Isospin breaking and f₀(980)-a₀(980) mixing in the η(1405) → π⁰f₀(980) reaction

¹ Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigación de Paterna, Aptdo. 22085, 46071 Valencia, Spain
² Physics Department, Guangxi Normal University, Guilin 541004, China
³ Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁴ State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
⁵ Theoretical Physics Center for Science Facilities, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

^a e-mail: aceti@ifi.uv.es
^b e-mail: oset@ific.uv.es

Published online: 9 June 2014

Abstract

We make a theoretical study of the η(1405) → π⁰f₀(980) and η(1405) → π⁰a₀(980) reactions to determine the isospin violation and the mixing of the f₀(980) and a₀(980) resonances. We make use of the chiral unitary approach where these two resonances appear as dynamically generated by the meson-meson interaction provided by chiral Lagrangians. We obtain a very narrow shape for the f₀(980) production in agreement with a BES experiment. As to the amount of isospin violation, assuming constant vertices for the primary η(1405) → π⁰KK̅ and η(1405) → π⁰π⁰η production, we find results which are much smaller than found in the experimental BES paper. The problem is solved by using the primary production driven by η' → K*K̅ followed by K^∗→ Kπ. Thus, we can predict absolute values for the ratio Γ(π⁰,π⁺π⁻)/Γ(π⁰,π⁰η) which are in fair agreement with experiment.