Triangle mechanisms in the build up and decay of the $N^{\ast }(1875)$

Abstract

We have studied the $N^{\ast }(1875)(3/2^{-})$ resonance with a multichannel unitary scheme, considering the $\Delta \pi$ and ${\Sigma }^{\ast }K$, with their interaction extracted from chiral Lagrangians, and then have added two more channels, the $N^{\ast }(1535)\pi$ and $N\sigma$, which proceed via triangle diagrams involving the ${\Sigma }^{\ast }K$ and $\Delta \pi$ respectively in the intermediate states. The triangle diagram in the $N^{\ast }(1535)\pi$ case develops a singularity at the same energy as the resonance mass. We determine the couplings of the resonance to the different channels and the partial decay widths. We find a very large decay width to ${\Sigma }^{\ast }K$, and also see that, due to interference with other terms, the $N\sigma$ channel has an important role in the $\pi \pi$ mass distributions at low invariant masses, leading to an apparently large $N\sigma$ decay width. A discussion is done, justifying the convenience of an experimental reanalysis of this resonance to the light of the findings of the paper, using multichannel unitary schemes.

14 pages, 18 figures

References in corpus (11)

• A Discussion on Triangle Singularities in the ${\Lambda }_b\to J/\psi K^{-}p$ Reaction
• $B^0$ and $B_s^0$ decays into $J/\psi$ $f_0(980)$ and $J/\psi$ $f_0(500)$ and the nature of the scalar resonances
• On the nature of $a_1(1420)$
• Interaction of vector mesons with baryons and nuclei
• The "$a_1(1420)$" peak as the $\pi f_0(980)$ decay mode of the $a_1(1260)$
• $f_1(1285)$ decays into $a_0(980){\pi }^0$, $f_0(980){\pi }^0$ and isospin breaking
• Role of a triangle singularity in the $\gamma p\to K^{+}\Lambda (1405)$ reaction
• Amplitude analysis of the ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ decays
• Revising the $f_1(1420)$ resonance
• Role of a triangle singularity in the $\pi \Delta$ decay of the $N(1700)(3/2^{-})$
• $f_2(1810)$ as a triangle singularity

Cited by in corpus (12)

• Hadronic molecules
• Decay behavior of the strange and beauty partners of $P_c$ hadronic molecules
• Considerations on the Schmid theorem for triangle singularities
• Abnormal isospin violation and $a_0-f_0$ mixing in the $D_s^{+}\to {\pi }^{+}{\pi }^0{a}_0(980)(f_0(980))$ reactions
• Triangle singularities in $B^{-}\to D^{\ast 0}{\pi }^{-}{\pi }^0\eta$ and $B^{-}\to D^{\ast 0}{\pi }^{-}{\pi }^{+}{\pi }^{-}$
• Triangle singularity in ${\tau }^{-}\to {\nu }_{\tau }{\pi }^{-}{f}_0(980)$ ($a_0(980)$) decays
• Towards the Minimal Spectrum of Excited Baryons
• Detecting the pure triangle sigularity effect through the $\psi (2S)\to p\bar{p}\eta /p\bar{p}{\pi }^0$ process
• 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 triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Interactions of the Pseudoscalar Meson Octet and the Baryon Decuplet in the Continuum and a Finite Volume
• Box Singularity Conditions in Box Diagrams of Decay Processes