## Seminar on Theoretical Nuclear Physics

## 8.06.10 16:15

# eta-eta' Mixing from Chiral Lagrangian

## V. Mathieu (Universidad de Valencia,Spain)

Under large-N arguments the flavor singlet eta_0 can be considered as the ninth Goldstone boson. Its inclusion in a effective low-energy Lagrangian, the chiral Lagrangian, leads to a mixing with eta_8 forming two physical states, eta and eta'.

The eta-eta' mixing scheme is studied at leading order and next to leading order in the momentum expansion. It is demonstrated that the leading order is not sufficient to reproduce the dynamics of the eta-eta' system. I will expose two improvements. The first one consists on the inclusion at leading order of third state mainly gluonic and the second on going at next to leading order in the momentum expansion.

The next to leading order terms accommodate the two physical particles but involve low-energy constants without a clear physical meaning. It will be shown how to reorganize the low energy constants to express the mass matrix in terms of the decay constants. Under a well defined hypothesis, the decay constants and the mixing angle of the eta-eta' system is predicted in agreement with experimental data.

This procedure leads to the explanation the Feldmann, Kroll and Stech formalism without resorting to an *ad hoc* assumption about the decay constants. The same mass matrix, and hence the same predictions, are recovered with a better understanding.**References**

1. V. Mathieu and V. Vento,

``Pseudoscalar glueball and eta-eta' mixing,''

Phys. Rev. D 81 (2010) 034004, arXiv:0910.0212 [hep-ph].

2. V. Mathieu and V. Vento,

``eta-eta' Mixing in the Flavor Basis and Large N,''

Phys. Lett. B 688 (2010) 314, arXiv:1003.2119 [hep-ph].