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

TL;DR

This paper investigates the decay patterns of the $Z_b$ states to confirm their molecular nature, providing parameter-free predictions for decay ratios and branching fractions, especially emphasizing the importance of $P$-wave transitions.

Contribution

It offers the first nonrelativistic effective field theory analysis of $Z_b$ decays, predicting decay ratios and branching fractions without free parameters to test their molecular structure.

Findings

Predicted decay ratios for $h_b(mP)\pi$ and $\chi_{bJ}(mP)\gamma$ final states.

Branching fractions for neutral $Z_b$ states to $\chi_{bJ}\gamma$ are of order $10^{-4}$--$10^{-3}$.

$P$-wave transitions are identified as the best probes for the molecular nature of $Z_b$ states.

Abstract

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 $J=0,1,2$) are investigated within a nonrelativistic effective field theory. It is argued that, while the decays to $\Upsilon(nS) \pi$ 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 $h_b(mP)\pi$ and $\chi_{bJ}(mP)\gamma$. In addition, the branching fractions for the neutral $Z_b$-states to $\chi_{bJ}\gamma$ are predicted to be of order $10^{-4}$--$10^{-3}$. This provides a fine test of the molecular nature in future high-luminosity experiments.