Testing axial and electromagnetic nucleon form factors in time-like regions in the processes $\bar p + n\to \pi^- +\ell^-+\ell^+$ and $\bar p+ p\to \pi^0 +\ell^- + \ell^+$, $\ell=e$, $\mu$

23 pages, 9 figuresIn frame of a phenomenological approach based on Compton-like Feynman amplitudes, we study the annihilation channel in antiproton nucleon collisions with production of a single charged or neutral pion and a lepton-antilepton pair. These reactions allow to access nucleon and axial electromagnetic form factors in time-like region and offer a unique possibility to study the kinematical region below two nucleon threshold. The differential cross section in an experimental set-up where the pion is fully detected is given with explicit dependence on the relevant nucleon form factors. The possibility to measure heavy charged pion in the annihilation channel is also discussed