Color superconductivity under neutron-star conditions at next-to-leading order

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 $Δ_{\rm CFL} \lesssim 140~{\rm MeV}$ at a baryon chemical potential $μ_{\rm B} = 2.6~{\rm GeV}$, even when allowing for a wide range of possible behaviors for the dependence of the gap on the chemical potential.

Figures (2)

• Figure 1: Two-dimensional prior (gray) and posterior distributions (orange, green) for the magnitude of the CFL gap $\Delta_\mathrm{CFL}^*$ and the scaling parameter $\sigma$. The orange posterior corresponds to the conservative ensemble, while the green corresponds to the symmetric one (see main text).
• Figure 2: Left: Normalized pressure as a function of baryon chemical potential. Right: Speed of sound as a function of baryon density in units of nuclear saturation density. The dotted lines in both panels denote the baryon chemical potential at $\mu_\mathrm{B}^*= 2.6$ GeV. The uncertainty bands stem from the usual renormalization-scale variation (see main text).