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 ${\rm Y}(5S)\to {\rm Y}(nS){\pi }^{+}{\pi }^{-}$ for $n$ = 1, 2, or 3, and ${\rm Y}(5S)\to h_b(mP){\pi }^{+}{\pi }^{-}$ for $m=1$ or 2. These resonances lie very close to the $B^{\ast }\bar{B}$ and $B^{\ast }{\bar{B}}^{\ast }$ thresholds, respectively. A recent Belle analysis of the three-body decays ${\rm Y}(5S)\to [B^{(\ast )}{\bar{B}}^{(\ast )}{]}^{\mp }{\pi }^{\pm }$ 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 ${\rm Y}(5S)\to B^{(\ast )}{\bar{B}}^{(\ast )}$ decays, which requires the inclusion of heavy quark spin symmetry (HQSS) violating operators. We then calculate the differential distribution for ${\rm Y}(5S)\to B^{(\ast )}{\bar{B}}^{(\ast )}\pi$ as a function of the invariant mass of the $B^{(\ast )}{\bar{B}}^{(\ast )}$ pair, obtaining qualitative agreement with experimental data. We also calculate angular distributions in the decay ${\rm Y}(5S)\to Z_b^{(\prime )}\pi$ which are sensitive to the molecular character of the $Z_b^{(\prime )}$.

Comments: 21 pages, 5 figures