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

TL;DR

This work investigates the onset of hard/soft factorization in exclusive pion electroproduction by measuring the beam-spin observable $A_{LU}$ in $p(\vec{e},e'\pi^+)n$ over $2<Q^2<6\,\text{GeV}^2$ with KaonLT at Jefferson Lab. The key quantity extracted is $\frac{\sigma_{LT'}}{\sigma_0}$ from $A_{LU}^{\sin\phi}$, analyzed as a function of $-t$ at fixed $(Q^2,x_B)$ and, combined with CLAS/CLAS12 data, as a function of $Q^2$ at fixed $(t,x_B)$. Across the kinematics, Regge-based models describe the data better than the GPD-based GK approach, suggesting that the factorization regime has not yet been reached in this region. The results underscore the need for model-independent tests (e.g., Rosenbluth separations) before unambiguously extracting GPDs from this reaction, and point to future KaonLT measurements in additional channels to further constrain hadronic structure. $A_{LU}$ and $\sigma_{LT'}/\sigma_0$ thus provide crucial insight into the interplay between soft and hard dynamics in exclusive meson production.

Abstract

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.

Figures (13)

• Figure 1: Reaction diagram for $p(\vec{e},e'\pi^+)n$. The angle $\phi$ is defined as the azimuthal angle between the electron scattering plane (defined by $e$ and $e'$) and the hadron reaction plane (defined by $\pi^+$ and $n$).
• Figure 2: Exclusive $\pi^+$ electroproduction from the proton. (a) Factorization of the reaction into a hard scattering part and a soft part described by a GPD. An additional soft part known as the pion distribution amplitude (DA) describes the final state pion formation. (b) A Regge process, in which $X$ represents the exchange of several particles along a Regge trajectory up to a cutoff.
• Figure 3: Coincidence time and missing mass spectra for Q$^2$=3.0 GeV$^2$, $x_B$=0.25, center SHMS setting. (a) Coincidence time between the HMS and SHMS. The prompt peak selected is highlighted in grey, and the windows used to subtract random coincidences are hatched. (b) Missing mass distribution of $p(\vec{e},e'\pi^+)n$. The solid line shows the upper missing mass cut used, and the dashed lines show the variation of the cut used to calculate a cut dependence. The lower missing mass cut is 0.91 GeV, and its contribution to the cut dependence is evaluated by removing this cut entirely.
• Figure 4: (Color online) Phase space plot of the kinematics for which $\sigma_{LT'}/\sigma_0$ has been measured Diehl_2023Diehl_2020 [This work]. The error bars indicate the standard deviations in $x_B$ and $Q^2$ spanned by each data point. Note that 3 variables $(Q^2,x_B,t)$ are required to fully describe exclusive reaction kinematics, the different data points are taken at different $t$-values not indicated here. Each grouping of data points represents one setting, where $-t$ increases from left to right. For both CLAS datasets, only $-t<0.8$ GeV$^2$ data are shown, corresponding to the upper range of the KaonLT data. By combining these data sets, the $Q^2$ dependence of $\sigma_{LT'}/\sigma_0$ can be determined at fixed $-t$ for two values of $x_B$, shown as dashed lines.
• Figure 5: $A_{LU}$ as a function of $\phi$ for the first four $t$-bins for central values of $Q^2=3$ GeV$^2$, $x_B=$0.25. The solid line shows the data fit with Eqn. \ref{['eqn:functional']} and the dashed line Eqn. \ref{['eqn:approx']} (see text for explanation). Uncertainties are statistical only.