Hansen MT, Briceño RA, Edwards RG, Thomas CE, Wilson DJ. Energy-Dependent π^{+}π^{+}π^{+} Scattering Amplitude from QCD.
Phys Rev Lett 2021;
126:012001. [PMID:
33480796 DOI:
10.1103/physrevlett.126.012001]
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Abstract
Focusing on three-pion states with maximal isospin (π^{+}π^{+}π^{+}), we present the first nonperturbative 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.
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