The reaction antirproton-proton into pi+pi-: relativistic aspects and final-state interaction in the pion wave functions

We use a distorted wave approximation approach which includes $^3P_0$ and $^3S_1$ quark-antiquark annihilation mechanisms to reproduce the data set from LEAR on $\bar p p\to \pi^+\pi^-$ in the range from 360 to 1550 MeV/c. Improvements of the model are sought by implementing final-state interactions of the pions and by observing that the annihilation is too short-ranged in earlier attempts to describe the data. While the former improvement is due to to the final-state $\pi\pi$ wave functions solely, the latter one originates from quark wave functions for proton, antiproton, and pions with radii slightly larger than the respective measured charge radii. This increase in hadron radius, as compared with typically much smaller radii used before in the quark model, increases the annihilation range and thereby the amplitudes for $J\ge2$ are much higher. Finally, given the very high kinetic energy of the final pions, we investigate the role of relativistic corrections in the pion wave functions when boosted into the center-of-mass frame.