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The decays of the $Z_b(10610)$ and the $Z_b(10650)$ to $\Upsilon(nS)\pi$,$h_b(mP)\pi$ and $\chi_{bJ}(mP)\gamma$ ($n=1,2,3$, $m=1,2$ and $J=0,1,2$) areinvestigated within a nonrelativistic effective field theory. It is arguedthat, while the decays to $\Upsilon(nS) \pi$ suffer from potentially largehigher order corrections, the $P$-wave transitions of the $Z_b$ states offerthe best possibility to confirm the nature of the $Z_b$ states as molecularstates and to further study their properties. We give nontrivial andparameter-free predictions for the ratios of various partial widths for finalstates with $h_b(mP)\pi$ and $\chi_{bJ}(mP)\gamma$. In addition, the branchingfractions for the neutral $Z_b$-states to $\chi_{bJ}\gamma$ are predicted to beof order $10^{-4}$--$10^{-3}$. This provides a fine test of the molecularnature in future high-luminosity experiments.

Confirming the molecular nature of the $Z_b(10610)$ and the $Z_b(10650)$