Abstract
We study the phase structure of the two-flavor Nambu--Jona-Lasinio (NJL) model in the chiral limit, extending a previous study of the competition of an inhomogeneous chiral phase and a two-flavor color-superconducting (2SC) phase [1, 2]. There, an analytic expression for the dispersion relations for quasiparticle excitations in the presence of both a particular inhomogeneous chiral condensate, the so-called chiral density wave (CDW), and a homogeneous 2SC condensate was found. In this work we show how to determine the dispersion relations for arbitrary modulations of the chiral condensate in the presence of a homogeneous 2SC condensate, if the dispersion relations in the absence of color superconductivity are known. In our calculations, we employ two different Ans\"atze for the inhomogeneous chiral condensate, the CDW as well as the real-kink crystal (RKC). Depending on the value of the diquark coupling we find a region of the phase diagram where the inhomogeneous chiral and the 2SC condensates coexist, confirming results of Refs. [1, 2]. Decreasing the diquark coupling favors the inhomogeneous phase over the coexistence phase. On the other hand, increasing the diquark coupling leads to a larger 2SC phase, while the inhomogeneous chiral and the coexistence phases become smaller. In agreement with previous studies the RKC Ansatz is energetically preferred over the CDW Ansatz. Both Ans\"atze lead to a qualitatively similar phase diagram, however the coexistence phase is smaller for the RKC Ansatz.
Highlights
The exploration of the QCD phase diagram is one of the major topics in contemporary high-energy nuclear physics
Depending on the value of the diquark coupling we find a region of the phase diagram where the inhomogeneous chiral and the 2SC condensates coexist, confirming results of Refs. [1, 2]
In this paper we have investigated the phase diagram of the chirally symmetric two-flavor NJL model with twoflavor color superconductivity
Summary
The exploration of the QCD phase diagram is one of the major topics in contemporary high-energy nuclear physics. Reference [20] confirmed the existence of a coexistence phase at T = 0 using the Pauli-Villars regularization scheme and extended this study to nonvanishing isospin chemical potential. We derive a method to compute the quasi-particle dispersion relations for arbitrary modulations of the chiral condensate in the presence of a homogeneous 2SC condensate, if the dispersion relations in the absence of the latter are known We subsequently apply this method to the RKC in addition to the CDW. We present the method to compute the quasi-particle dispersion relations for arbitrary modulations of the chiral condensate in the presence of a 2SC color-superconducting condensate and apply this to compute the grand potential for the CDW and the RKC Ansatz, respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
