Speaker
Description
The non-diagonal hard exclusive reactions admitting a description in terms of generalized parton distributions (GPDs) with transition $N\to\Delta, N^*$ provide insight into the internal dynamics of hadron excitations. A unified description of these reactions in the complete resonance region can be performed by introducing the concept of $N \to N \pi$ transition GPDs.
In this study, we investigate a toy model of non-diagonal hard exclusive reaction involving spinless hadrons, the deeply virtual Compton scattering (DVCS) process $\gamma^* \pi \to \gamma \pi \pi$, within the framework of $\pi\to\pi\pi$ GPD. We analyze this reaction in the vicinity of intermediate resonance states, in particular, $\rho(770)$, using the partial-wave expansion and dispersive techniques.
We calculate the pion decay angular distributions of the $e^-\pi^+ \to e^- \gamma \rho^+ \to e^- \gamma \pi^+ \pi^0$ cross section, incorporating both the Bethe-Heitler and DVCS contributions. The shape of these angular distributions turns out to be sensitive to the polarization states of produced $\rho(770)$ resonance. We also construct dispersive approach based on the Omnés representation to build a phenomenological model for the $\pi\to\pi\pi$ transition GPDs. Furthermore, the application of the Froissart-Gribov projection technique to the unpolarized $\pi\to\pi\pi$ Compton form factor is examined, enabling the exploration of hadron excitation induced by a cross channel local probe with arbitrary spin.
