Locating the QCD critical endpoint through finite-size scaling

Abstract

Considering the 3d Ising universality class of the QCD critical endpoint we use a universal effective action for the description of the baryon-number density fluctuations around the critical region. Calculating the baryon-number multiplicity moments and determining their scaling with system's size we show that the critical region is very narrow in the direction of the baryon chemical potential µ and wide in the temperature direction T for T > Tc. In this context, published experimental results on local proton density-fluctuation measurements obtained by intermittency analysis in transverse momentum space in NA49 central A+A collisions at √ sNN = 17.2 GeV (A=C,Si,Pb), restrict significantly the location (µc, Tc) of the QCD critical endpoint. The main constraint is provided by the freeze-out chemical potential of the Si+Si system, which shows non-conventional baryon density fluctuations, restricting (µc, Tc) within a narrow domain, 119 MeV ≤ Tc ≤ 162 MeV, 252 MeV ≤ µc ≤ 258 MeV, of the phase diagram.

Highlights from NA61/SHINE: Proton Intermittency Analysis

“…Critical intermittency index φ 2 values are still to be properly evaluated, taking into account the magnitude of SSFM uncertainties, and the fact that F 2 (M) values for distinct M are correlated; the quality of ∆F 2 (M) power-law scaling remains to be established, and an estimation of φ 2 confidence intervals is still pending. However, one may qualitatively observe that intermittent behavior in Ar + Sc shows centrality dependence possibly due to the change of baryochemical potential and the small extent of the critical region in the phase diagram [37]. The observed effect is also sensitive to proton-purity selection and increases with the increase of the purity threshold.…”

An Alternative Approach to the Static Spherically Symmetric, Vacuum Global Solution to the Einstein Equations

“…The standard description insists on keeping the curved two surface involved (θ, φ surface) unchanged but does not describe an everywhere vacuum, static situation. We have no difficulty with this description and furthermore are fully aware of the fact that it had produced an impressive wealth of research work ( just as a sample see [9,10,11,12,13,14,15,16,17] and references therein). However, we do believe that a static vacuum at all times and places should be possible.…”

Finite-size scaling and intermittency studies in crucial measurements for the QCD critical point

“…This is clearly shown in [7], where, employing a suitable partition function (Ising-QCD), the size of the critical region along the chemical potential direction is estimated to be of the order of a few (≈ 5) MeV. As discussed in [7,8], this extreme narrowness of the critical region has significant consequences on its reachability. In particular, the beam energy scan in STAR experiment (RHIC, BES I) cannot achieve freeze-out states entering into the critical region, since in this protocol the chemical potential varies in steps of ≈ 50 MeV.…”

“…As shown in [8], employing the Ising-QCD partition function, all the freeze-out states with constant intermittency index φ 2 define an (approximately) piecewise linear line in the (ln ζ ,t)plane with ln ζ = µ b −µ c k B T c , t = T −T c T c and µ c the (unknown) critical chemical potential. This line can be determined by a linear fit in each of its branches obtaining this way a set of two linear relations (for t > 0 and t < 0 respectively) between t and ln ζ .…”

“…Finite-size scaling and intermittency in A+A collisions F. K. Diakonos Figure 2: The critical region (red shaded area) in the (ln ζ ,t) plane determined using the Ising-QCD partition function [8,10] and assuming T c ≈ 164 MeV. The colored points indicate the location of the different freezeout states measured in NA49 experiment [12] or expected to be measured in the NA61 experiment.…”