Multichannel 0-to-2 and 1-to-2 transition amplitudes for arbitrary spin particles in a finite volume

TL;DR

This paper derives a model-independent, exact relation connecting finite-volume matrix elements to infinite-volume transition amplitudes for particles of any spin, applicable to complex multi-channel systems in relativistic quantum field theory.

Contribution

It extends previous finite-volume formalism to include particles with arbitrary spin and multiple coupled channels, providing a comprehensive framework for lattice QCD calculations.

Findings

Derived a relativistic, non-perturbative relation for transition amplitudes.

Includes all angular momentum states and multiple coupled channels.

Applicable to systems with particles of any intrinsic spin.

Abstract

We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volume $\textbf{0}\rightarrow\textbf{2}$ and $\textbf{1}\rightarrow\textbf{2}$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory, and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utility of our general result, we discuss how it can be implemented for studies of $N+\mathcal{J}~\rightarrow~(N\pi,N\eta,N\eta',\Sigma K,\Lambda K)$ transitions, where $\mathcal{J}$ is a generic external current. The reduction of rotational symmetry, due to the cubic finite volume, manifests in this example through the mixing of S- and P-waves when the system has nonzero total momentum.