Remarks on decays ofhb(2P)

Abstract

We consider hadronic transitions from the ${h}_{b}(2P)$ bottomonium resonance to lower states of bottomonium with emission of either a $\ensuremath{\omega}$ meson, or two pions, or a $\ensuremath{\eta}$ meson. For the former two transitions the branching ratios are related to similar transitions from ${\ensuremath{\chi}}_{b1}(2P)$ and the recently measured 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 ${\ensuremath{\chi}}_{b1}(1,2P)$. The contradiction gets even stronger, if the transition ${h}_{b}(2P)\ensuremath{\rightarrow}\ensuremath{\Upsilon}(1S)\ensuremath{\eta}$ has a branching fraction of a few percent or more. We argue that, although quite uncertain, the latter fraction may indeed be that significant.