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

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 ${\Lambda }_b\to J/\psi K^{-}p$ process via ${\Lambda }^{\ast }$-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 ${\Lambda }^{\ast }$ hyperons produce less dramatic peaks from the threshold singularity alone. For the case of ${\chi }_{c1}p\to J/\psi p$ 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 ${\chi }_{c1}p\to J/\psi p$ 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.

17 pages, 7 figures, 2 Tables

References in corpus (4)

• Prediction of narrow $N^{\ast }$ and ${\Lambda }^{\ast }$ resonances with hidden charm above 4 GeV
• On the nature of $a_1(1420)$
• $f_1(1285)$ decays into $a_0(980){\pi }^0$, $f_0(980){\pi }^0$ and isospin breaking
• Observation of the ${\Lambda }_b^0\to J/\psi p{\pi }^{-}$ decay

Cited by in corpus (58)

• Pentaquark and Tetraquark states
• Exotics: Heavy Pentaquarks and Tetraquarks
• Emergence of a complete heavy-quark spin symmetry multiplet: seven molecular pentaquarks in light of the latest LHCb analysis
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• 50 Years of Quantum Chromodynamics
• Interpretation of the LHCb $P_c$ States as Hadronic Molecules and Hints of a Narrow $P_c(4380)$
• Isospin breaking decays as a diagnosis of the hadronic molecular structure of the $P_c(4457)$
• Revisiting the nature of the $P_c$ pentaquarks
• The "$a_1(1420)$" peak as the $\pi f_0(980)$ decay mode of the $a_1(1260)$
• Novel Method for Precisely Measuring the $X(3872)$ Mass
• Coupled-channel effects of the ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$-${\Lambda }_c(2595)\bar{D}$ system and molecular nature of the $P_c$ pentaquark states from one-boson exchange model
• Role of a triangle singularity in the $\gamma p\to K^{+}\Lambda (1405)$ reaction
• Structure and decays of hidden heavy pentaquarks
• Novel approaches in Hadron Spectroscopy
• Heavy-Quark Symmetry Partners of the Pc(4450) Pentaquark
• Compositeness of S-wave weakly-bound states from next-to-leading order Weinberg's relations
• Hidden Charm Pentaquark $P_c(4380)$ and Doubly Charmed Baryon ${\Xi }_{cc}^{\ast }(4380)$ as Hadronic Molecule States
• Triangle singularity in the $J/\psi \to K^{+}{K}^{-}{f}_0(980)(a_0(980))$ decays
• Revising the $f_1(1420)$ resonance
• Hidden charm pentaquark states in a diquark model
• Triangular singularity and a possible $\varphi p$ resonance in the ${\Lambda }_c^{+}\to {\pi }^0\varphi p$ decay
• A combined analysis of the $Z_c(3900)$ and the $Z_{cs}(3985)$ exotic states
• Triangle singularity mechanism for the $pp\to {\pi }^{+}d$ fusion reaction
• Review of the low-lying excited baryons ${\Sigma }^{\ast }(1/2^{-})$
• Hidden Bottom Pentaquark States with Spin 3/2 and 5/2
• Triangle singularities in $B^{-}\to D^{\ast 0}{\pi }^{-}{\pi }^0\eta$ and $B^{-}\to D^{\ast 0}{\pi }^{-}{\pi }^{+}{\pi }^{-}$
• Abnormal isospin violation and $a_0-f_0$ mixing in the $D_s^{+}\to {\pi }^{+}{\pi }^0{a}_0(980)(f_0(980))$ reactions
• Production of $P_c$ states in ${\Lambda }_b$ decays
• Investigation of hidden-charm double strange pentaquark candidate $P_{css}$ via its mass and strong decays
• $f_2(1810)$ as a triangle singularity
• Possibility of $T_{c\bar{s}}(2900)$ as the resonance-like structure induced by threshold effects
• Threshold effects as the origin of $Z_{cs}(4000)$, $Z_{cs}(4220)$ and $X(4700)$ observed in $B^{+}\to J/\psi \varphi K^{+}$
• Strong Interaction Physics at the Luminosity Frontier with 22 GeV Electrons at Jefferson Lab
• $P_c$ states and their open-charm decays with the complex scaling method
• Hidden charm pentaquark and $\Lambda (1405)$ in the ${\Lambda }_b^0\to {\eta }_c{K}^{-}p(\pi \Sigma )$ reaction
• Decay $X(3872)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and $S$-wave $D^0{\bar{D}}^0\to {\pi }^{+}{\pi }^{-}$ scattering length
• Observation of a structure in the M${}_{p\eta }$ invariant mass distribution near 1700 MeV/$c^2$ in the $\gamma \mathbf{p}\to \mathbf{p}{\pi }^0\eta$ reaction
• Investigation of a candidate spin-$\frac{1}{2}$ hidden-charm triple strange pentaquark state $P_{csss}$
• Sequential single pion production explaining the dibaryon "$d^{\ast }(2380)$" peak
• Reply to "Comment on Sequential Single-pion Production Explaining the dibaryon $d^{\ast }(2380)$ peak''
• Effects of Final State Interactions on Landau Singularities
• Molecular pentaquark states with open charm and bottom flavors
• The $\pi f_0(500)$ decay of the $a_1(1260)$
• Studying triangle singularity through spin observables
• The role of triangle singularity in isospin breaking process $J/\psi \to \Lambda \bar{\Lambda }\pi$ and the possible evidence of ${\Sigma }^{\ast }({\frac{1}{2}}^{-})$ states
• The role of meson interactions in the $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}\eta$ decay
• $\Lambda (1405)$ mediated triangle singularity in the $K^{-}d\to p{\Sigma }^{-}$ reaction
• The axial charges of the hidden-charm pentaquark states
• Hadronic decay $D^{+}\to {\pi }^{+}\eta \eta$ and the $a_0(980)$ and $f_0(1370)$ contributions
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Triangle mechanism in the decay process $B_0\to J/\psi K^0{f}_0(980)(a_0(980))$
• First observation of the ${\Lambda }_b^0\to {\Lambda }_c^{+}{D}_s^{-}{K}^{+}{K}^{-}$ decay and search for pentaquarks in the ${\Lambda }_c^{+}{D}_s^{-}$ system
• Analysis of the hidden-charm pentaquark candidates in the $J/\psi p$ mass spectrum with QCD sum rules
• Hadronic molecules and multiquark states
• What can we learn from the radiative decays of the $D_{s1}(2460)$ meson?
• The dynamically generated $h_1$ state by the $K^{\ast }{\bar{K}}^{\ast }$ interaction and its $K_1(1270)\bar{K}$ and $b_1(1235)\pi$ decays
• Proposal to detect a moving triangle singularity in $\psi (2S)\to {\pi }^{+}{\pi }^{-}{K}^{+}{K}^{-}$ process
• Box Singularity Conditions in Box Diagrams of Decay Processes