Functional renormalisation group for few-nucleon systems: SU(4) symmetry and its breaking

TL;DR

This paper uses the functional renormalisation group to analyze few-nucleon systems, exploring SU(4) symmetry and its breaking, deriving flow equations, and calculating scattering lengths with implications for nuclear physics.

Contribution

It introduces a novel application of the functional renormalisation group to few-nucleon systems, including symmetry considerations and flow equations derivation.

Findings

Flow equations decouple in the SU(4) symmetric limit.

Universal features emerge in the unitary limit.

Calculated neutron-deuteron and deuteron-deuteron scattering lengths.

Abstract

We apply the functional renormalisation group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The evolution of the coupling constants in this action is described by a renormalisation group flow. We derive these flow equations both in the limit of exact Wigner SU(4) symmetry and in the realistic case of broken symmetry. In the symmetric limit we find that the renormalisation flow equations decouple, and can be combined into two sets, one of which matches the known results for bosons, and the other result matches the one for fermions with spin degrees only. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and quintet channels.