Implementing the finite-volume three-pion scattering formalism across all non-maximal isospins

TL;DR

This paper numerically applies the relativistic-field-theory formalism to three-pion systems with all non-maximal isospins, providing baseline energy spectra predictions for future lattice QCD studies to detect three-body interactions.

Contribution

It extends the RFT formalism to all non-maximal isospin channels for three pions and implements an open-source Python tool for spectrum predictions.

Findings

Predicted three-pion energy spectra for various isospins and momenta.

Provided baseline spectra assuming no intrinsic three-body interactions.

Enabled future detection of three-body effects in lattice QCD.

Abstract

We present a numerical exploration of the relativistic-field-theory (RFT) formalism for three pions with all possible values of non-maximal isospin, $I_{\pi\pi\pi} = 2$, $1$ and $0$. Using the generic-isospin extension of the RFT formalism and applying our open-source Python library to implement the framework, we predict a range of three-pion energies for illustrative values of the two-to-two scattering amplitudes for various finite-volume irreps also with non-zero total momentum $\boldsymbol P$ in the finite-volume frame. The results restrict attention to the case of a vanishing intrinsic three-body interaction so that the spectra can be understood as a baseline. In future lattice QCD calculations, deviations from these values will be translated into evidence for intrinsic three-body effects in the various scattering channels.