The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD

Abstract

Focusing on three-pion states with maximal isospin (${\pi }^{+}{\pi }^{+}{\pi }^{+}$), we present the first non-perturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.

Comments: 22 pages, 7 figures, 11 tables, CERN-TH-2020-147, JLAB-THY-20-3242, v2: minor edits, add references, added a curve to Fig. 2; corresponds to version published in PRL