$Z_b$ and $Z_c$ Exotic States as Coupled Channel Cusps

Abstract

It is demonstrated that the candidate tetraquark states $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$, and $Z_c(4025)$ are coupled channel cusp effects. The model explains in a natural way the masses and quantum numbers of the putative states and the near equality of the widths of the $Z_b$ states. It is argued that the $Z_c(3900)$ and $Z_c(4025)$ should be visible in ${\bar{B}}^0\to J/\psi {\pi }^0{\pi }^0$ or $B^{-}\to J/\psi {\pi }^{-}{\pi }^0$, but should {\it not} appear in ${\bar{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$, in agreement with recent LHCb results. Additional tests for cusp effects are suggested.

Comments: 9 pages, 9 figures. Expanded discussion of previous work; expanded discussion of B decays; analysis of Zc(4025) added; additional implications added