Scaling study of the pion electroproduction cross sections

The ${}^1\mathrm{H}(e,\hspace{0.5em}{e}^{\text{'}}{\pi }^{+})n$ cross section was measured for arange of four-momentum transfer up to $Q^2=3.91\hspace{0.5em}{\mathrm{GeV}}^2$ at values of the invariant mass $W$ above the resonance region. The $Q^2$ dependence of the longitudinal component was found to be consistent with the $Q^2$-scaling prediction for hard exclusive processes. This suggests that the QCD factorization theorem is applicable at rather low values of $Q^2$. The transverse term falls off slower than the naive $Q^{-8}$ expectation and remains appreciable even at $Q^2=3.91\hspace{0.5em}{\mathrm{GeV}}^2$.

Figure 1

The $t$ dependence of the separated cross sections from E01-107 data. The error bars include the statistical and uncorrelated systematic uncertainty combined in quadrature, and the error band includes the correlated and $t$-correlated systematic uncertainties. The solid black lines denote the best fit of the VGL/Regge model [6] to the data. The fit parameter is the pion cutoff, which relates to the pion form factor in a monopole form. The fit value for the pion cutoff is ${\Lambda }_{\pi }^2=0.518\hspace{0.5em}{\mathrm{GeV}}^2$ at $Q^2=2.15\hspace{0.5em}{\mathrm{GeV}}^2$, and ${\Lambda }_{\pi }^2=0.584\hspace{0.5em}{\mathrm{GeV}}^2$ at $Q^2=3.91\hspace{0.5em}{\mathrm{GeV}}^2$. The value for the ρ cutoff was taken to be ${\Lambda }_{\rho }^2=1.7\hspace{0.5em}{\mathrm{GeV}}^2$ at both values of $Q^2$. The red-dashed curve shows the result of a calculation using the VGG/GPD model [7].

Figure 2

The $Q^2$ dependence of the separated cross sections at fixed values of $-t$ and $x_B$. The error bars denote the statistical and systematic uncertainties combined in quadrature. The red, solid curve shows a fit of the form $Q^{-6}$ for ${\sigma }_L$ and $Q^{-8}$ for ${\sigma }_T$. The green dotted line is a GPD calculation from Ref. [7]. In this calculation, power corrections to the leading order are included. The blue dashed line is a VGL/Regge [6] calculation using ${\Lambda }_{\pi }^2$ from a global fit to $F_{\pi }$.