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Abstract

We study the S-1(0) proton pairing gap in beta-equilibrated neutron star
matter within the framework of chiral effective field theory. We focus
on the role of three-body forces, which strongly modify the effective
proton-proton spin-singlet interaction in dense matter. We find that
three-body forces generically reduce both the size of the pairing gap
and the maximum density at which proton pairing may occur. The pairing
gap is computed within Bardeen-Cooper-Schrieffer theory using a
single-particle dispersion relation calculated up to second order in
perturbation theory. Model uncertainties are estimated by varying the
nuclear potential (its order in the chiral expansion and high-momentum
cutoff) and the choice of single-particle spectrum in the gap equation.
We find that a second-order perturbative treatment of the
single-particle spectrum suppresses the proton S-1(0) pairing gap
relative to the use of a free spectrum. We estimate the critical
temperature for the onset of proton superconductivity to be T-c =
(3.2-5.1) x 10(9) K, which is consistent with previous theoretical
results in the literature and marginally within the range deduced from a
recent Bayesian analysis of neutron star cooling observations.