Hindered magnetic dipole transitions between P-wave bottomonia and coupled-channel effects

In the hindered magnetic dipole transitions of heavy quarkonia, the coupled-channel effects originating from the coupling of quarkonia to a pair of heavy and anti-heavy mesons can play a dominant role. Here, we study the hindered magnetic dipole transitions between two $P$-wave bottomonia, $\chi_b(n P)$ and $h_b(n^\prime P)$, with $n\neq n^\prime$. In these processes the coupled-channel effects are expected to lead to partial widths much larger than the quark model predictions. We estimate these partial widths which, however, are very sensitive to unknown coupling constants related to the vertices $\chi_{b0}(nP)B\bar B$. A measurement of the hindered M1 transitions can shed light on the coupled-channel dynamics in these transitions and hence on the size of the coupling constants. We also suggest to check the coupled-channel effects by comparing results from quenched and fully dynamical lattice QCD calculations.