Lattice QCD results on cumulant ratios at freeze-out

Abstract

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.

Searching for the QCD Critical Point with Net-Proton Number Fluctuations

“…We find a strong dependence of all ratios which is expected since in our refined model the nth cumulant scales as 2 , according to Eqs. (7) and (11)- (13). When our model results are compared to the STAR data [5], we find a qualitative agreement with the 2 / 1 and 4 / 2 ratios.…”

“…Recent, but still preliminary results of the STAR Colc ○ MICHA L SZYMAŃSKI, MARCUS BLUHM, KRZYSZTOF REDLICH, CHIHIRO SASAKI, 2018 laboration [3][4][5] show a non-monotonic beam energy dependence of the ratios of higher order net-proton number cumulants. However, the interpretation of the data is still unclear [6][7][8][9] and therefore effective models are needed to improve our understanding of these quantities. One of such models was developed in [10], where the impact of resonance decays on net-proton number cumulant ratios was studied.…”

Net-proton number fluctuations in the presence of the QCD critical point

“…As a result of the phenomenological implementation in Eq. (20), the scaling of C n at the CP is weakened by an additional nβ factor in the critical exponents. Moreover, the factor gσ differs from the vacuum proton mass m p in Eq.…”

“…Measurements of event-by-event fluctuations in the net-proton number [14,29,30,32], as a proxy for net-baryon number, the net-electric charge [33] and the net-kaon number [34], as a proxy for net-strangeness, have been performed in heavy-ion collisions at RHIC and LHC energies. While non-monotonic structures, in the still preliminary STAR Collaboration data on higher-order net-proton fluctuations were indeed observed [30][31][32], their unambiguous interpretation as the consequence of the presence of the CP has not been achieved yet [19,20,35,36].…”

The Compressed Baryonic Matter experiment at FAIR

“…Event-by-event fluctuations are thus one of the experimental measurements that can rather directly be compared to lattice QCD calculations [19]. Measurements of event-by-event fluctuations have been performed in order to search for the critical point or signs of a first order phase transition, however, always have to fight with the many experimental artefacts that can mimic fluctuations.…”