Implementing the three-neutron quantization condition

TL;DR

This paper details the implementation of a relativistic three-neutron finite-volume quantization condition, including spin rotations, symmetry decompositions, and numerical predictions for finite-volume spectra based on experimental two-particle interactions.

Contribution

It provides a comprehensive implementation of the three-neutron quantization condition with practical formulas, symmetry analysis, and numerical predictions for realistic parameters.

Findings

Finite-volume spectrum predictions for three-neutron systems.

Inclusion of Wigner rotations in the quantization condition.

Numerical results based on experimental two-particle interactions.

Abstract

We describe in detail the implementation of the relativistic three-neutron finite-volume quantization condition derived in Ref. [1]. In particular, we show how the complications due to Wigner rotations acting on spins are included, and present concrete formulas for the case when the angular momenta within pairs is restricted to be less than 2. We describe the symmetries of the matrices appearing in the quantization condition, and decompose solutions into irreducible representations of the appropriate doubled finite-volume symmetry groups. We present an implementation of the three-particle K matrix, keeping the two lowest-order terms in the threshold expansion. We provide numerical predictions for the finite-volume spectrum for a setup with nearly physical parameters, including two-particle interactions that are based on experimental results. This exploratory study shows the how lattice QCD calculations of the three-neutron spectrum with sufficient precision can provide detailed information on both two- and three-particle interactions.