Applied nonrelativistic conformal field theory: scattering-length and effective-range corrections to unnuclear physics

TL;DR

This paper develops a nonperturbative formalism for nonrelativistic conformal field theory applied to neutron interactions, calculating corrections to nuclear reaction rates influenced by scattering length and effective range.

Contribution

It introduces a formalism for defining local operators nonperturbatively and computes first-order corrections to scale-invariant nuclear reaction rates.

Findings

Calculated scattering-length corrections to two-point functions.

Derived effective-range corrections to primary charge-three operators.

Provided first corrections to neutron-involved nuclear reaction rates.

Abstract

Due to an accidentally large $s$-wave scattering length, in a relatively wide range of energy, neutrons are approximately described by the nonrelativistic conformal field theory of unitarity fermions, perturbed by one relevant and an infinite number of irrelevant operators. We develop a formalism which provides a nonperturbative definition of local operators in that nonrelativistic conformal field theory. We compute the scattering-length and effective-range corrections to the two-point functions of primary charge-three operators using the technique of conformal perturbation theory. These calculations allow us to find the first corrections to the scale-invariant behavior of the rate of nuclear reactions with three neutrons in the final state in the regime when the neutrons have small relative momenta.