Probing hard/soft factorization via beam-spin asymmetry in exclusive pion electroproduction from the proton

Deep exclusive meson production (DEMP) reactions, such as $p(\vec{e},e’π^+)n$, provide opportunities to study the three-dimensional structure of the nucleon through differential cross section and beam- and target-spin asymmetry measurements. This work aims to probe the onset of the hard/soft factorization regime through the exclusive $p(\vec{e},e’π^+)n$ reaction, as measured in the KaonLT experiment at Jefferson Lab Hall C. A 10.6 GeV longitudinally polarized electron beam was incident on an unpolarized liquid hydrogen target, and the scattered electron and produced meson were detected in two magnetic focusing spectrometers, enabling precision cross section measurements. The cross section ratio $σ_{LT’}/σ_0$ was extracted from the beam-spin asymmetry $A_{LU}$. The $t$-dependence of $σ_{LT’}/σ_0$ was determined at fixed $Q^2$ and $x_B$ over a range of kinematics from $2<Q^2<6$ GeV$^2$ above the resonance region ($W>2$ GeV). Furthermore, these data are combined with recent results from CLAS/CLAS12 to determine the $Q^2$-dependence of $σ_{LT’}/σ_0$ at two ($x_B$, $t$) settings. This was fairly flat, with $Q^2$ not having a measurable effect on the value of $σ_{LT’}/σ_0$ in the range explored. Results are compared to predictions from the generalized parton distribution (GPD) formalism, which relies explicitly on hard/soft factorization, and Regge formalism. The Regge models better predict $σ_{LT’}/σ_0$, which suggests that the factorization regime is not yet reached.

💡 Research Summary

The paper investigates whether the hard/soft factorization theorem, which underpins the Generalized Parton Distribution (GPD) framework, is applicable to exclusive charged‑pion electroproduction (p(e, e′π⁺)n) in the kinematic regime accessible at Jefferson Lab. Using the KaonLT experiment (E12‑09‑011) in Hall C, a 10.6 GeV longitudinally polarized electron beam (≈ 89 % polarization) was incident on an unpolarized liquid‑hydrogen target. Scattered electrons were detected in the High Momentum Spectrometer (HMS) and the produced π⁺ mesons in the newly commissioned Super High Momentum Spectrometer (SHMS). The setup allowed precise determination of the four‑momentum transfer Q² (2–6 GeV²), Bjorken‑x (≈ 0.2–0.4) and the Mandelstam variable t (−t = 0.02–0.16 GeV²) with fine binning in the azimuthal angle ϕ.

The observable of interest is the beam‑spin asymmetry A_LU, defined as the helicity‑dependent yield difference normalized by the sum. In the one‑photon exchange approximation A_LU contains a sin ϕ term whose amplitude A_sin ϕ is proportional to √