Functional renormalization group studies of nuclear and neutron matter

Abstract

Functional renormalization group (FRG) methods applied to calculations of isospinsymmetric and asymmetric nuclear matter as well as neutron matter are reviewed. The approach is based on a chiral Lagrangian expressed in terms of nucleon and meson degrees of freedom as appropriate for the hadronic phase of QCD with spontaneously broken chiral symmetry. Fluctuations beyond mean-field approximation are treated solving Wetterich's FRG flow equations. Nuclear thermodynamics and the nuclear liquid-gas phase transition are investigated in detail, both in symmetric matter and as a function of the proton fraction in asymmetric matter. The equations of state at zero temperature of symmetric nuclear matter and pure neutron matter are found to be in good agreement with advanced ab-initio many-body computations. Contacts with perturbative many-body approaches (in-medium chiral perturbation theory) are discussed. As an interesting test case, the density dependence of the pion mass in the medium is investigated. The question of chiral symmetry restoration in nuclear and neutron matter is addressed. A stabilization of the phase with spontaneously broken chiral symmetry is found to persist up to high baryon densities once fluctuations beyond mean-field are included. Neutron star matter including beta equilibrium is discussed under the aspect of the constraints imposed by the existence of two-solar-mass neutron stars.

Scale-invariant hidden local symmetry, topology change, and dense baryonic matter. II.

“…Following the argument given in Section 3.3, we take the results of the skyrmion crystal using sHLS Lagrangian, i.e., Skyrmion sHLS , to be equivalent to the mean-field results of bsHLS with the IDDs properly taken into account. Now from (28) of Skyrmion sHLS , we have for n > n 1/2…”

Effective repulsion in dense quark matter from nonperturbative gluon exchange

“…τ = g (8) τ = 3 2 g V , indicating an vectorisovector energy comparable to the vector-isoscalar energy for significant differences in flavor densities. It is an interesting future problem to estimate the in-medium values of g (3,8) τ as well as g V by matching with, e.g., the chiral nucleon-meson model [31].…”

Quarkyonic Matter and Neutron Stars

“…In high density quark models, there is no analog of the composite vector field to raise the zero point of the baryon energies. Recent efforts based on the Functional Renormalization Group attempt to circumvent these problems to extend a description based only on nucleons and mesons to larger density [18]. Quarkyonic Matter offers a radical alternative where both quarks and nucleons appear as quasiparticles [19,20].…”