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

• Received 17 September 2019

DOI:https://doi.org/10.1103/PhysRevLett.124.032001

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Published by the American Physical Society