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A Discussion on Triangle Singularities in the $\Lambda_b \to J/\psi K^{-} p$ Reaction

4 Pith papers cite this work. Polarity classification is still indexing.

4 Pith papers citing it
abstract

We have analyzed the singularities of a triangle loop integral in detail and derived a formula for an easy evaluation of the triangle singularity on the physical boundary. It is applied to the $\Lambda_b \rightarrow J/\psi K^{-} p$ process via $\Lambda^*$-charmonium-proton intermediate states. Although the evaluation of absolute rates is not possible, we identify the $\chi_{c1}$ and the $\psi(2S)$ as the relatively most relevant states among all possible charmonia up to the $\psi(2S)$. The $\Lambda(1890)\, \chi_{c1}\, p$ loop is very special as its normal threshold and triangle singularities merge at about 4.45 GeV, generating a narrow and prominent peak in the amplitude in the case that the $\chi_{c1}\, p$ is in an $S$-wave. We also see that loops with the same charmonium and other $\Lambda^*$ hyperons produce less dramatic peaks from the threshold singularity alone. For the case of $\chi_{c1}\, p \rightarrow J/\psi\, p$ and quantum numbers $3/2^-$ or $5/2^+$ one needs $P$- and $D$-waves, respectively, in the $\chi_{c1}\, p$, which drastically reduce the strength of the contribution and smooth the threshold peak. In this case we conclude that the singularities cannot account for the observed narrow peak. In the case of $1/2^+$, $3/2^+$ quantum numbers, where $\chi_{c1}\, p \rightarrow J/\psi\, p$ can proceed in an $S$-wave, the $\Lambda(1890)\,\chi_{c1}\,p$ triangle diagram could play an important role, though can neither assert their strength without further input from experiments and lattice QCD calculations.

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representative citing papers

Effects of Final State Interactions on Landau Singularities

hep-ph · 2024-07-25 · unverdicted · novelty 5.0

Triangle singularities mimicking resonances are analyzed in the presence of final-state rescattering using Landau equations and a scattering formalism enforcing two- and three-body unitarity.

Neutrinoless double-beta decay of the $\Delta^-$ resonance

hep-ph · 2026-04-14 · unverdicted · novelty 5.0

Chiral EFT derivation of the Δ⁻ → p e⁻ e⁻ amplitude including long-range neutrino loops, short-range counterterms, pion-mass dependence for collinear electrons, and a long-range prediction in the degenerate Δ-nucleon mass limit.

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