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Color Superconductivity under Neutron-Star Conditions at Next-to-Leading Order

Andreas Geißel1,*, Tyler Gorda2,†, and Jens Braun1,3,‡

  • *Contact author: andreas.geissel@tu-darmstadt.de
  • †Contact author: gorda@itp.uni-frankfurt.de
  • ‡Contact author: jens.braun@physik.tu-darmstadt.de
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Phys. Rev. Lett. 135, 211901 – Published 17 November, 2025

DOI: https://doi.org/10.1103/54g5-43nk

Abstract

The equation of state of deconfined strongly interacting matter at high densities remains an open question, with effects from quark pairing in the preferred color-flavor-locked (CFL) ground state possibly playing an important role. Recent studies suggest that at least large pairing gaps in the CFL phase are incompatible with current astrophysical observations of neutron stars. At the same time, it has recently been shown that in two-flavor quark matter, subleading corrections from pairing effects can be much larger than would be naïvely expected, even for comparatively small gaps. In the present Letter, we compute next-to-leading-order corrections to the pressure of quark matter in the CFL phase arising from the gap and the strong coupling constant, incorporating neutron-star equilibrium conditions and current state-of-the-art perturbative QCD results. We find that the corrections are again quite sizable, and they allow us to constrain the CFL gap in the quark energy spectrum to ΔCFL≲140  MeV at a baryon chemical potential μB=2.6  GeV, even when allowing for a wide range of possible behaviors for the dependence of the gap on the chemical potential.

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Phys. Rev. Lett. 135, 211901– Published 17 November, 2025
  • Received 19 May 2025
  • Revised 10 September 2025
  • Accepted 2 October 2025
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