$η-η^\prime$ Mixing in the Flavor Basis and Large N

Details $η-η^\prime$ Mixing in the Flavor Basis and Large N $η-η^\prime$ Mixing in the Flavor Basis and Large N

2010-03-10

arxiv.org/abs/1003.2119v2

Phys.Lett.B688:314-318,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

10 pages, 2 figures, to be published in Phys. Lett. B

Scientific paper

10.1016/j.physletb.2010.04.021

The mass matrix for $\eta-\eta^\prime$ is derived in the flavor basis at ${\cal O}(p^4)$ of the chiral Lagrangian using the large $N$ approximation. Under certain assumptions, the mixing angle $\phi=41.4^\circ$ and the decay constants ratio $f_K/f_\pi=1.15$ are calculated in agreement with the data. It appears that the FKS scheme arises as a special limit of the chiral Lagrangian. Their mass matrix is obtained without the hypothesis on the mixing pattern of the decay constants.

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