Lorentz contraction, geometry and range in antiproton-proton annihilation into two pions

We present a geometric interpretation of the so-called annihilation range in reactions of the type p-barp → two light mesons based upon Lorentz effects in the highly relativistic final states (γ = Ecm/2mc2 ≅ 6.8 - 8.0). Lorentz-boosted meson wave functions, within the framework of the constituent quark model, result in a richer angular dependence of the annihilation amplitudes and thus in higher partial wave contributions (J > 1) than usually obtained. This approach sheds some light on what could be a 'short' annihilation range and how it is influenced by the angular distribution of the final states