General Analysis of the Reaction e^+ + e^- → N + Ñ + π^0

Abstract

The general analysis of the reaction , in the case of longitudinally polarized electron beam, has been performed in the one-photon-nnihilation approximation, accounting for the polarization states of the final nucleon. This analysis is useful for the description of the continuum (non-resonant) and resonant (with different possible vector mesons or excited baryons in the intermediate virtual states of the Feynman diagrams) contributions. The conservation of the hadron electromagnetic currents and P-invariance of the hadron electromagnetic interaction were used to express the matrix element in terms of the six complex independent invariant amplitudes. The general structure of the hadronic tensor for the case of unpolarized final hadrons and polarized nucleon has been derived. The spin-independent part of the hadronic tensor is determined by five structure functions and the spin-dependent one by 13 structure functions. The transversal, longitudinal and normal components of the nucleon polarization four-vector are expressed by means of the four-vectors of the particle momenta. The five independent invariant variables which describe the reaction have been introduced. The limits of the changing of these variables have been considered. The kinematical double invariant variables regions are given in the figure. The kinematics, suitable to study the invariant mass distributions, is investigated.