Remarks on decays of h_b(2P)

We consider hadronic transitions from the $h_b(2P)$ bottomonium resonance to lower states of bottomonium with emission of either $ω$ meson, or two pions, or $η$ meson. For the former two transitions the branching ratios are related to similar transitions from $χ_{b1}(2P)$ and the recently measured by Belle fractions of the radiative decays of $h_b(2P)$. We argue that the fraction of the $h_b(2P)$ total decay rate remaining for the annihilation rate is on the verge of contradiction with the `parton' picture of bottomonium annihilation resulting in similarity between the decays of $h_b(1,2P)$ and $χ_{b1}(1,2P)$. The contradiction gets even stronger, if the transition $h_b(2P) \to Υ(1S) \, η$ has branching fraction of a few percent or more. We argue that, although quite uncertain, the latter fraction may indeed be that significant.

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