Relativistic, model-independent, multichannel $2\to 2$ transition amplitudes in a finite volume

Abstract

We derive formalism for determining $\text{2}+\mathcal{J}\to \text{2}$ infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the $\rho$-meson form factor, in which the unstable nature of the $\rho$ is rigorously accommodated.

35 pages, 11 figures

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