Implementing the RFT finite-volume formalism for three pions across all non-maximal isospins

TL;DR

This paper numerically investigates the RFT formalism for three pions in finite volume, focusing on non-maximal isospins and setting three-particle interactions to zero as a baseline for future lattice QCD studies.

Contribution

It extends the RFT formalism to all non-maximal isospin states of three pions and provides a numerical baseline for future interaction studies.

Findings

Results for all non-maximal isospin values ($I=2,1,0$)

Analysis across different total momenta and symmetry representations

Set-up with zero three-particle interactions as a baseline

Abstract

We present a numerical investigation of the relativistic-field-theoretic (RFT) formalism, used to predict the discrete energy spectrum of three pions in a finite volume. Applying the previously derived generalization, we extract results for all non-maximal isospin values ($I_{\pi\pi\pi} = 2,1,$ and $0$), for different total momenta $\boldsymbol{P}$, and for various irreducible representations of the finite-volume symmetry group. We restrict attention to the unphysical scenario in which the three-particle interactions are set to zero. This set-up thus serves as a baseline for future lattice QCD calculations that will aim to extract such three-body interactions.