Relativistic effects in proton-antiproton annihilation into two mesons.

Abstract

The effects of the small components of Dirac spinors, used to describe quark and antiquark wave functions in clusters, and the Lorentz contraction of cluster wave functions associated with the Lorentz transformation to the overall center of momentum frame are considered in the proton-antiproton annihilation into two final state mesons. A quark-antiquark pair annihilation and creation model in the planar picture that reproduces the principly observed final states in the nonrelativistic case is used. The effects are studied by taking the nonrelativistic model as a base of comparison. The introduction of small components in the quark wave functions has little influence on predictions of relative ratios of annihilation amplitudes into final state mesons in the same relative angular momentum state of the initial proton and antiproton. In contrast, the small components give a large contribution to the absolute value of the annihilation amplitude in dependence on the initial relative angular momentum. The effects of including the Lorentz contraction of the cluster wave functions appear in the annihilation amplitudes of two meson final states. By using Lorentz transformed Gaussian wave functions for the clusters, subsequent effects on the annihilation amplitudes into two mesons, such as \ensuremath{\pi}\ensuremath{\pi}, \ensuremath{\rho}\ensuremath{\pi}, and \ensuremath{\rho}\ensuremath{\rho}, are studied. For a nucleon radius of 〈${\mathit{r}}^{2}$${\mathrm{〉}}_{\mathit{N}}^{1/2}$=0.62 fm and a global meson radius of 〈${\mathit{r}}^{2}$${\mathrm{〉}}_{\mathit{M}}^{1/2}$=0.50 fm, the production of two final state pions is enhanced upon including the Lorentz contraction effects.