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

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 $\mathbf{P}$ 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.

Comments: 27 pages, 5 figures, 9 tables