Threshold pion electroproduction at large momentum transfers

We consider pion electroproduction close to threshold for $Q^2$ in the region $1–10{\mathrm{GeV}}^2$ on a nucleon target. The momentum transfer dependence of the S-wave multipoles at threshold, $E_{0+}$ and $L_{0+}$, is calculated in the chiral limit using light-cone sum rules. Predictions for the cross sections in the threshold region are given taking into account P-wave contributions that, as we argue, are model independent to a large extent. The results are compared with the SLAC E136 data on the structure function $F_2(W,Q^2)$ in the threshold region.

Figure 1

Schematic structure of the light-cone sum rule for pion electroproduction.

Figure 2

The LCSR-based model (solid curves) for the $Q^2$ dependence of the electric and longitudinal partial waves at threshold $E_{0+}$ and $L_{0+}$, (3.1), in units of ${\mathrm{GeV}}^{-1}$, normalized to the dipole formula (3.5).

Figure 3

The differential cross section $d{\sigma }_{{\gamma }^{*}p\to {\pi }^{0}p}/d{\Omega }_{\pi }$ (in $\mu b$) as a function of $\cos \theta$ for ${\varphi }_{\pi }=135$ grad for $Q^2=4.2{\mathrm{GeV}}^2$ and $W=1.11\mathrm{GeV}$.

Figure 4

The integrated cross section $Q^6{\sigma }_{{\gamma }^{*}p\to {\pi }^{0}p}$ (in units of $\mu b\times {\mathrm{GeV}}^6$) as a function of $Q^2$ for $W=1.11\mathrm{GeV}$ (lower curve) and $W=1.15\mathrm{GeV}$ (upper curve).

Figure 5

The structure function $F_2^p(W,Q^2)$ as a function of $W^2$ scaled by a factor ${10}^3$ compared to the SLAC E136 data [22] at the average value $Q^2=7.14{\mathrm{GeV}}^2$ (upper panel) and $Q^2=9.43{\mathrm{GeV}}^2$ (lower panel).

Figure 6

The S-wave (solid line) vs the P-wave (dashed line) contribution to the structure function $F_2^p(W,Q^2)$ as a function of $W^2$ for $Q^2=7.14{\mathrm{GeV}}^2$.

Figure 7

The contribution of the ${\pi }^{0}p$ final state to the structure function $F_2^p(W,Q^2)$ as a function of $W^2$ for $Q^2=3{\mathrm{GeV}}^2$ (upper curve) and $Q^2=9{\mathrm{GeV}}^2$ (lower curve).

Figure 8

Schematic structure of the pole terms in the correlation function (a1)

Figure 9

The ratios of the LCSR predictions for the generalized form factors $G_1^{{\pi }^{0}p}$ (upper panel) and $G_2^{{\pi }^{0}p}$ (lower panel) to the corresponding results in the soft-pion limit, Eq. (3.3). The solid and the dashed curves correspond to the calculation with Borel parameter $M^2=2{\mathrm{GeV}}^2$ and $M^2=1{\mathrm{GeV}}^2$, respectively.

Figure 10

The LCSR-based model (solid curves) for the $Q^2$ dependence of the form factors $G_{1,2}^{{\pi }^{0}p}$ (left) and $G_{1,2}^{{\pi }^{+}n}$ (right), (3.1), normalized to the dipole formula (3.5). The pure LCSR predictions (all form factors and other input taken directly from the sum rules) are shown by the dashed curves for comparison.

Figure 11

The LCSR-based model (solid curves) for the $Q^2$ dependence of the form factors $G_{1,2}^{{\pi }^{0}n}$ (left) and $G_{1,2}^{{\pi }^{-}p}$ (right), normalized to the dipole formula (3.5). The pure LCSR predictions (all form factors and other input taken directly from the sum rules) are shown by the dashed curves for comparison.