η-η′ mixing in the flavor basis and large N

The mass matrix for η-η′ is derived in the flavor basis at O(p4) of the chiral Lagrangian using the large N approximation. Under certain assumptions, the mixing angle ϕ=41.4° and the decay constants ratio fK/fπ=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.