Non-diagonal DVCS and transition GPDs: a unified framework for spinless hadron case γ * π → γππ - Sangyeong Son; Kirill M. Semenov-Tian-Shansky (Journal of High Energy Physics)
Abstract Hadron-to-two-hadron transition generalized parton distributions (GPDs) extend the concept of hadron-to-resonance transition GPDs and provide a unified description of non-diagonal hard exclusive reactions in the generalized Bjorken limit. We present the formalism for the case of spinless hadrons addressing the non-diagonal deeply virtual Compton scattering γ * π → γππ in terms of π → ππ transition GPDs, which generalize GPDs for π → f 0, ρ, f 2, ⋯ transitions. We work out the basic properties of π → ππ transition GPDs and establish the soft pion theorems at the 2π production threshold. We construct the partial wave expansion of π → ππ transition GPDs in the two-pion decay angles and employ the dispersive approach to constrain π → ππ transition GPDs in terms of ππ-scattering phases with help of the Omnès representation. We estimate the e − π + → e − γπ + π 0 cross section in the kinematics of the JLab@12 GeV incorporating the isolated ρ(770) resonance state and work out the angular distributions of the cross section, specifying the observables sensitive to the polarization states of the produced ρ(770) resonance.