Non-diagonal DVCS and transition GPDs: a unified framework for spinless hadron case γ*π → γππ

초록

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 gamma*pi -> gamma pi pi in terms of pi -> pi pi transition GPDs, which generalize GPDs for pi -> f0, rho, f2, & ctdot; transitions. We work out the basic properties of pi -> pi pi transition GPDs and establish the soft pion theorems at the 2 pi production threshold. We construct the partial wave expansion of pi -> pi pi transition GPDs in the two-pion decay angles and employ the dispersive approach to constrain pi -> pi pi transition GPDs in terms of pi pi-scattering phases with help of the Omn & egrave;s representation. We estimate the e-pi+ -> e-gamma pi+pi 0 cross section in the kinematics of the JLab@12 GeV incorporating the isolated rho(770) resonance state and work out the angular distributions of the cross section, specifying the observables sensitive to the polarization states of the produced rho(770) resonance.

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