Measurement of Single- and Double-Spin Asymmetries in Deep Inelastic Pion Electroproduction with a Longitudinally Polarized Target

We report the first measurement of the transverse momentum dependence of double-spin asymmetries in semi-inclusive production of pions in deep-inelastic scattering off the longitudinally polarized proton. Data have been obtained using a polarized electron beam of 5.7 GeV with the CLAS detector at the Jefferson Lab (JLab). Modulations of single spin asymmetries over the azimuthal angle between lepton scattering and hadron production planes $\varphi$ have been measured over a wide kinematic range in Bjorken $x$ and virtual photon squared four-momentum $Q^2$. A significant nonzero $\sin 2\varphi$ single spin asymmetry was observed for the first time indicating strong spin-orbit correlations for transversely polarized quarks in the longitudinally polarized proton.

Figure 1

The double-spin asymmetry $A_1$ as a function of transverse momentum $P_T$, integrated over all kinematical variables. The open band corresponds to systematic uncertainties. The dashed, dotted, and dash-dotted curves are calculations for different values for the ratio of transverse momentum widths for $g_1$ and $f_1$ (0.40, 0.68, 1.0) for a fixed width for $f_1$ ($0.25{\mathrm{GeV}}^2$) [5]. The lower panel shows the relative contributions to the data from simulated charged and neutral exclusive $\rho$ production.

Figure 2

Azimuthal modulation of the target single spin asymmetry $A_{\mathrm{UL}}$ for pions integrated over the full kinematics. Only statistical uncertainties are shown. Fit parameters $p_1/p_2$ are ($0.047\pm 0.010$, $-0.042\pm 0.010$), ($-0.046\pm 0.016$, $-0.060\pm 0.016$), ($0.059\pm 0.018$, $0.010\pm 0.019$) for ${\pi }^{+}$, ${\pi }^{-}$, and ${\pi }^0$, respectively. Dotted and dash-dotted lines for ${\pi }^{+}$ show separately contributions from $\sin \varphi$ and $\sin 2\varphi$ moments, whereas the solid line shows the sum.

Figure 3

The measured $x$ dependence of the longitudinal target SSA $A_{\mathrm{UL}}^{\sin 2\varphi }$ (triangles). The squares show the existing measurement of $A_{\mathrm{UL}}^{\sin 2\varphi }$ from HERMES. The lower band shows the systematic uncertainty. The upper band shows the existing theory predictions with uncertainties due to the Collins function [30, 48].