Competition of inhomogeneous chiral phases and two-flavor color superconductivity in the NJL model

Phillip Lakaschus (Institute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany) ; Michael Buballa (Technische Universität Darmstadt, Department of Physics, Institut für Kernphysik, Theoriezentrum, Schlossgartenstr. 2, D-64289 Darmstadt, Germany; Helmholtz Research Academy Hesse for FAIR, Campus Riedberg, Max-von-Laue-Str. 12, D-60438 Frankfurt am Main, Germany) ; Dirk H. Rischke (Institute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany; Helmholtz Research Academy Hesse for FAIR, Campus Riedberg, Max-von-Laue-Str. 12, D-60438 Frankfurt am Main, Germany)

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 [M. Sadzikowski, Phys. Lett. B 553, 45 (2003); M. Sadzikowski, Phys. Lett. B 642, 238 (2006)]. 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 Ansätze 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 M. Sadzikowski [Phys. Lett. B 553, 45 (2003); 642, 238 (2006)]. 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 Ansätze lead to a qualitatively similar phase diagram, however, the coexistence phase is smaller for the RKC Ansatz.

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      "value": "We study the phase structure of the two-flavor Nambu\u2013Jona-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 [M. Sadzikowski, Phys. Lett. B 553, 45 (2003); M. Sadzikowski, Phys. Lett. B 642, 238 (2006)]. 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\u00e4tze 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 M. Sadzikowski [Phys. Lett. B 553, 45 (2003); 642, 238 (2006)]. 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\u00e4tze lead to a qualitatively similar phase diagram, however, the coexistence phase is smaller for the RKC Ansatz."
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Published on:
26 February 2021
Publisher:
APS
Published in:
Physical Review D , Volume 103 (2021)
Issue 3
DOI:
https://doi.org/10.1103/PhysRevD.103.034030
arXiv:
2012.07520
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: