$I=3$ three-pion scattering amplitude from lattice QCD

Abstract

We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass $M\approx 200$MeV in Ref. [1]. Using the relativistic three-particle quantization condition, we find $\sim 2\sigma$ evidence for a nonzero value for the contact part of the three-${\pi }^{+}$ ($I=3$) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold, and some tension in the energy dependent part of the three-${\pi }^{+}$scattering amplitude. We also find that the two-${\pi }^{+}$ ($I=2$) spectrum is fit well by an $s$-wave phase shift that incorporates the expected Adler zero.

Comments: Corrected Figs S1 and S2 in supplementary material. Main text and conclusions unchanged