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

Abstract

The decays of the $Z_b(10610)$ and the $Z_b(10650)$ to $Υ(nS)π$, $h_b(mP)π$ and $χ_{bJ}(mP)γ$ ($n=1,2,3$, $m=1,2$ and $J=0,1,2$) are investigated within a nonrelativistic effective field theory. It is argued that, while the decays to $Υ(nS) π$ suffer from potentially large higher order corrections, the $P$-wave transitions of the $Z_b$ states offer the best possibility to confirm the nature of the $Z_b$ states as molecular states and to further study their properties. We give nontrivial and parameter-free predictions for the ratios of various partial widths for final states with $h_b(mP)π$ and $χ_{bJ}(mP)γ$. In addition, the branching fractions for the neutral $Z_b$-states to $χ_{bJ}γ$ are predicted to be of order $10^{-4}$--$10^{-3}$. This provides a fine test of the molecular nature in future high-luminosity experiments.