Non-diagonal DVCS with spinless hadron-to-two-hadron transition ${\gamma }^{\ast }\pi \to \gamma \pi \pi$

Abstract

We present the formalism of hadron-to-two-hadron transition generalized parton distributions (GPDs) for spinless hadron case. Definitions of the twist-2 unpolarized and polarized $\pi \to \pi \pi$ transition GPDs are introduced with a particular choice of kinematic variables that characterize the produced two-pion system. In the vicinity of $\rho (770)$, we work out the two-pion decay angular distributions of the $e^{-}\pi \to e^{-}\gamma \pi \pi$ cross section, incorporating both the Bethe-Heitler and deeply virtual Compton scattering processes. Each cross section exhibits a distinctive angular distribution, which is sensitive to the polarization states of the produced $\rho (770)$ resonance. In addition, we construct the double partial-wave expansion of $\pi \to \pi \pi$ transition GPDs in the two-pion decay angles as a generalization of GPDs for transition from a pion to a spin-$\ell$ resonance state. With the help of the Omnès representation, we constrain the $\pi \to \pi \pi$ transition GPDs in terms of the low energy $\pi \pi$ scattering phase shift and build a phenomenological model for these GPDs.

Comments: 7 pages, 3 figures, Contribution to The 21st International Conference on Hadron Spectroscopy and Structure (HADRON2025)