From pole parameters to line shapes and branching ratios

L. A. Heuser; G. Chanturia; F.-K. Guo; C. Hanhart; M. Hoferichter; B. Kubis

doi:10.1140/epjc/s10052-024-12884-6

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 599
https://doi.org/10.1140/epjc/s10052-024-12884-6

Regular Article - Theoretical Physics

From pole parameters to line shapes and branching ratios

L. A. Heuser¹^,2^a, G. Chanturia², F.-K. Guo³^,4^,5, C. Hanhart¹, M. Hoferichter⁶ and B. Kubis²

¹ Forschungszentrum Jülich, Institute for Advanced Simulation, 52425, Jülich, Germany
² Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115, Bonn, Germany
³ CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China
⁴ School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
⁵ Peng Huanwu Collaborative Center for Research and Education, Beihang University, 100191, Beijing, China
⁶ Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

^a heuser@hiskp.uni-bonn.de

Received: 27 March 2024
Accepted: 5 May 2024
Published online: 10 June 2024

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 $ρ (770)$ $\rho (770)$ and $f_{0} (500)$ $$f_0(500)$$ 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.

© The Author(s) 2024

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