Planar and non-planar baryon-antibaryon annihilation into two mesons and meson-nucleon scattering in the 1/Nc expansion

It is argued that in the antiproton-proton annihilation into two mesons p̄p −→ m1m2, the origin of different angular momentum selection rules commonly obtained for planar annihilation diagrams A2 and for non-planar rearrangement diagrams R2 lies in the omission of momentum transfer between an annihilated antiquark-quark pair and a remaining quark or antiquark. Therefore, there is no reason for dismissing non-planar R2 diagrams in favor of planar A2 diagrams. Some considerations in the related crossed-channel meson-nucleon scattering m1N −→ m2N , within the framework of QCD in the limit of large Nc, shed light on the planar and non-planar contributions to the total annihilation amplitude. In this limit of QCD, it is shown that the N̄N annihilation into two mesons is of order N c for A2 and Nc for R2 diagrams. This Nc-order in the A2 case is already known from baryon-meson scattering as investigated by Witten. ∗ [email protected] Unité de Recherche des Universités Paris 6 et Paris 7, associée au CNRS