Effective repulsion in dense quark matter from nonperturbative gluon exchange

Abstract

A moderately strong vector repulsion between quarks in dense quark matter is needed to explain how a quark core can support neutron stars heavier than two solar masses. We study this repulsion, parametrized by a four-fermion interaction with coupling gV , in terms of non-perturbative gluon exchange in QCD in the Landau gauge. Matching the energy of quark matter, gV n 2 q (where nq is the number density of quarks) with the quark exchange energy calculated in QCD with a gluon propagator parametrized by a finite gluon mass mg and a frozen coupling αs, at moderate quark densities, we find that gluon masses mg in the range 200 -600 MeV and αs = 2 -4 lead to a gV consistent with neutron star phenomenology. Estimating the effects of quark masses and a colorflavor-locked (CFL) pairing gap, we find that gV can be well approximated by a flavor-symmetric, decreasing function of density. We briefly discuss similar matchings for the isovector repulsion and for the pairing attraction.

Delineating the properties of neutron star matter in cold, dense QCD

“…[60]. The attempt to estimate g V and H from the high density regime can be found in [61]; the estimates show remarkable agreement with the estimate based on the NS physics (see below).…”

Implications of NICER for neutron star matter: the QHC21 equation of state

“…The coupling constant G and the ultraviolet cutoff Λ of the NJL model, specified in Baym et al (2018), are the relevant parameters describing chiral symmetry breaking. In addition, we include the short range density-density repulsion in QCD (Kunihiro 1991;Song et al 2019), of strength measured by a coupling constant g V , and an attraction between quarks, proportional to a coupling H, which governs the color superconductivity pairing gap. 4 The quark equations of state, parametrized by given (g V , H), and the nuclear equation of state are first interpolated in a given range (n L , n U ) by using fifth order interpolating polynomials in µ B , for which the coefficients are uniquely fixed by six boundary conditions.…”

Nonperturbative quark matter equations of state with vector interactions

“…Vector interactions are expected to add repulsion [61]. This can be seen from classical models of the nucleon-nucleon interaction, from phenomenological models allowing for hyperons in the neutron star core, see e.g.…”