Neutron Star Observations Challenge a Large Colour-Superconducting Gap in Dense Quark Matter

Abstract

At asymptotically high density, quantum chromodynamics (QCD) predicts that quark matter becomes a colour superconductor in the colour-flavour-locked (CFL) phase, yet, away from the asymptotic regime, the magnitude of the pairing gap is uncertain. Here we combine multi-messenger neutron star observations with perturbative QCD and chiral effective field theory inputs in a Bayesian inference built on a flexible Gaussian-process--neural-network representation of the equation of state (EOS). By matching the EOS at a baryon chemical potential of 2.6 GeV to the perturbative QCD prediction supplemented by the next-to-leading-order CFL contribution, we infer a gap of $\Delta^{*}_{\rm CFL}=34^{+32}_{-28}$ MeV and a 95% credible upper limit of about 66 MeV, which is a factor of two tighter than previous bounds and at the lower edge of most microscopic model predictions. We further place the first data-driven constraint on the unknown high-order constant of the perturbative QCD pressure, i.e., $c_0=-21^{+9}_{-8}$. Our results indicate that colour-superconducting pairing makes only a subdominant contribution to dense matter pressure, tightening the connection between neutron star data and the QCD phase diagram.