# $a_0-f_0$ mixing in the Khuri-Treiman equations for $\eta\to 3\pi$

Abstract : A reliable determination of the isospin breaking double quark mass ratio from precise experimental data on $\eta\to 3\pi$ decays should be based on the chiral expansion of the amplitude supplemented with a Khuri-Treiman type dispersive treatment of the final-state interactions. We discuss an extension of this formalism which allows to estimate the effects of the $a_0(980)$ and $f_0(980)$ resonances and their mixing on the $\eta\to 3\pi$ amplitudes. Matrix generalisations of the equations describing elastic $\pi\pi$ rescattering with $I=0,\,2$ are introduced which accomodate both $\pi\pi/K\bar{K}$ and $\eta\pi/K\bar{K}$ coupled-channel rescattering. Isospin violation induced by the physical $K^+-K^0$ mass difference and by direct $u-d$ mass difference effects are both accounted for in the dispersive integrals. Numerical solutions are constructed which illustrate how the large resonance effects at 1 GeV propagate down to low energies. They remain small in the physical region of the decay, due to the matching constraints with the NLO chiral amplitude, but they are not negligible and go in the sense of further improving the agreement with experiment for the Dalitz plot parameters.
Type de document :
Pré-publication, Document de travail
10 pages, to appear in the proceedings of the 8th International Workshop on Chiral Dynamics, Pisa.. 2015

http://hal.in2p3.fr/in2p3-01234950
Contributeur : Sophie Heurteau <>
Soumis le : vendredi 27 novembre 2015 - 14:34:15
Dernière modification le : jeudi 11 janvier 2018 - 06:12:41

### Identifiants

• HAL Id : in2p3-01234950, version 1
• ARXIV : 1510.06626

### Citation

M. Albaladejo, B. Moussallam. $a_0-f_0$ mixing in the Khuri-Treiman equations for $\eta\to 3\pi$. 10 pages, to appear in the proceedings of the 8th International Workshop on Chiral Dynamics, Pisa.. 2015. 〈in2p3-01234950〉

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