Non-diagonal DVCS with spinless hadron-to-two-hadron transition $γ^* π\to γππ$

TL;DR

The work generalizes generalized parton distributions to hadron-to-two-hadron transitions in non-diagonal hard exclusive processes, focusing on the spinless π→ππ case. It defines twist-2 unpolarized and polarized π→ππ transition GPDs from non-local light-cone quark operators in generalized Bjorken kinematics, including the extra final-state variables $W_{ππ}^2$, $θ_{π}^*$, and $φ_{π}^*$. The formalism is applied to the DVCS subprocess γ*π→γππ, with BH contributions and a ρ(770) resonance, revealing polarization-dependent angular structures in the 2π final state that help separate BH and DVCS. A dispersive framework is built by expanding the π→ππ GPDs in partial waves and employing a Muskhelishvili-Omnès representation to constrain the $W_{ππ}^2$ dependence via low-energy ππ phase shifts, yielding a phenomenological PW GPD $H^{ℓ,m}$, notably for ℓ=1, m=−1, constrained by data. The approach provides a path to study baryon resonances through non-diagonal hard exclusive reactions and can be extended to N → πN transitions using Froissart-Gribov projections.

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 $π\toππ$ transition GPDs are introduced with a particular choice of kinematic variables that characterize the produced two-pion system. In the vicinity of $ρ(770)$, we work out the two-pion decay angular distributions of the $e^-π\to e^-γππ$ 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 $ρ(770)$ resonance. In addition, we construct the double partial-wave expansion of $π\toππ$ 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 $π\toππ$ transition GPDs in terms of the low energy $ππ$ scattering phase shift and build a phenomenological model for these GPDs.

Figures (3)

• Figure 1: Factorization mechanism of the DVCS process with $\pi\to\pi\pi$ transition GPDs. The invariant variables relevant to the kinematics of the $e^-\pi\to e^-\gamma\pi\pi$ process are indicated. The diagram with crossed virtual and real photon lines is not shown explicitly.
• Figure 2: The $\cos\theta_\pi^*$ distributions of the $e^-\pi^+\to e^-\gamma\rho^+ \to e^-\gamma \pi^+\pi^0$ differential cross section. The figures are taken from Ref. Son:2024uxa.
• Figure 3: The $W_{\pi\pi}$ distribution of the real and imaginary parts of the PW GPD $H^{\ell = 1, m=-1}(\xi,\xi,t;W_{\pi\pi}^2)$ on the crossover line $x = \xi \simeq 0.15$ and $t = t_{\min}$. This figure is taken from Ref. Son:2024uxa.