Scattering of two and three physical pions at maximal isospin from lattice QCD

TL;DR

This paper reports the first direct lattice QCD calculations of two- and three-pion scattering at the physical point, comparing results with phenomenology and chiral perturbation theory, and providing new insights into multi-pion interactions.

Contribution

It presents novel lattice QCD computations of two- and three-pion scattering at the physical point, including analysis of quark mass dependence and comparison with theoretical models.

Findings

Good agreement with phenomenology for two-pion phase shifts in s- and d-waves.

Determination of the pion scattering length as M_pi a_0 = -0.0481(86).

Observation of a mildly attractive three-particle contact term at threshold.

Abstract

We present the first direct $N_f=2$ lattice QCD computation of two- and three-$\pi^+$ scattering quantities that includes an ensemble at the physical point. We study the quark mass dependence of the two-pion phase shift, and the three-particle interaction parameters. We also compare to phenomenology and chiral perturbation theory (ChPT). In the two-particle sector, we observe good agreement to the phenomenological fits in $s$- and $d$-wave, and obtain $M_\pi a_0 = -0.0481(86)$ at the physical point from a direct computation. In the three-particle sector, we observe reasonable agreement at threshold to the leading order chiral expansion, i.e.\@ a mildly attractive three-particle contact term. In contrast, we observe that the energy-dependent part of the three-particle quasilocal scattering quantity is not well described by leading order ChPT.