Helicity amplitudes and crossing relations for one-photon exchange antiproton proton reactions

Antiproton proton annihilation reactions allow unique access to the moduli and phases of nucleon electromagnetic form factors in the time-like region. We present the helicity amplitudes for the unequal-mass single-photon reaction p¯ → l + l - in the s channel including the lepton mass. The relative signs of these amplitudes are determined using simple invariance properties. Helicity amplitudes for one-photon exchange annihilation reaction p¯ → B¯ are also given, where B is any spin-one-half particle with structure. Crossing relations between the ep → ep scattering and the p¯ → l + l - annihilation channels are discussed and the crossing matrix for the helicity amplitudes is given. This matrix may be used to verify known expressions for the space-like helicity amplitudes due to one-photon exchange