Renormalization group evolution and power counting in nuclear matter

TL;DR

This paper explores how renormalization group methods simplify the effective field theory description of nuclear matter at long distances, leading to a mean-field approximation with perturbative contact interactions and density-dependent terms.

Contribution

It demonstrates that in nuclear matter, RG evolution causes the effective couplings to freeze, making the leading EFT equivalent to mean-field and perturbative contact interactions, connecting to Skyrme forces.

Findings

RG evolution freezes couplings above the healing distance

Leading order EFT corresponds to mean-field approximation

Density-dependent terms are essential in the equation of state

Abstract

In nuclear matter, for interparticle separations larger than the healing distance (a characteristic long-distance scale of finite-density fermionic systems), the in-medium two-body wave function is essentially a free wave function. In terms of the renormalization group (RG), this implies that the running of the effective field theory (EFT) couplings freezes for r-space cutoffs above this distance (or p-space cutoffs below the corresponding healing momentum scale). As a consequence the leading order EFT description of nuclear matter (understood here as the infrared limit of the RG) corresponds to the mean-field approximation and a set of tree-level (i.e. perturbative) leading contact-range couplings. Though the contacts do in principle inherit the power counting they had in the vacuum, their iteration is suppressed in the infrared, explaining why they become perturbative in nuclear matter. In addition to the contact-range potential, RG evolution requires the inclusion of density-dependent terms in the equation of state that can be represented by a pseudo-potential, which (unlike the genuine contacts) should not be iterated. The LO EFT description ends up being a subset of Skyrme forces previously identified by the Orsay group.