Exploring possible triangle singularities in the $\hat{I}{ž}_b^{-}\to K^{-}J/\ddot{I}ˆ\hat{I}›$ decay

Abstract

We analyze possible singularities in the $J/\ddot{I}ˆ\hat{I}›$ invariant mass distribution of the $\hat{I}{ž}_b^{-}\to K^{-}J/\ddot{I}ˆ\hat{I}›$ process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with $\hat{I}{ž}^{\ast }$-charmonium-$\hat{I}›$ intermediate states, the one from the $\ddot{I}{‡}_{c1}\hat{I}ž(2120)\hat{I}›$ loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs $S$- and $P$-waves in $\ddot{I}{‡}_{c1}\hat{I}›$ and $J/\ddot{I}ˆ\hat{I}›$ systems, respectively, when the quantum numbers of these systems are $1/2^{+}$ or $3/2^{+}$. When the quantum numbers of the $\hat{I}ž(2120)$ are $J^P=1/2^{+}$, $1/2^{-}$ or $3/2^{+}$, the peak structure should be sharper than the other $J^P$ choices. This suggests that although the whole strength is unknown, we should pay attention to the contributions from the $\hat{I}{ž}^{\ast }$-charmonium-$\hat{I}›$ triangle diagram if structures are observed in the $J/\ddot{I}ˆ\hat{I}›$ invariant mass spectrum experimentally. In addition, a few triangle diagrams with the $D_{s1}^{\ast }(2700)$ as one of the intermediate particles can also produce singularities in the $J/\ddot{I}ˆ\hat{I}›$ distribution, but at higher energies above 4.9 GeV.