Note on the definitions of branching ratios of overlapping resonances

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 multichannel 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 f0(980). & COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

Branching ratios for decay of hadrons are dependent on their definition in the cases of large width or near thresholds. This study tests different definitions and shows that different branching ratios can be obtained. Integration over the spectral functions is required for wide resonances and sequential decays with wide intermediate resonances. The results are based on the latest Bonn-Gatchina multichannel analysis solution and published values for residues of light scalar mesons. If a resonance overlaps with a threshold and its pole lies in a non-adjacent sheet, the total width necessary for branching ratios does not correspond to the imaginary part of the pole position. The findings are illustrated using the Madrid-Krakow dispersive parameterizations with the f0(980).