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We analyze the spectrum of two- and three-pion states of maximal isospinobtained recently for isosymmetric QCD with pion mass $M\approx 200\;$MeV inRef. [1]. Using the relativistic three-particle quantization condition, we find$\sim 2 \sigma$ evidence for a nonzero value for the contact part of thethree-$\pi^+$ ($I=3$) scattering amplitude. We also compare our results toleading-order chiral perturbation theory. We find good agreement at threshold,and some tension in the energy dependent part of the three-$\pi^+$scatteringamplitude. 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.

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