Electroproduction of pseudoscalar mesons on the deuteron

A general analysis of polarization phenomena for coherent meson electroproduction on deuterons, $e+ d\to e+ d +P^0$, where $P^0$ is a pseudoscalar $\pi ^0$ or $\eta$-meson, is presented. The spin structure of the electromagnetic current for $P^0$-production at threshold is parametrized in terms of specific (inelastic) threshold electromagnetic form factors which depend on the momentum transfer squared and the effective mass of the produced hadronic system. We give expressions for the structure functions of the reaction $e+\vec{d}\to e +d+ P^0$ (where the deuteron target is polarized) in terms of these threshold form factors. The spin and isospin structures of the $\gamma ^{*}+d\to d+P^0$ amplitudes (where $\gamma ^*$ is a virtual photon) is established in the framework of the impulse approximation and relationships between meson electroproduction on deuterons and on nucleons are given. The reaction of $\pi^0$ electroproduction on deuterons is investigated in detail both at threshold and in the region of $\Delta$-isobar excitation, using the effective Lagrangian approach for the calculation of the amplitudes of the elementary process $\gamma^*+N\to N+\pi$. Special attention is devoted to the analysis of all standard contributions to the exclusive cross section for $d(e,e\pi^0)d$, which are functions of the momentum transfer square, $k^2$, of the excitation energy of the produced hadrons and of the pion production angle, in a region of relatively large momentum transfer. The sensitivity of these contributions to different parametrizations of the $\gamma^*\pi\omega$ form factor as well as to the choice of $NN-$potential is discussed.