Relativistic treatment of pion wave functions in the annihilation p ¯ p → π − π +

Quark model intrinsic wave functions of highly energetic pions in the reaction $\overline{p}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ 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 $^{3}P_{0}$ and $^{3}S_{1}$ 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.