Relativistic treatment of pion wave functions in the annihilation p̄p→π^-π⁺

Quark model intrinsic wave functions of highly energetic pions in the reaction p̄p→π^-π⁺ are subjected to a relativistic treatment. The annihilation is described in a constituent quark model with A2 and R2 flavor-flux topology, and the annihilated quark-antiquark pairs are in ³P₀ and ³S₁ states. We study the effects of pure Lorentz transformations on the antiquark and quark spatial wave functions and their respective spinors in the pion. The modified quark geometry of the pion has considerable impact on the angular dependence of the annihilation mechanisms.