Abstract. Ratios of cumulants of net proton-number fluctuations measured by the STAR Collaboration show strong deviations from a skellam distribution, which should describe thermal properties of cumulant ratios, if proton-number fluctuations are generated in equilibrium and a hadron resonance gas (HRG) model would provide a suitable description of thermodynamics at the freeze-out temperature. We present some results on 6 th order cumulants entering the calculation of the QCD equation of state at non-zero values of the baryon chemical potential (µB) and discuss limitations on the applicability of HRG thermodynamics deduced from a comparison between QCD and HRG model calculations of cumulants of conserved charge fluctuations. We show that basic features of the µB-dependence of skewness and kurtosis ratios of net protonnumber fluctuations measured by the STAR Collaboration resemble those expected from a O(µ 2 B ) QCD calculation of the corresponding net baryon-number cumulant ratios.
IntroductionA major goal in current experimental and theoretical studies of the thermodynamics of strong interaction matter is the exploration of its phase diagram. The hope is to find evidence for the existence of a second order phase transition point -the chiral critical point (CCP) -located at some value of the chemical potential, µ crit B [1]. This would be the starting point for a line of first order phase transitions at larger values of the baryon chemical potential µ B .At RHIC a dedicated research program -the beam energy scan (BES) -has been established that seeks evidence for the existence and location of the CCP. By varying the beam energy properties of matter in a regime of temperatures (T ) up to about three times the transition temperature, T pc ∼ 155 MeV [2,3], and baryon chemical potential up to µ B 3T can be probed. It is generally expected that conserved charge fluctuations, which are generated close to, or at the freeze-out temperature, T f (µ B ), can provide insight into the existence and location of the CCP. An important prerequisite for such studies, however, is to understand the thermodynamics of hot and dense matter in the crossover region and, in particular, close to freeze-out in QCD.In the following we will point out the importance of characterizing this regime in terms of QCD rather than hadron resonance gas (HRG) model calculations, which are quite successful in approximating QCD thermodynamics at sufficiently low temperatures, but definitely fail to capture important aspects of QCD thermodynamics visible in conserved charge fluctuations at temperatures T > ∼ 160 MeV.