Extraction of Beam-Spin Asymmetries from the Hard Exclusive ${\pi }^{+}$ Channel off Protons in a Wide Range of Kinematics

We have measured beam-spin asymmetries to extract the $\sin \varphi$ moment $A_{LU}^{\sin \varphi }$ from the hard exclusive $\overrightarrow{e}p\to e^{\prime }n{\pi }^{+}$ reaction above the resonance region, for the first time with nearly full coverage from forward to backward angles in the center of mass. The $A_{LU}^{\sin \varphi }$ moment has been measured up to $6.6{\mathrm{GeV}}^2$ in $-t$, covering the kinematic regimes of generalized parton distributions (GPD) and baryon-to-meson transition distribution amplitudes (TDA) at the same time. The experimental results in very forward kinematics demonstrate the sensitivity to chiral-odd and chiral-even GPDs. In very backward kinematics where the TDA framework is applicable, we found $A_{LU}^{\sin \varphi }$ to be negative, while a sign change was observed near 90° in the center of mass. The unique results presented in this Letter will provide critical constraints to establish reaction mechanisms that can help to further develop the GPD and TDA frameworks.

Figure 1

(a) Exclusive electroproduction of a pion on the proton in very forward kinematics ($-t/Q^2\ll 1$), described by GPDs [2, 3]. (b) Factorization of the same reaction in very backward kinematics ($-u/Q^2\ll 1$), described by TDAs [13, 14].

Figure 2

Beam-spin asymmetry as a function of $\varphi$ for ${\pi }^{+}$ emitted in the forward (left) and backward (right) regions, integrated over all other kinematic variables. The vertical error bars show the statistical uncertainty of each point, while the horizontal bars correspond to the bin width. The red line shows the fit with the functional form of Eq. (1).

Figure 3

$A_{LU}^{\sin \varphi }$ (black rectangles) as a function of $-t$ in the forward kinematic regime and their systematic uncertainty (gray bins). For comparison, the theoretical prediction from the GPD-based Goloskokov-Kroll model (blue band) is shown. The band of the theoretical prediction corresponds to the range accessible with our measurements in $Q^2$ and $x_B$.

Figure 4

$A_{LU}^{\sin \varphi }$ as a function of $-t$. The shaded area represents the systematic uncertainty.

Figure 5

$A_{LU}^{\sin \varphi }$ as a function of $Q^2$ (top) and $x_B$ (bottom) for pions going in the forward (left) and backward (right) regions. The shaded area represents the systematic uncertainty.