$\eta -{\eta }^{\prime }$ Mixing in the Flavor Basis and Large N

Abstract

The mass matrix for $\eta -{\eta }^{\prime }$ is derived in the flavor basis at $\mathcal{O}(p^4)$ of the chiral Lagrangian using the large $N$ approximation. Under certain assumptions, the mixing angle $\varphi =41.4^{\circ }$ 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.

arXiv comment10 pages, 2 figures, to be published in Phys. Lett. B

References in corpus (12)

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