Helicity amplitudes and crossing relations for 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 $p \bar{p}\to l^+ l^-$ in the s channel including the lepton mass. The relative signs of these amplitudes are determined using simple invariance properties. Helicity amplitudes for the annihilation reaction $p \bar{p} \to N \bar{N}$ are also given, where $N$ is any spinor particle with structure. Crossing relations between the $e p \to e p$ scattering and the $p \bar{p}\to l^+ l^-$ 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.