πNtransition distribution amplitudes: Their symmetries and constraints from chiral dynamics

Abstract

Baryon to meson transition distribution amplitudes (TDAs) extend the concept of generalized parton distributions. Baryon to meson TDAs appear as building blocks in the collinear factorized description of amplitudes for a class of hard exclusive reactions, prominent examples of which being hard exclusive meson electroproduction off a nucleon in the backward region and baryonantibaryon annihilation into a meson and a lepton pair. We study the general properties of these objects following from the underlying symmetries of QCD. In particular, the Lorentz symmetry results in the polynomiality property of the Mellin moments in longitudinal momentum fractions.We present a detailed account of the isotopic and permutation symmetry properties of nucleon to pion (πN ) TDAs. This restricts the number of independent leading twist πN TDAs to eight functions, providing description of all isotopic channels. Using chiral symmetry and the crossing relation between πN TDAs and πN generalized distribution amplitudes we establish soft pion theorems for πN TDAs, which determine the magnitude of πN TDAs. Finally, we build a simple resonance exchange model for πN TDAs considering N and ∆(1232) exchange contributions into the isospin-1 2 and isospin-3 2 πN TDAs.

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“…Similarly to (8), one can consider the near-forward (see the right panel of Fig. 4) and the near-backward kinematic regimes symmetric due to charge conjugation invariance.…”

“…An alternative parametrization which is better suited to address the symmetry properties of πN TDAs was introduced in [8]. In particular, within this latter parametrization πN TDAs turn to satisfy the polynomiality property of the Mellin moments in x i in its most simple form.…”

“…In particular, within this latter parametrization πN TDAs turn to satisfy the polynomiality property of the Mellin moments in x i in its most simple form. The relation between the two parametrizations in presented in the Appendix C of [8].…”

“…The suggested reaction mechanism manifests itself through the characteristic forward and backward peaks of the NN → γ * M cross section. The characteristic features of the TDA-based description of (8) are the scaling behavior in 1/q 2 of the cross-section and the specific behavior in cos θ * (by θ * we denote the lepton polar angle defined in the CMS of the lepton pair) resulting from the leading twist dominance of the transverse polarization of the virtual time-like photon. A detailed feasibility study for accessing πN TDAs through p p → γ * π 0 → e + e − π 0 atPANDA was performed in [11].…”

“…In Ref. [8] the contribution of the cross-channel ∆(1232) into πN TDAs was worked out explicitly. Finally, very recently in Ref.…”