Electroproduction, photoproduction, and inverse electroproduction of pions in the first resonance region

Methods are set forth for determining the hadron electromagnetic structure in the sub-$N\stackrel{̲}{N}$-threshold timelike region of the virtual-photon “mass” and for investigating the nucleon weak structure in the spacelike region from experimental data on the process $\pi N\to e^{+}{e}^{-}N$ at low energies. These methods are formulated using the unified description of photoproduction, electroproduction, and inverse electroproduction of pions in the first resonance region in the framework of the dispersion-relation model and on the basis of the model-independent properties of inverse electroproduction. Applications of these methods are also shown.

Figure 1

Differential cross section for $\gamma n\to p{\pi }^{-}$ as a function of energy in (a) and (b) and pion angle in (c) and (d). Experimental data are taken from Ref. 33.

Figure 2

W and ${\lambda }^2$ dependences of the transversal ${\sigma }_T$ and longitudinal ${\sigma }_L$ parts of the cross section (20) for the inclusive pion (${\pi }^{+}$ and ${\pi }^0$) electroproduction on the proton in the first resonance region. Experimental data on the inclusive $p(e,e\text{'})$ process are from Ref. 34 and the photoproduction points, squares in (c) and (d), are from Ref. 35.

Figure 3

${\lambda }^2$ dependence of the differential cross section for the forward electroproduction of pions by transversal (a) and longitudinal (b) virtual photons. Experimental data are from Refs. 36 and [37].

Figure 4

Comparison of CA calculations for $E_{0+}-2E_{2-}$ of the ${\pi }^{-}p\to {\gamma }^{*}n$ process with experimental data: dashed and solid curves correspond to the cases when $G_P$ is approximated by the pion pole $G_P^{\pi }$ and the prescription (31) is assumed, respectively. See the text for explanation of the data points.

Figure 5

Ratio $G_P(t)/G_P^{\pi }(t)$ as calculated with formula (31). The points on the curve with the error bar indicate the error corridor for this curve. Results of the data analysis on the μ capture in hydrogen (▽) [41] and on the ${\pi }^{+}$ electroproduction off the proton near the threshold (△) [45] are also depicted.

Figure 6

Compensation curves for $\gamma p\to {\pi }^{+}n$ and $\gamma n\to {\pi }^{-}p$. Along these curves the differential cross section is described by EBM. At high energies, the compensation curve passes through the scattering angles corresponding to the value of the invariant momentum transfer $t\simeq -0.04\hspace{1em}(\mathrm{GeV}/c){}^2$.