Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD

TL;DR

This paper computes the scattering amplitudes of two- and three-meson systems with physical quark masses using lattice QCD, providing new insights into meson interactions and validating theoretical models.

Contribution

It presents the first determination of physical-point three-meson scattering amplitudes from lattice QCD, including multiple partial waves and comparison with chiral theory.

Findings

First physical-point three-meson scattering amplitudes obtained

Accurate phase shifts for two-meson systems calculated

Results agree with chiral perturbation theory and phenomenology

Abstract

We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with $a\approx 0.063\;$fm, including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two and three-meson K matrices, including not only the leading $s$ wave, but also $p$ and $d$ waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for $3\pi^+$, $3K^+$, $\pi^+\pi^+ K^+$ and $K^+ K^+ \pi^+$ systems. These are determined for total angular momentum $J^P=0^-$, $1^+$, and $2^-$. We also obtain accurate results for $2\pi^+$, $\pi^+ K^+$, and $2K^+$ phase shifts. We compare our results to Chiral Perturbation Theory, and to phenomenological fits.