Exploring possible triangle singularities in the $\Xi^-_{b} \to K^- J/\psi \Lambda$ decay

TL;DR

This paper investigates triangle singularities in the decay $ ext{Xi}_b^- o K^- J/ ext{psi} ext{Lambda}$, identifying specific loop diagrams that could produce observable effects in the $J/ ext{psi} ext{Lambda}$ invariant mass spectrum, especially around 4628 MeV.

Contribution

It is the first detailed analysis of triangle singularities in this decay process, highlighting the most likely diagrams and conditions for observable effects.

Findings

Triangle singularities are found in 18 diagrams, notably around 4628 MeV.

The peak sharpness depends on the quantum numbers of involved particles.

Additional singularities may occur at energies above 4.9 GeV with different intermediate states.

Abstract

We analyze possible singularities in the $J/\psi \Lambda$ invariant mass distribution of the $\Xi^-_{b}~\to~K^- J/\psi \Lambda$ process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with $\Xi^*$-charmonium-$\Lambda$ intermediate states, the one from the $\chi_{c1} \Xi(2120) \Lambda$ loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs $S$- and $P$-waves in $\chi_{c1} \Lambda$ and $J/\psi \Lambda$ systems, respectively, when the quantum numbers of these systems are $1/2^+$ or $3/2^+$. When the quantum numbers of the $\Xi(2120)$ 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 $\Xi^*$-charmonium-$\Lambda$ triangle diagram if structures are observed in the $J/\psi \Lambda$ invariant mass spectrum experimentally. In addition, a few triangle diagrams with the $D_{s1}^*(2700)$ as one of the intermediate particles can also produce singularities in the $J/\psi\Lambda$ distribution, but at higher energies above 4.9 GeV.