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

Abstract

Abstract We present the first direct $$N_f=2$$ N f = 2 lattice QCD computation of two- and three- $$\pi ^+$$ π + 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 $$M_\pi a_0 = -0.0481(86)$$ M π 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.