Planar versus non-planar N̅ N annihilation into mesons in the light of q̅ q operators and the 1/N_c expansion

It is argued that in the antiproton-proton annihilation into two mesons, p̅ p→m₁m₂, the origin of different restrictive 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. If momentum transfer is included, there is no reason for dismissing one type of diagram in favor of another one. Some considerations in the large-N_c limit of QCD equally shed light on the planar and non-planar contributions to the total N̅ N→m₁m₂ annihilation amplitude.