A doubly critical point in the color-superconducting regime of the RG-consistent NJL model

Abstract

Nambu--Jona-Lasinio (NJL) models of color-superconducting quark matter suffer from cutoff artifacts once temperature or quark chemical potential become comparable to the model cutoff. These artifacts can be removed employing a renormalization-group (RG) consistent regularization scheme. In this article we perform a systematic study of neutral beta-equilibrated quark matter within the three-flavor NJL model with RG consistent regularization. Varying the coupling constant in the scalar diquark channel, we map out the phase diagram in the plane of chemical potential and temperature, and identify the gapless domains. We particularly focus on the melting pattern of the color-flavor locked (CFL) phase. At larger couplings the CFL phase melts through a so-called $d$SC phase, as expected from leading-order Ginzburg--Landau analyses. Lowering the coupling, the phase structure becomes markedly richer: While at large densities the CFL phase still melts through a $dSC$ phase, we find a $uSC$ phase at lower chemical potential. These phases, $uSC$ and $dSC$ meet at a doubly critical point whose existence had been anticipated long ago but was never demonstrated explicitly in a model.

Comments: 13 pages, 3 figures. Contributed proceeding for the 2nd Workshop on Matter, Astrophysics, Gravitation, Ions and Cosmology (MAGIC 2025), Buenos Aires, September 2025. Comments are welcome