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<p>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 <i>γ</i><sup><i>*</i></sup><i>π</i> → <i>γππ</i> in terms of <i>π</i> → <i>ππ</i> transition GPDs, which generalize GPDs for <i>π</i> → <i>f</i><sub>0</sub>, <i>ρ</i>, <i>f</i><sub>2</sub>, ⋯ transitions. We work out the basic properties of <i>π</i> → <i>ππ</i> transition GPDs and establish the soft pion theorems at the 2<i>π</i> production threshold. We construct the partial wave expansion of <i>π</i> → <i>ππ</i> transition GPDs in the two-pion decay angles and employ the dispersive approach to constrain <i>π</i> → <i>ππ</i> transition GPDs in terms of <i>ππ</i>-scattering phases with help of the Omnès representation. We estimate the <i>e</i><sup><i>−</i></sup><i>π</i><sup>+</sup> → <i>e</i><sup><i>−</i></sup><i>γπ</i><sup>+</sup><i>π</i><sup>0</sup> cross section in the kinematics of the JLab@12 GeV incorporating the isolated <i>ρ</i>(770) resonance state and work out the angular distributions of the cross section, specifying the observables sensitive to the polarization states of the produced <i>ρ</i>(770) resonance.</p>

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

  • 期刊论文

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  • 发表日期：

    2025年1月23日

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  • Sangyeong Son,
  • Kirill M. Semenov-Tian-Shansky

摘要

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 → f0, ρ, f2, ⋯ 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+π0 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.