Mixing of partial waves near $B^* \bar B^*$ threshold in $e^+e^-$ annihilation

We consider the production of $B^* \bar B^*$ meson pairs in $e^+e^-$ annihilation near the threshold. The rescattering due to pion exchange between the mesons results in a mixing between three partial wave amplitudes: two $P$-wave with the total spin of the meson pair S=0 and S=2 and an F-wave amplitude. The mixing due to pion exchange with a low momentum transfer is calculable up to c.m. energy $E \approx 15 \div 20$\,MeV above the threshold. We find that the $P-F$ mixing is numerically quite small in this energy range, while the mixing of the two P-wave amplitudes is rapidly changing with energy and can reach of order one at such low energies.