Progress in three-particle scattering from LQCD

TL;DR

This paper discusses recent progress in extracting three-particle scattering observables from lattice QCD by relating finite-volume spectra to scattering amplitudes, including extensions to systems with two-to-three transitions.

Contribution

It extends the formalism for three-particle scattering in lattice QCD to include two-to-three transitions and verifies the approach by reproducing known energy shifts.

Findings

Extended formalism to include two-to-three transitions.

Reproduced finite-volume energy shift of a three-particle bound state.

Progress in validating and applying the three-particle scattering method.

Abstract

We present the status of our formalism for extracting three-particle scattering observables from lattice QCD (LQCD). The method relies on relating the discrete finite-volume spectrum of a quantum field theory with its scattering amplitudes. As the finite-volume spectrum can be directly determined in LQCD, this provides a method for determining scattering observables, and associated resonance properties, from the underlying theory. In a pair of papers published over the last two years, two of us have extended this approach to apply to relativistic three-particle scattering states. In this talk we summarize recent progress in checking and further extending this result. We describe an extension of the formalism to include systems in which two-to-three transitions can occur. We then present a check of the previously published formalism, in which we reproduce the known finite-volume energy shift of a three-particle bound state.