Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in finite-volume

TL;DR

This paper demonstrates that finite-volume lattice QCD can be used to constrain coupled-channel transition amplitudes involving multi-hadron final states, providing a practical framework and proof-of-principle for future calculations.

Contribution

It introduces a formalism and practical approach for extracting coupled-channel transition amplitudes from finite-volume lattice QCD data, with illustrative synthetic data examples.

Findings

Feasibility of constraining coupled-channel amplitudes demonstrated

Provides a practical roadmap for lattice QCD calculations

Synthetic data validates the approach

Abstract

Whether one is interested in accessing the excited spectrum of hadrons or testing the standard model of particle physics, electroweak transition processes involving multi-hadron channels in the final state play an important role in a variety of experiments. Presently the primary theoretical tool with which one can study such reactions is lattice QCD, which is defined in a finite spacetime volume. In this work, we investigate the feasibility of implementing existing finite-volume formalism in realistic lattice QCD calculation of reactions in which a stable hadron can transition to one of several two-hadron channels under the action of an external current. We provide a conceptual description of the coupled-channel transition formalism, a practical roadmap for carrying out a calculation, and an illustration of the approach using synthetic data for two non-trivial resonant toy models. The results provide a proof-of-principle that such reactions can indeed be constrained using modern-day lattice QCD calculations, motivating explicit computation in the near future.