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arXiv · 2508.11627

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

Athari Alotaibi·Maxwell T. Hansen·Raúl A. Briceño
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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.

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Athari Alotaibi, Maxwell T. Hansen, Raúl A. Briceño. 2025-08-15. Implementing the finite-volume three-pion scattering formalism across all non-maximal isospins. https://arxiv.org/abs/2508.11627

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