Polarization effects in the N̄ + N → π + ℓ + + ℓ − reaction: General analysis and numerical estimations

A general formalism is developed to calculate the cross section and the polarization observables for the reaction N̄+N→π+ℓ++ℓ-. The matrix element and the observables are expressed in terms of six scalar amplitudes (complex functions of three kinematical variables) that determine the reaction dynamics. The numerical predictions are given in the frame of a particular model in the kinematical range accessible in the antiproton annihilation at Darmstadt (PANDA) experiment at the Facility for Antiproton and Ion Research (FAIR).