The seesaw mechanism at arbitrary order: disentangling the small scale from the large scale

We develop a recipe which allows one to recursively and uniquely decouple t he large scale from the small scale in mass matrices of the seesaw type, up to any order in the inverse of the large scale. Our method allows one to c alculate the mass matrix of the light neutrinos with arbitrary precision. T he same method can be applied in the case of quark mass matrices in an exte nsion of the Standard Model with vector-like quarks which have mass terms a t a scale much higher than the electroweak scale.