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We present the first direct $N_f=2$ lattice QCD computation of two- andthree-$\pi^+$ scattering quantities that includes an ensemble at the physicalpoint. We study the quark mass dependence of the two-pion phase shift, and thethree-particle interaction parameters. We also compare to phenomenology andchiral perturbation theory (ChPT). In the two-particle sector, we observe goodagreement to the phenomenological fits in $s$- and $d$-wave, and obtain $M_\pia_0 = -0.0481(86)$ at the physical point from a direct computation. In thethree-particle sector, we observe reasonable agreement at threshold to theleading order chiral expansion, i.e.\@ a mildly attractive three-particlecontact term. In contrast, we observe that the energy-dependent part of thethree-particle quasilocal scattering quantity is not well described by leadingorder ChPT.

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