Vertex renormalization of weak interactions and Cooper-pair breaking in cooling compact stars

Abstract

Below the critical temperature of superfluid phase transition baryonic matter emits neutrinos by breaking and recombination of Cooper pairs formed in the condensate. The weak vector and axial-vector vertices and the neutrino loss rates via pair breaking are modified by strong interactions in nuclear medium. We study these modifications nonperturbatively by summing infinite series of particle-hole loops in S-wave superfluid neutron matter. The interactions in the particle-hole channel are described within the Landau Fermi-liquid framework with the Landau parameters derived from the microscopic theory. The S-wave superfluid is described within the BCS theory. We derive the renormalized three-point vector and axial-vector vertices and the complete polarization tensor of matter and its low momentum transfer expansion. The leading-order term in this expansion and the associated neutrino losses arise at O(q2), consistent with the f-sum rule. The neutrino emission rate due to the pair breaking is parametrically suppressed compared to its one-loop counterpart by the ratio of the neutron recoil energy to the temperature, which is of order 5×10−3. The approximations to the normal and anomalous self-energies that guarantee the conformity of the theory with the generalized Ward identities are established.

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