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 2 solar masses. We study this repulsion, parametrized by a four-fermion interaction with coupling $g_V$, in terms of nonperturbative 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 ${\alpha }_s=2–6$ 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.

• Received 7 May 2019

DOI:https://doi.org/10.1103/PhysRevD.100.034018