The LHCb state $P_{\psi s}^\Lambda(4338)$ as a triangle singularity

TL;DR

This paper models the $J/ar{ ext{}}$ spectrum in certain decays, explaining the $P_{ ext{}}$ baryon as a triangle singularity, and predicts related signals and isospin effects.

Contribution

It introduces a triangle diagram model to interpret the $P_{ ext{}}$ baryon as a singularity, providing a novel explanation for its observed peak.

Findings

The $P_{ ext{}}$ peak is explained as a triangle singularity.

Predicted similar signals in $ ext{eta}_c ext{Lambda}$ decays.

Possible large isospin mixing effects in certain decay channels.

Abstract

We present a model for the $J/\psi\Lambda$ spectrum in $B^-\to J/\psi \Lambda \bar{p}$ decays, including the $P_{\psi s}^\Lambda(4338)$ baryon recently observed by the LHCb collaboration. We assume production via triangle diagrams which couple to the final state via non-perturbative interactions which are constrained by heavy-quark and $SU_3$-flavor symmetry. The bulk of the distribution is described by a triangle diagram with a color-favored electroweak vertex, while the sharp $P_{\psi s}^\Lambda(4338)$ enhancement is due to the triangle singularity in another diagram featuring a $1/2^-$ baryon consistent with $\Sigma_c(2800)$. We predict a comparable $P_{\psi s}^\Lambda(4338)$ signal in $\eta_c \Lambda$, and anticipate possible large isospin mixing effects through decays to $J/\psi \Sigma^0$ and $\eta_c \Sigma^0$