Probing generalized parton distributions in pi N -> l+ l- N

TL;DR

This paper proposes using exclusive timelike photon production in $\\pi N$ scattering, $\\pi N \to \\gamma^* N$, to access generalized parton distributions of the nucleon. In the large-$Q'^2$ scaling limit, the amplitude factorizes into a hard subprocess convoluted with the pion distribution amplitude and nucleon GPDs, yielding a calculable cross section with dominant longitudinal polarization and specific $Q'^2$- and $t$-dependent scaling; the authors provide explicit LO formulas and numerical estimates using an asymptotic pion DA and modeled GPDs, and they analyze the crucial role of the pion-pole contribution via $F_{pole}(t)$ and the non-pole terms. They also discuss radiative corrections, power corrections beyond the scaling limit, and resonance effects, arguing that timelike measurements, when compared with spacelike processes and $e^+e^-\to \pi\pi$ data, offer a complementary path to test factorization, disentangle correction mechanisms, and refine the extraction of the spacelike pion form factor. Overall, the work outlines a viable experimental program to illuminate GPDs and pion dynamics with high-intensity hadron beams and highlights the importance of modeling and controlling power and radiative corrections.

Abstract

We study the exclusive reactions pi- p -> l+ l- n and pi+ n -> l+ l- p$ in view of possible future experiments with high-intensity pion beams. For large invariant mass of the lepton pair l+ l- and small squared momentum transfer to the nucleon these are hard-scattering processes providing access to generalized parton distributions. We estimate the cross section for these reactions, explore their connection with the pion form factor, and discuss the role they can play in improving our understanding of the relevant reaction mechanisms.

Figures (5)

• Figure 1: Sample Feynman diagrams at leading order in $\alpha_s$ for pion electroproduction (a) and its timelike counterpart (b) in the scaling limit. In both cases three other diagrams are obtained by attaching the photon to the quark lines in all possible ways. The plus-momentum fractions $x$ and $\eta$ refer to the average nucleon momentum $\frac{1}{2}(p+p')$.
• Figure 2: (a) Cross section estimates (full lines) for $\pi^- p \to \gamma^* n$ for $Q'^2=5 \,{\rm GeV}^2$ and $\tau = 0.2$, calculated from (\ref{['full-result']}) with the models (\ref{['h-ansatz']}) and (\ref{['e-ansatz']}). Separate contributions are shown for the terms with $|\tilde{\cal H}|^2$ (dashed), $\hbox{Re} ( \tilde{\cal H}^*\, \tilde{\cal E} )$ (dash-dotted), and $|\tilde{\cal E}|^2$ (dotted). (b) The same calculated with the pole-term form factor $F_{\mathrm{pole}}(t)$ instead of $F(t)$.
• Figure 3: (a) As Fig. \ref{['fig:t-plot']}a but as a function of $\tau$ at fixed $Q'^2=5 \,{\rm GeV}^2$ and $|t|= 0.2 \,{\rm GeV}^2$. (b) The same for $\pi^+ n \to \gamma^* p$.
• Figure 4: The part of the diagrams in Fig. \ref{['fig:hard']} due to the pion pole contribution to the distribution $\tilde{E}$.
• Figure 5: The soft overlap in $\gamma^* N\to \pi N$ (a and b) and $\pi N\to \gamma^* N$ (c and d). Plus-momenta $\mathrel{\vcenter {\hbox{$>$}\hbox{$\sim$}}} 0$ of the soft partons refer to the average nucleon momentum $\frac{1}{2}(p+p')$. Diagrams a, c, and d have analogs in the space- or timelike pion form factor, with the lower blob replaced by a quark-pion vertex.