A model for QCD at high density and large quark mass

Abstract

We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov type of loops as the main dynamical variables representing the fermionic matter. To get a first idea of the phase structure, the model is analyzed in strong coupling expansion and using a mean field approximation. In numerical simulations, the model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the Monte Carlo ensemble with the true one. We review the main features of the model and present calculations concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the diquark susceptibility, which may be used to characterize the various phases expected at high baryonic density. We obtain in this way information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints for the behaviour of non-zero density QCD.

QCD at nonzero chemical potential: Recent progress on the lattice

“…The static limit clearly has some shortcomings, such as immediate saturation after onset at T = 0 and coincidence of m B /3 and m π /2. These limitations are already overcome by including the lowest O(κ 2 ) [29,30] and O(κ 4 ) [26,27,28,33] corrections. However, an extension to higher order is typically quite involved.…”

Controlling complex Langevin dynamics at finite density

“…This theory retains many of the features of QCD and represents an approximation to the latter in the large mass, large chemical potential region (heavy dense QCD) [37,38]. For Wilson fermions, with hopping parameter κ, it is based on a resummed hopping parameter expansion, retaining only time-like Polyakov loops, which can formally be obtained from the limit κ → 0, µ → ∞, with κe µ fixed.…”

Imaginary chemical potentials and the phase of the fermionic determinant

“…Various possibilities have been explored to circumvent the problem, like reweighting techniques [1,2,3], the use of an imaginary chemical potential either for analytic continuation [4,5,6,7,8,9,10] or for reconstructing the canonical partition function [11,12,13], Taylor expansion techniques [14,15] and non-relativistic expansions [16,17,18]. The same is not true in the case of a finite isospin density, i.e.…”