a₀(980)–f₀(980) mixing in χ_c1 decay

Abstract

We investigate the isospin breaking in the ${\chi _{c1}} \to {\pi ^0}{\pi ^ + }{\pi ^ - }$ and ${\chi _{c1}} \to {\pi ^0}{\pi ^0}\eta $ decays and its relation to the a0(980) – f0(980) mixing, which was measured by the BESIII Collaboration. The isospin violation is introduced through the use of different masses for the charged and neutral kaons, either in the propagators of pairs of mesons created in the χc1 decay, or in the propagators inside the T matrix. We find that the most important effect in the total amplitude is the isospin breaking inside the T matrix which is essential to get a good agreement with the experimental measurement of the mixing.