I=3 Three-Pion Scattering Amplitude from Lattice QCD

We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass M≈200 MeV in Hörz and Hanlon, [Phys. Rev. Lett. 123, 142002 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.142002]. Using the relativistic three-particle quantization condition, we find ∼2σ evidence for a nonzero value for the contact part of the 3π^{+} (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 3π^{+} scattering amplitude. We also find that the 2π^{+} (I=2) spectrum is fit well by an s-wave phase shift that incorporates the expected Adler zero.