Physical Review D
We derive formalism for determining 2+𝓙 → 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 nonidentical and, in the latter case, can be either degenerate or nondegenerate. We further accommodate any number of strongly coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the ρ-meson form factor, in which the unstable nature of the ρ is rigorously accommodated.
Original Publication Citation
Briceño, R.A. & Hansen, M.T. (2016) Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume. Physical Review D, 94(1) 1-36, Article 013008. https://doi.org/10.1103/PhysRevD.94.013008
Briceño, Raúl A. and Hansen, Maxwell T., "Relativistic, Model-Independent, Multichannel 2 → 2 Transition Amplitudes in a Finite Volume" (2016). Physics Faculty Publications. 625.