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arXiv · 1812.10504

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

Alessandro Baroni·Raúl A. Briceño·Maxwell T. Hansen·Felipe G. Ortega-Gama
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Abstract

In this work we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $\textbf 2 + \mathcal J \to \textbf 2$ 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 $ππ+ \mathcal J \to ππ$ amplitude in the $ρ$ channel, for which the single-pion form factor, $F_π(Q^2)$, as well as the scattering phase, $δ_{ππ}$, 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.

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Alessandro Baroni, Raúl A. Briceño, Maxwell T. Hansen, Felipe G. Ortega-Gama. 2018-12-26. Form factors of two-hadron states from a covariant finite-volume formalism. https://doi.org/10.1103/physrevd.100.034511

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