Thermodynamic phases and mesonic fluctuations in a chiral nucleon-meson model

Abstract

Studies of the QCD phase diagram must properly include nucleonic degrees of freedom and their thermodynamics in the range of baryon chemical potentials characteristic of nuclear matter. A useful framework for incorporating relevant nuclear physics constraints in this context is a chiral nucleon-meson effective Lagrangian. In the present paper, such a chiral nucleon-meson model is extended with systematic inclusion of mesonic fluctuations using the functional renormalization group approach. The resulting description of the nuclear liquid-gas phase transition shows a remarkable agreement with three-loop calculations based on in-medium chiral effective field theory. No signs of a chiral first-order phase transition and its critical endpoint are found in the region of applicability of the model, i.e. up to twice the density of normal nuclear matter and at temperatures T 100 MeV. Fluctuations close to the critical point of the first-order liquid-gas transition are also examined with a detailed study of chiral and baryon number susceptibilities.

Functional renormalization group studies of nuclear and neutron matter

“…This is the mean-field approximation, applied to the ChNM model in the present context [48,44,46]. Only rotationally invariant solutions are considered, so the spatial components of the vector fields vanish.…”

“…Nonetheless, as explained in Ref. [44], the input parameters need to be readjusted in order to reproduce the correct nuclear saturation density, because the dependence of the minimum of the effective potential U k on the chemical potentials is influenced by the fluctuations. Again, the coupling G τ is fixed to reproduce a symmetry energy of E sym = 32 MeV.…”

“…For isospin-symmetric matter, ChEFT calculations of the in-medium chiral condensate have been performed to three-loop order by directly computing the dependence of F(n, T ) on the pion mass [91,143], while σ/f π as function of baryon density and temperature has been calculated in Refs. [48,44] using the ChNM model. In mean-field approximation [48], chiral symmetry gets restored in a firstorder transition at a density as low as n 1.6 n 0 .…”

“…In mean-field approximation [48], chiral symmetry gets restored in a firstorder transition at a density as low as n 1.6 n 0 . Once fluctuations are taken into account [44], the chiral restoration transition is shifted to chemical potentials well beyond µ ∼ 1 GeV or densities exceeding 3 n 0 . Similar trends are found in ChEFT calculations of the in-medium chiral condensate.…”

Chiral mirror-baryon-meson model and nuclear matter beyond mean-field approximation

“…Nevertheless, using a phenomenological parametrization of the effective action at zero-temperature and density as the input, it has recently received renewed interest. This is because it then proved to be very useful for the investigation of nuclear and neutron matter at small temperatures both in the mean-field approximation [13] and beyond [14][15][16].…”