Note on the definitions of branching ratios of overlapping resonances

Abstract

Branching ratios for the decay of hadrons with large width or near thresholds depend on their definition. We test different definitions and show that rather different branching ratios can be obtained. For wide resonances and for sequential decays with wide intermediate resonances, integration over the spectral functions is mandatory. The tests are performed exploiting the latest solution of the Bonn-Gatchina multi-channel analysis and published values for residues of light scalar mesons. For a resonance overlapping with a threshold, in case its pole lies in a non-adjacent sheet, we show how the total width, needed for the branching ratios, does not correspond to the imaginary part of the pole position. We use the Madrid-Krakow dispersive parameterizations to illustrate this situation with the $f_0(980)$.

arXiv commentReport, 9 pages (extended to light scalar mesons)

References in corpus (15)

• Big-Bang Nucleosynthesis
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• Partial wave decomposition of pion and photoproduction amplitudes
• Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semilocal duality
• The Mixing Angle of the Lightest Scalar Nonet
• High statistics study of the reaction $\gamma p\to p2{\pi }^0$
• Scalar isoscalar mesons and the scalar glueball from radiative $J/\psi$ decays
• Partial decay widths of baryons in the spin-momentum operator expansion method
• Global parameterization of $\pi \pi$ scattering up to 2 GeV
• Chiral dynamics in U(3) unitary chiral perturbation theory
• $N^{\ast }$ decays to $N\omega$ from new data on $\gamma p\to \omega p$
• Two-Pion production in the second resonance region in ${\pi }^{-}p$ collisions with HADES
• Analysis on the composite nature of the light scalar mesons $f_0(980)$ and $a_0(980)$
• The f0(1370) controversy from dispersive meson-meson scattering data analyses

Cited by in corpus (7)

• From pole parameters to line shapes and branching ratios
• Compositeness of hadrons, nuclei, and atomic systems
• The pion-kaon scattering amplitude and the $K^0(700)$ and $K^{\ast }(892)$ resonances at finite temperature
• Prediction of an $I(J^P)=0(1^{-})$ $\bar{b}\bar{b}ud$ Tetraquark Resonance Close to the $B^{\ast }{B}^{\ast }$ Threshold Using Lattice QCD Potentials
• Advanced parametrisations for hadronic form factors
• Amplitude determination for $MM\to MM$, $M=\pi ,K$ and cross-sections for $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0,{\pi }^0\eta$ in a chiral model
• Dispersive determination of resonances from $\pi \pi$ scattering data