Interplay between inhomogeneous chiral and crystalline color-superconducting phases in the two-flavor NJL model

Abstract

We study the interplay between the chiral density wave (CDW) and the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of color-superconducting matter in two-flavor quark matter at vanishing and non-vanishing temperature $T$, quark number chemical potential $\mu$ and isospin chemical potential $\delta \mu$. The analysis is performed within the two-flavor Nambu--Jona-Lasinio (NJL) model in the chiral limit, using a three-momentum cutoff scheme. Treating the CDW wave vector $\vec{q}$ and the LOFF pair momentum $\vec{q}{}^{\prime }$ as independent variational parameters, we minimize the mean-field effective potential with respect to both amplitudes and both wave vectors, without constraining their relative orientation, and map out the $T$-$\mu$ and $\mu$-$\delta \mu$ phase diagrams for a range of diquark couplings $G_D$. Our central result is that $\vec{q}$ and $\vec{q}{}^{\prime }$ are never simultaneously nonzero: inhomogeneous chiral and diquark condensates do not coexist across the entire parameter range.

Comments: 13 pages, 9 figures, 1 table. Comments are welcome