Planar versus non-planar anti-NN annihilation into mesons in the light of anti-qq operators and the 1/Nc expansion

Abstract

It is argued that in the antiproton-proton annihilation into two mesons $\bar pp\longrightarrow m_1 m_2$, 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 it 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 $\bar NN\to m_1 m_2$ annihilation amplitude.