# Effective repulsion in dense quark matter from non-perturbative gluon exchange

## TL;DR

This paper investigates the origin of vector repulsion in dense quark matter using non-perturbative gluon exchange in QCD, providing parameter ranges consistent with neutron star observations and exploring effects of quark masses and pairing gaps.

## Contribution

It connects non-perturbative gluon exchange parameters to effective quark repulsion, offering a QCD-based explanation aligned with neutron star data.

## Key findings

- Gluon masses 200-600 MeV and alpha_s=2-4 yield consistent g_V values.
- g_V decreases with density and is flavor-symmetric.
- Estimated effects of quark masses and pairing gaps are incorporated.

## 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 g_V, in terms of non-perturbative gluon exchange in QCD in the Landau gauge. Matching the energy of quark matter, g_V n_q^2 (where n_q is the number density of quarks) with the quark exchange energy calculated in QCD with a gluon propagator parametrized by a finite gluon mass m_g and a frozen coupling alpha_s, at moderate quark densities, we find that gluon masses m_g in the range 200 - 600 MeV and alpha_s = 2 - 4 lead to a g_V consistent with neutron star phenomenology. Estimating the effects of quark masses and a color-flavor-locked (CFL) pairing gap, we find that g_V 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.