Ising-QCD phenomenology close to the critical point

Abstract

We employ the recently introduced Ising-QCD partition function (N. G. Antoniou et al., Phys. Rev. D 97, 034015 (2018)) to explore in detail the behaviour of the moments of the baryon-number, within the critical region around the critical endpoint. Our analysis is based on the relation of finite-size scaling in real space with intermittency in transverse momentum space. It demonstrates in practice the recent observation (N. G. Antoniou et al., Phys. Rev. D 97, 034015 (2018)) that combined measurements of the intermittency index φ2 and the freeze-out parameters µ b (baryochemical potential), T (temperature), provide us with a powerful tool to detect the critical point. We also show that the finite-size scaling (FSS) region, as a part of the critical region, is very narrow in both the chemical potential and the temperature direction, even for light nuclei. Furthermore, using published experimental results for (µ b , T, φ2) in A+A collisions at √ sNN = 17.2 GeV (NA49 experiment, CERN-SPS), we are able to make a set of predictions for the freeze-out states of Ar + Sc and Xe + La collisions at the same energy in the NA61/SHINE experiment (CERN-SPS). In particular, we find that the Ar + Sc system freezes out outside the FSS region but very close to its boundary, a property which may leave characteristic traces in intermittency analysis.

Finite-size scaling, Intermittency and the QCD critical point

“…As a consequence we predict strong intermittency effect in peripheral Ar+Sc collisions at √ s ≈ 17 GeV (NA61/SHINE experiment) [10].…”

“…T c | the infinite system correlation length and V the volume of the finite system. For medium size nuclei (20 < A < 50) we find 3 MeV < ∆T < 5 MeV for the extension of the FSS region along the temperature axis [10].…”

“…We define as critical region the cut between the two sets. According to this definition the critical-region size along µ is 3 MeV ≤ ∆µ ≤ 11MeV for all values of α [10]. This results disfavours the search for the critical point using ion collisions with fixed size nuclei colliding with energy varying in large steps [11].…”

Overview of Results from NA61/SHINE: Uncovering Critical Structures

“…2 (b)). The latter statement is particularly valid in view of theoretical arguments suggesting the narrowness of the critical region [17].…”

Charting the scaling region of the Ising universality class in two and three dimensions

“…In particular it is widely expected that the hadronic phase (low T, low μ) should be separated from the quark-gluon plasma phase (high T, high μ) by a line of first order transitions with a critical end point at finite critical values of T and μ (see Fig. 5) which should again belong to the Ising universality class [58][59][60][61][62][63][64][65].…”