Isospin breaking andf0(980)-a0(980) mixing in theη(1405) →π0f0(980) reaction

F Aceti,E Oset,B.S Zou,W.H Liang,J.J Wu

doi:10.1051/epjconf/20147303005

Abstract

We make a theoretical study of the η (1405) → π 0 f 0 (980) and η (1405) → π 0 a 0 (980) reactions to determine the isospin violation and the mixing of the f 0 (980) and a 0 (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 f 0 (980) production in agreement with a BES experiment. As to the amount of isospin violation, assuming constant vertices for the primary η (1405) → π 0 K K and η (1405) → π 0 π 0 η 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 *K followed by K ∗ → K π . Thus, we can predict absolute values for the ratio Γ(π 0 ,π + π − )/Γ(π 0 ,π 0 η ) which are in fair agreement with experiment.

Highlights

In a recent paper the BES team has reported an unusually large isospin violation in the decay of the (1405) → 0f0(980) compared to the (1405) → 0a0(980) reaction [1]
In this work we first discussed the problem assuming a contact → 0KKvertex, while the second part is devoted to the explicit study of the triangular mechanism of [2] which is quite unique to the present reaction and, together with the use of the chiral unitary approach, enables us to evaluate the ratio for isospin violation rather reliably, obtaining a good agreement with experiment
In the first part of the work we assumed the primary production of 0P P to be given by a contact term and we obtained a rate of + − production versus 0 of the order of one percent, very small compared with the results claimed by [1]

Summary

Introduction

In a recent paper the BES team has reported an unusually large isospin violation in the decay of the (1405) → 0f0(980) compared to the (1405) → 0a0(980) reaction [1]. A theoretical description of such a large rate is difficult, unless the same (1405) state already contains a large mixture of I = 0 and I = 1, in which case the natural width of the f0(980) of about 50 MeV would be shown instead of the 9 MeV observed in the BES experiment [1]. In this work we first discussed the problem assuming a contact → 0KKvertex, while the second part is devoted to the explicit study of the triangular mechanism of [2] which is quite unique to the present reaction and, together with the use of the chiral unitary approach, enables us to evaluate the ratio for isospin violation rather reliably, obtaining a good agreement with experiment

Formalism

Results with the local vertices

Results with the triangular diagram

Conclusions