Hard Exclusive Electroproduction of Pions

TL;DR

Hard exclusive $\pi^+$ electroproduction is analyzed within PQCD factorization for longitudinal photons, separating the amplitude into short-distance and long-distance parts described by the pion distribution amplitude and nucleon double distributions. The authors show the amplitude contains a pseudovector part tied to polarized forward distributions and a pseudoscalar pion-pole part tied to the pion cloud and the pion form factor, modeling the latter via the pion DA and a $t$-channel exchange. Numerical results at $Q^2=10$ GeV$^2$ indicate the pseudovector contribution dominates at $x_{\rm Bj}\lesssim 0.1$, while the pion-pole contribution dominates for $0.1< x_{\rm Bj}<0.4$; the balance between mechanisms also depends on $t$ and the chosen double-distribution models. The work provides a framework to extract nucleon structure from exclusive meson production and highlights where data can discriminate between polarized PDFs and pion-cloud effects.

Abstract

We investigate the exclusive electroproduction of pi^+ mesons from nucleons. To leading twist, leading order alpha_s accuracy the corresponding production amplitude can be decomposed into pseudovector and pseudoscalar parts. Both can be expressed in terms of quark double distribution functions of the nucleon. While the pseudovector contribution is connected to ordinary polarized quark distributions, the pseudoscalar part can be related to one pion t-channel exchange. We observe that the pseudovector part of the production amplitude is important at x < 0.1. On the other hand, for 0.1 < x < 0.4 contributions from one pion exchange dominate.

Figures (5)

• Figure 1: Differential production cross section for exclusive $\pi^+$ production through the scattering of longitudinally polarized photons from protons at $t=t_{\rm min}$ and $Q^2 = 10$ GeV$^2$. The dotted and dot-dashed curves show the pseudovector and pseudoscalar contributions, respectively. The upper figure corresponds to model $A$, the lower one to model $B$.
• Figure 2: Differential production cross section for exclusive $\pi^+$ production through the scattering of longitudinally polarized photons from protons at $t=-0.4$ GeV$^2$ and $Q^2 = 10$ GeV$^2$ . The dotted and dot-dashed curves show the pseudovector and pseudoscalar contributions, respectively. The upper figure corresponds to model $A$, the lower one to model $B$.
• Figure 3: Ratio of the differential production cross sections for exclusive $\pi^+$ and $\pi^0$ production through the scattering of longitudinally polarized photons from protons at $t=t_{\rm min}$ and $Q^2 = 10$ GeV$^2$ for model $A$. The dotted curve corresponds to the pseudovector contribution alone.
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