
Physics 2015
Relativistic, modelindependent, multichannel $2\to2$ transition amplitudes in a finite volumeAbstract: We derive formalism for determining $\textbf{2} + \mathcal J \to \textbf{2}$ infinitevolume transition amplitudes from finitevolume matrix elements. Specifically, we present a relativistic, modelindependent relation between finitevolume matrix elements of external currents and the physically observable infinitevolume matrix elements involving twoparticle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or nonidentical and, in the latter case, can be either degenerate or nondegenerate. We further accommodate any number of stronglycoupled twoscalar 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.
