Study of resonant processes for multi-pion production in $bar p +ptoell ^++ell^- +n_pi pi$ annihilation

In frame of a phenomenological approach based on Compton-like Feynman amplitudes, we study multi-pion production in antiproton nucleon collisions. The main interest of this reaction is related to the possibility to study the properties of the presumable $bar N N$ atom and of its resonances. For the case of formation of a scalar or pseudoscalar resonant state, with $I^G(J^{P})=1^-(0^{pm}),~0^+(0^-)$ numerical results are obtained. The differential cross section in an experimental set-up where the pions invariant mass is measured, is given with explicit dependence on the lepton pair and pions invariant mass.