Internal particle width effects on the the triangle singularity mechanism in the study of the $\eta (1405)$ and $\eta (1475)$ puzzle

Abstract

In this article, the analyticity of triangle loop integral with complex masses of internal particles is discussed in a new perspective, base on which we obtain the explicit width dependence of the absorptive part of the triangle amplitude. We reanalyze the decay pattern of $\eta (1405/1475)$ with the width effects included in the triangle singularity (TS) mechanism. Based on the present experimental information, we provide a self-consistent description of the $K\bar{K}\pi$, $\eta \pi \pi$, and $3\pi$ decay channels for $\eta (1405/1475)$. Our results confirm the claim that the TS mechanism plays a decisive role in the understanding of the $\eta (1405)$ and $\eta (1475)$ puzzle. Namely, the observed differences of $\eta$ resonances within the mass region of $1.40\sim 1.48$ GeV are originated from the same state. For the isospin violated process $J/\psi \to \gamma \eta (1405/1475)\to f_0(980)\pi \to 3\pi$, we identify an additional contribution to the $a_0(980)-f_0(980)$ mixing via the TS mechanism.

arXiv comment28 pages, 13 figures, an error is corrected and Figs. 11, 12, 13 are updated. The main conclusion is unchanged. Revised version accepted by Phys. Rev. D

References in corpus (36)

• The glueball spectrum from an anisotropic lattice study
• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• Glueball Spectrum and Matrix Elements on Anisotropic Lattices
• A comprehensive lattice study of SU(3) glueballs
• Study of the Decay phi --> pi0 pi0 gamma with the KLOE Detector
• Confirmation of the X(1835) and observation of the resonances X(2120) and X(2370) in J/psi->gamma pi^+pi^-eta'
• The puzzle of anomalously large isospin violations in $\eta (1405/1475)\to 3\pi$
• Determining the Gluonic Content of Isoscalar Mesons
• Searching for observable effects induced by anomalous triangle singularities
• Study of the Decay phi --> eta pi0 gamma with the KLOE detector
• First observation of $\eta (1405)$ decays into $f_0(980){\pi }^0$
• Isospin breaking and $f_0(980)$-$a_0(980)$ mixing in the $\eta (1405)\to {\pi }^0{f}_0(980)$ reaction
• Understanding the property of $\eta (1405/1475)$ in the $J/\psi$ radiative decay
• Decay of the pseudoscalar glueball into scalar and pseudoscalar mesons
• Pseudoscalar glueball mass from $\eta$-${\eta }^{\prime }$-$G$ mixing
• Glueballs, closed fluxtubes and eta(1440)
• Isospin breaking decay $\eta (1405)\to f_0(980){\pi }^0\to 3\pi$
• Possibility of measuring a0(980)-f0(980) mixing from J/psi -> phi a0
• Categorizing resonances X(1835), X(2120) and X(2370) in the pseudoscalar meson family
• Glueball mass measurements from improved staggered fermion simulations
• Decays of $J/\psi$ and ${\psi }^{\prime }$ into vector and pseudoscalar meson and the pseudoscalar glueball-$q\bar{q}$ mixing
• Study a0(980)-f0(980) mixing from a0(980) -> f0(980) transition
• Propagators of light scalar mesons
• Glueball spectrum from $N_f=2$ lattice QCD study on anisotropic lattices
• Pseudoscalar glueball and $\eta -{\eta }^{\prime }$ mixing
• Observation of $a_0^0(980)$-$f_0(980)$ Mixing
• Study of resonant structure around 1.8 GeV/$c^2$ and $\eta (1405)$ in $J/\psi \to \omega \eta {\pi }^{+}{\pi }^{-}$
• eta(1405) in a chiral approach based on mixing of the pseudoscalar glueball with the first radial excitations of eta and eta'
• A Study of J/psi-->gamma gamma V(rho,phi) Decays with the BESII Detector
• Triangle singularities in $B^{-}\to D^{\ast 0}{\pi }^{-}{\pi }^0\eta$ and $B^{-}\to D^{\ast 0}{\pi }^{-}{\pi }^{+}{\pi }^{-}$
• Pseudoscalar Glueball Mass: QCD vs. Lattice Gauge Theory Prediction
• ${\eta }_c$ mixing effects on charmonium and $B$ meson decays
• Correlation and localization properties of topological charge density and the pseudoscalar glueball mass in SU(3) lattice Yang-Mills theory
• Revisiting the pseudoscalar meson and glueball mixing and key issues in the search for pseudscalar glueball state
• Disentangling the role of the $Y(4260)$ in $e^{+}{e}^{-}\to D^{\ast }{\bar{D}}^{\ast }$ and $D_s^{\ast }{\bar{D}}_s^{\ast }$ via line shape studies
• Chiral field theory of $0^{-+}$ glueball

Cited by in corpus (19)

• Resonant $a_0(980)$ state in triangle rescattering $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decays
• Can the nature of $a_0(980)$ be tested in the $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decay?
• Visible narrow cusp structure in ${\Lambda }_c^{+}\to p{K}^{-}{\pi }^{+}$ enhanced by triangle singularity
• Dispersive analysis of glueball masses
• Triangle singularities in $J/\psi \to \eta {\pi }^0\varphi$ and ${\pi }^0{\pi }^0\varphi$
• The $D_s^{+}\to a_0(980)e^{+}{\nu }_e$ reaction and the $a_0(980)-f_0(980)$ mixing
• Comprehensive study of light axial vector mesons with the presence of triangle singularity
• Three-body unitary coupled-channel approach to radiative $J/\psi$ decays and $\eta (1405/1475)$
• Role of the triangle mechanism in the ${\Lambda }_b\to {\Lambda }_c{\pi }^{-}{f}_0(980)$ reaction
• The vertex corrections due to the triangle singularity mechanism in the light axial vector meson couplings to $K^{\ast }\bar{K}+c.c.$
• Three-Body Unitary Coupled-Channel Analysis on $\eta (1405/1475)$
• The $\pi f_0(500)$ decay of the $a_1(1260)$
• Detecting the pure triangle sigularity effect through the $\psi (2S)\to p\bar{p}\eta /p\bar{p}{\pi }^0$ process
• 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
• 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
• Study of $f_1(1420)$ and $\eta (1405)$ in the decay $J/\psi \to \gamma {\pi }^0{\pi }^0{\pi }^0$
• Observation of $\psi (3686)\to \gamma \eta (1405)$ via $\eta (1405)\to f_0(980){\pi }^0$