Mass Insertions vs. Mass Eigenstates calculations in Flavour Physics

We present and prove a theorem of matrix analysis, the Flavour Expansion Theorem (or FET), according to which, an analytic function of a Hermitian matrix can be expanded polynomially in terms of its off-diagonal elements with coefficients being the divided differences of the analytic function and arguments the diagonal elements of the Hermitian matrix. The theorem is applicable in case of flavour changing amplitudes. At one-loop level this procedure is particularly natural due to the observation that every loop function in the Passarino-Veltman basis can be recursively expressed in terms of divided differences. FET helps to algebraically translate an amplitude written in mass eigenbasis into flavour mass insertions, without performing diagrammatic calculations in flavour basis. As a non-trivial application of FET up to a third order, we demonstrate its use in calculating strong bounds on the real parts of flavour changing mass insertions in the up- squark sector of the MSSM from neutron Electric Dipole Moment (nEDM) measurements, assuming that CP-violation arises only from the CKM matrix.