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Pion condensation versus color superconductivity, speed of sound, and charge neutrality effects in the quark-meson diquark model

Jens O. Andersen* and Mathias P. Nødtvedt†

  • *Contact author: jens.andersen@ntnu.no
  • †Contact author: mathias.p.nodtvedt@ntnu.no
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Phys. Rev. D 113, 014026 – Published 23 January, 2026

DOI: https://doi.org/10.1103/vwbc-n1rt

Abstract

We employ the two-flavor quark-meson diquark model as a low-energy model for QCD at nonzero quark and isospin chemical potentials μ and μI, and at zero temperature. We map out the phase diagram in the μ–μI plane, which has four phases: a vacuum phase, a phase with condensed charged pions/Cooper pairs of u and d¯ quarks, a normal quark matter (NQM) phase, and a color superconducting phase (2SC phase). The global symmetry breaking SU(3)c→SU(2)c in the 2SC phase gives rise to a number of Nambu-Goldstone bosons. We classify them and briefly discuss their properties. We calculate the speed of sound cs in the two special cases, finite μI and μ=0, and finite μ and μI=0. In both cases, the speed of sound exhibits a maximum and approaches the conformal limit from above as the density increases. For nonzero isospin μI, this behavior is in agreement with the speed of sound obtained from lattice simulations. In the 2SC phase, the behavior is qualitatively the same if we impose local charge neutrality. Finally, we discuss the possibility of having a mixed phase of negatively charged NQM and positively charged 2SC matter with global color charge neutrality imposed on the latter.

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Phys. Rev. D 113, 014026– Published 23 January, 2026
  • Received 28 March 2025
  • Accepted 28 August 2025
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