Form factors of two-hadron states from a covariant finite-volume formalism

Abstract

In this work we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $\text{2}+\mathcal{J}\to \text{2}$ transition amplitudes. We also give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when $\mathcal{J}$ couples to one of the two hadrons. This also leads to a new finite-volume function, denoted $G$, the numerical evaluation of which is described in detail. As an example we discuss the determination of the $\pi \pi +\mathcal{J}\to \pi \pi$ amplitude in the $\rho$ channel, for which the single-pion form factor, $F_{\pi }(Q^2)$, as well as the scattering phase, ${\delta }_{\pi \pi }$, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.

Comments: 42 pages, 11 figures, JLAB-THY-18-2878, CERN-TH-2018-263