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arXiv · 2009.04931

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

Maxwell T. Hansen·Raul A. Briceño·Robert G. Edwards·Christopher E. Thomas·David J. Wilson
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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.

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Maxwell T. Hansen, Raul A. Briceño, Robert G. Edwards, Christopher E. Thomas, David J. Wilson. 2020-09-10. The energy-dependent $\pi^+ \pi^+ \pi^+$ scattering amplitude from QCD. https://doi.org/10.1103/physrevlett.126.012001

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