Relativistically invariant analysis of $\Delta $--isobar production in deuteron electrodisintegration: $e^-+d\to e^-+\Delta +N:$ general analysis of polarization effects

TL;DR

This paper develops a relativistically invariant formalism to analyze polarization effects in $$-isobar production during deuteron electrodisintegration, providing general expressions for cross sections and polarization observables based on structure functions.

Contribution

It introduces a comprehensive, general formalism for polarization effects in deuteron electrodisintegration, applicable to various polarization states and kinematic variables, based on structure functions and reaction amplitudes.

Findings

Derived expressions for differential cross sections and polarization observables.

Analyzed dependence of asymmetries on azimuthal angle and photon polarization.

Calculated polarization effects due to strong $ N$ interactions in the final state.

Abstract

The differential cross section and the polarization observables for $\Delta $--isobar production in the deuteron electrodisintegration process, $e^-+d\to e^-+\Delta +N$, are calculated in a general formalism based on structure functions. The obtained expressions have a general nature, hold for one--photon--exchange, assuming P--invariance of the electromagnetic interaction and the conservation of the hadron electromagnetic current. The dependence of the differential cross section of the $e^-+d\to e^- +\Delta +N$ reaction on the vector and tensor polarizations of the deuteron target with unpolarized and longitudinally polarized electrons is considered. The general dependence of the asymmetries on two of five kinematic variables, the azimuthal angle $\phi$ and $\epsilon$ (linear polarization of the virtual photon) is calculated. A similar analysis is performed for the polarization of the nucleon produced in $\gamma ^*d \to \Delta N$ reaction provided the electron beam is unpolarized or longitudinally polarized. Polarization effects, which are due to the strong $\Delta N-$ interaction in the final state are calculated. The photoproduction of the $\Delta $--isobar on the deuteron target has been considered in detail, as a particular case. The differential cross section and various polarization observables have been derived in terms of the reaction amplitudes. The polarization observables due to the linear and circular polarizations of the photon, when the deuteron target is arbitrarily polarized have been derived in terms of the reaction amplitudes. The polarization of the final nucleon is also considered.