric charge, in the vicinity of the QCD transition in isospin-symmetric matter at vanishing quark chemical potential. We analyse second- and fourth-order cumulants of these fluctuations and argue that the ratio of quartic and quadratic cumulants reflects the relevant degrees of freedom that carry the quark number, isospin or charge, respectively. In the hadronic phase we find that an enhancement of charge fluctuations arises from contributions of doubly charged hadrons to the thermodynamics. The rapid suppression of fluctuations seen in the high-temperature phase suggests that in the QGP, net quark number and electric charge are predominantly carried by quasi-particles, with the quantum numbers of quarks.

Highlights

In a medium of strongly interacting elementary particles, described by equilibrium thermodynamics of Quantum Chromodynamics (QCD), the transition between the low-temperature hadronic and high-temperature quark– gluon phase occurs in a small temperature interval and leads to a rapid change in entropy and energy density
Deviations from criticality are controlled by a generalized version of the reduced temperature variable, which takes into account that the temperaturelike direction at non-vanishing quark chemical potential in general will be a mixture of the couplings tand μq/T
We have discussed some generic features of quark number, isospin and charge fluctuations in 2-flavour QCD

Summary

Introduction

In a medium of strongly interacting elementary particles, described by equilibrium thermodynamics of Quantum Chromodynamics (QCD), the transition between the low-temperature hadronic and high-temperature quark– gluon phase occurs in a small temperature interval and leads to a rapid change in entropy and energy density. Recent lattice studies of 2-flavour QCD at non-zero quark (μq) and isospin (μI) chemical potential [4,5,6,7] have sustain that higher-order derivatives of the QCD partition function (generalized susceptibilities), show even more pronounced variations with temperature in the vicinity of the QCD transition temperature. Quark number as well as charge and isospin fluctuations are obtained from the grand canonical partition function of QCD through appropriate combinations of derivatives with respect to quark chemical potentials. The fluctuations of quark number, isospin and charge as well as expectation values of higher-moments of these observables can be obtained from These susceptibilities, evaluated for vanishing quark chemical potentials, define the coefficients of a Taylor series for the pressure expanded simultaneously in terms of μu and μd. We briefly discuss the generic structure of second- and fourth-order cumulants expected to be found in the chiral limit

Chiral symmetry restoration and hadronic fluctuations

Hadronic fluctuations in a thermal medium

Fluctuations in hadronic matter

Fluctuations in the QGP

Findings

Conclusions