Sign of Kurtosis near the QCD Critical Point

M A Stephanov

doi:10.1103/physrevlett.107.052301

Abstract

We point out that the quartic cumulant (and kurtosis) of the order parameter fluctuations is universally negative when the critical point is approached on the crossover side of the phase separation line. As a consequence, the kurtosis of a fluctuating observable, such as, e.g., proton multiplicity, may become smaller than the value given by independent Poisson statistics. We discuss implications for the beam energy scan program at RHIC at BNL.

Highlights

We point out that the quartic cumulant of the order parameter fluctuations is universally negative when the critical point is approached on the crossover side of the phase separation line
The search for the B critical point is planned at the Relativistic Heavy Ion I Collider (RHIC) at BNL, the Super Proton Synchrotron (SPS) at CERN, the future Facility for Antiproton and
For the moments of the zero momentum mode σV ≡ d3x σ(x) in a system of volume V we find at tree level slowing down [5, 6], and the estimates of the maximum correlation length are in the range of at most 2 − 3 fm, T compared to the natural 0.5−1 fm away from the critical point

Summary

Sign of kurtosis near the QCD critical point

Stephanov Department of Physics, University of Illinois, Chicago, Illinois 60607, USA. We point out that the quartic cumulant (and kurtosis) of the order parameter fluctuations is universally negative when the critical point is approached on the crossover side of the phase separation line. The kurtosis of a fluctuating observable, such as, e.g., proton multiplicity, may become smaller than the value given by independent Poisson statistics. We discuss implications for the Beam Energy Scan program at RHIC

INTRODUCTION

KURTOSIS AND UNIVERSAL EFFECTIVE POTENTIAL

THE UNIVERSAL EQUATION OF STATE AROUND THE CRITICAL POINT

QGP critical point

EXPERIMENTAL OBSERVABLES