The nature of $Z_b$ states from a combined analysis of $\Upsilon(5S)\rightarrow h_b(mP) \pi^+ \pi^-$ and $\Upsilon(5S)\rightarrow B^{(\ast)}\bar B^{(\ast)}\pi$

TL;DR

This study analyzes the $Z_b$ states using combined decay data and effective field theory, suggesting they contain both molecular and compact components, with the latter possibly constituting up to 40% of the states.

Contribution

It introduces a combined analysis approach to determine the internal structure of $Z_b$ states, considering scenarios with pure molecular states and states with compact components.

Findings

Data favor $Z_b$ states having some compact components.

Probability of compact components in $Z_b$ states may be up to 40%.

Effective field theory effectively describes the resonance parameters.

Abstract

With a combined analysis of data on $\Upsilon(5S)\rightarrow h_b(1P,2P)\pi^+\pi^-$ and $\Upsilon(5S)\rightarrow B^{(\ast)}\bar B^{(\ast)}\pi$ in an effective field theory approach, we determine resonance parameters of $Z_b$ states in two scenarios. In one scenario we assume that $Z_b$ states are pure molecular states, while in the other one we assume that $Z_b$ states contain compact components. We find that the present data favor that there should be some compact components inside $Z_b^{(\prime)}$ associated with the molecular components. By fitting the invariant mass spectra of $\Upsilon(5S)\rightarrow h_b(1P,2P)\pi^+\pi^-$ and $\Upsilon(5S)\rightarrow B^{(\ast)}\bar B^{\ast}\pi$, we determine that the probability of finding the compact components in $Z_b$ states may be as large as about $40\%$.