From pole parameters to line shapes and branching ratios

Abstract

Resonances are uniquely characterized by their complex pole locations and the corresponding residues. In practice, however, resonances are typically identified experimentally as structures in invariant mass distributions, with branching fractions of resonances determined as ratios of count rates. To make contact between these quantities it is necessary to connect line shapes and resonance parameters. In this work we propose such a connection and illustrate the formalism with detailed studies of the $\rho (770)$ and $f_0(500)$ resonances. Based on the line shapes inferred from the resonance parameters along these lines, expressions for partial widths and branching ratios are derived and compared to other approaches in the literature.

17 pages, 4 figures, v2 as published in EPJC

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• Anomalous thresholds in $B\to (P,V){\gamma }^{\ast }$ form factors
• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• Advanced parametrisations for hadronic form factors
• Form factors of the $\rho$ meson from effective field theory and the lattice
• Dispersive analysis of the $J/\psi \to {\pi }^0{\gamma }^{\ast }$ transition form factor with $\rho$-$\omega$ mixing effects
• Scattering Theory
• Coupled-channel contributions to the GDH sum rule from the Jülich-Bonn approach