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

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 $Z_b^{(\prime)}$.