Partial waves in $B_s^* \bar B_s^*$ production in $e^+e^-$ annihilation near threshold

The production of the vector meson pairs $B_s^* \bar B_s^*$ in the $e^+e^-$ annihilation is generally contributed by two $P$ wave amplitudes with different total spin $S$ of the mesons, $S=0$ and $S=2$, and also by an $F$ wave amplitude. Belle has recently reported a study of the available data at the energy of the $\Upsilon(5S)$ peak in terms of the two $P$ wave contributions only. It is argued here that although at this energy the $F$ wave should be quite suppressed, especially for the strange-bottom vector mesons, the particular studied angular distribution is very sensitive to a presence of even small $F$ wave amplitude due to a significant interference with the dominant $S=2$ $P$ wave. Thus the available data are not conclusive with regards to the partial wave structure of the production amplitude. Additional angular correlations are discussed that can be measured for a full amplitude analysis of the production process.