Measurement of Exclusive ${\pi }^0$ Electroproduction Structure Functions and their Relationship to Transverse Generalized Parton Distributions

Exclusive ${\pi }^0$ electroproduction at a beam energy of 5.75 GeV has been measured with the Jefferson Lab CLAS spectrometer. Differential cross sections were measured at more than 1800 kinematic values in $Q^2$, $x_B$, $t$, and ${\varphi }_{\pi }$, in the $Q^2$ range from 1.0 to $4.6{\mathrm{GeV}}^2$, $-t$ up to $2{\mathrm{GeV}}^2$, and $x_B$ from 0.1 to 0.58. Structure functions ${\sigma }_T+ϵ{\sigma }_L$, ${\sigma }_{TT}$, and ${\sigma }_{LT}$ were extracted as functions of $t$ for each of 17 combinations of $Q^2$ and $x_B$. The data were compared directly with two handbag-based calculations including both longitudinal and transversity generalized parton distributions (GPDs). Inclusion of only longitudinal GPDs very strongly underestimates ${\sigma }_T+ϵ{\sigma }_L$ and fails to account for ${\sigma }_{TT}$ and ${\sigma }_{LT}$, while inclusion of transversity GPDs brings the calculations into substantially better agreement with the data. There is very strong sensitivity to the relative contributions of nucleon helicity-flip and helicity nonflip processes. The results confirm that exclusive ${\pi }^0$ electroproduction offers direct experimental access to the transversity GPDs.

Figure 1

Schematic diagram of the ${\pi }^0$ electroproduction amplitude in the framework of the handbag mechanism. The helicities of the initial and final nucleons are denoted by $\nu$ and ${\nu }^{\prime }$, the incident photon and produced meson by $\mu$ and ${\mu }^{\prime }$, and the active initial and final quark by $\lambda$ and ${\lambda }^{\prime }$. The arrows in the figure represent the corresponding helicities.

Figure 2

The extracted structure functions vs $t$ for the bins with the best kinematic coverage and for which there are theoretical calculations. The solid curves are theoretical predictions produced with the models of Ref. [15] and the dashed are from [16]. The data and curves are as follows: the positive value circles (black) and curves are ${\sigma }_U(={\sigma }_T+ϵ{\sigma }_L)$, the negative value triangles (blue) and curves are ${\sigma }_{TT}$, and the squares (red) with accompanying curves are ${\sigma }_{LT}$. The shaded bands reflect the experimental systematic uncertainties.