Pion-mediated Cooper pairing of neutrons: beyond the bare vertex approximation

TL;DR

This paper investigates neutron superfluidity mediated by pion exchange, emphasizing the importance of vertex corrections in non-perturbative Dyson-Schwinger equation analyses, which significantly alter the predicted critical parameters.

Contribution

It introduces a non-perturbative approach to neutron pairing that includes vertex corrections, improving the accuracy over the bare vertex approximation.

Findings

Vertex corrections are significant at low densities.

Including vertex corrections alters the critical density and temperature.

The transition line on the density-temperature plane is substantially changed.

Abstract

In some quantum many particle systems, the fermions could form Cooper pairs by exchanging intermediate bosons. This then drives a superconducting phase transition or a superfluid transition. Such transitions should be theoretically investigated by using proper non-perturbative methods. Here we take the neutron superfluid transition as an example and study the Cooper pairing of neutrons mediated by neutral $\pi$-mesons in the low density region of a neutron matter. We perform a non-perturbative analysis of the neutron-meson coupling and compute the pairing gap $\Delta$, the critical density $\rho_{c}$, and the critical temperature $T_c$ by solving the Dyson-Schwinger equation of the neutron propagator. We first carry out calculations under the widely used bare vertex approximation and then incorporate the contribution of the lowest-order vertex correction. This vertex correction is not negligible even at low densities and its importance is further enhanced as the density increases. The transition critical line on density-temperature plane obtained under the bare vertex approximation is substantially changed after including the vertex correction. These results indicate that the vertex corrections play a significant role and need to be seriously taken into account.