Formula omitted] annihilation and scattering in a quark model

Abstract

p p annihilation into mesons in flight and at rest are analysed in the constituent quark model with the 3P 0 and the 3S 1 model for the q q pair creation/annihilation vertex. In the 3P 0 model, one assumes that the created/annihilated q q pair has the quantum number of the vacuum, while in the 3S 1 model, it has the quantum number of a gluon. As the meson channels we consider combinations of s-wave mesons and p-wave mesons, and in the annihilation into two mesons we compare the annihilation model (A2), the rearrangement model with a 3P 0 vertex (R2) and the rearrangement with a 3S 1 vertex (S2). The initial state interaction is taken into account by solving the coupled Lippmann-Schwinger equation including virtual N Δ ± NΔ and Δ Δ channels. The combination of R3 and A2 in the 3P 0 model roughly reproduces the branching ratios of p p annihilation into mesons, while the combination of R3 and R2 and the combination of R3 and S2 show worse agreement with the experimental branching ratios. The total p p annihilation cross section turned out to be about 60% of the experimental value for R3 + A2 and R3 + R2 and about 70% for R3 + S2, which means that we need other mechanisms of p p annihilation into mesons. The channel of virtual Δ's modifies the branching ratios of certain partial waves, but in the total annihilation cross section, the effect of Δ's is not large.