Something, but not much follows from the quark line rule in nucleon-antinucleon annihilations

Abstract

Validity and consequences of the quark line rule (QLR) in nucleon (N)— antinucleon (¯N) annihilations into two or three mesons at LEAR energies are investigated. Recent data on proton-antiproton annihilation into anη orη′ together with additional non-strange pseudoscalar or vector meson (s) is used to successfully test the rule. We find that for present data any pseudoscalar meson mixing angle Φ_PS restricted to −26⁰<Φ_PS<−2.2⁰ is approximately consistent with the QLR. Since the assumptions leading to this test are valid in any present-day quark model of nucleon-antinucleon annihilation, improvement of the data will be of utmost importance. If proven valid, the QLR can be used to test if quark-antiquark annihilation dominates over quark exchange inN¯N → mesons at LEAR energies or vice versa. Previously proposed tests of the quark line diagrams (annihilation or rearrangement) describing the quark flavor flux under either of these assumptions are worked out. We investigate without a definite conclusion if dominance of annihilation over rearrangement is consistent with present data onp¯p → π⁰ π⁰,ηη, π⁰ρ⁰, π⁰ω, ηρ⁰,ηω, ρ⁰ρ⁰,ωω. As a main consequence, dominance of annihilation predicts without any ambiguity equality of the proton-antiproton annihilation cross sections σ(ωω) and σ(ρ⁰ρ⁰). Further consequences of dominance of either annihilation or rearrangement diagrams for proton-antiproton annihilation into two or three mesons are also worked out. We compare the predictions of the models we discuss to the sparse present data. It is emphasized that our predictions only exploit the quark flavor flux within the quark line diagrams that are assumed to dominate. They thus are independent of gluon contributions to these diagrams.