Line shapes in \Upsilon(5S) \to B^{(*)} \bar{B}^{(*)}\pi with Z(10610) and Z(10650) using effective field theory

TL;DR

This paper uses effective field theory to analyze the line shapes in  ext{Upsilon}(5S) decays involving Z(10610) and Z(10650), providing insights into their molecular nature and matching experimental data.

Contribution

The study develops an effective theory approach to describe  ext{Upsilon}(5S) decays involving Zb states, incorporating heavy quark spin symmetry violations and fitting existing decay data.

Findings

Qualitative agreement with experimental invariant mass distributions.

Angular distributions suggest molecular character of Zb states.

Parameters constrained using  ext{Upsilon}(5S) o B^{(*)}ar{B}^{(*)} decays.

Abstract

The Belle collaboration recently discovered two resonances, $Z_b(10610)$ and $Z_b(10650)$ --- denoted $Z_b$ and $Z_b^\prime$ --- in the decays $\Upsilon(5S) \to \Upsilon(nS) \pi^+ \pi^-$ for $n$ = 1, 2, or 3, and $\Upsilon(5S) \to h_b(mP) \pi^+ \pi^-$ for $m = 1$ or 2. These resonances lie very close to the $B^* \bar{B}$ and $B^* \bar{B}^*$ thresholds, respectively. A recent Belle analysis of the three-body decays $\Upsilon(5S) \to [B^{(*)} \bar{B}^{(*)}]^{\mp} \pi^\pm$ gives further evidence for the existence of these states. In this paper we analyze this decay using an effective theory of $B$ mesons interacting via strong short-range interactions. Some parameters in this theory are constrained using existing data on $\Upsilon(5 S) \to B^{(*)}\bar{B}^{(*)}$ decays, which requires the inclusion of heavy quark spin symmetry (HQSS) violating operators. We then calculate the differential distribution for $\Upsilon(5S) \to B^{(*)} \bar{B}^{(*)} \pi$ as a function of the invariant mass of the $B^{(*)} \bar{B}^{(*)}$ pair, obtaining qualitative agreement with experimental data. We also calculate angular distributions in the decay $\Upsilon(5S) \to Z_b^{(\prime)} \pi$ which are sensitive to the molecular character of the $Z_b^{(\prime)}$.