Use of the reciprocal basis in neutral meson mixing - art. no. 116008

In the presence of CP violation, the effective Hamiltonian matrix describin g a neutral meson-antimeson system does not commute with its Hermitian conj ugate. As a result, this matrix cannot be diagonalized by a unitary transfo rmation and one needs to introduce a reciprocal basis. Although known, this fact is seldom discussed and almost never used. Hen, we use this concept t o highlight a parametrization of the Hamiltonian matrix in terms of physica l observables, and we show that using it reduces a number of long and tedio us derivations into simple matrix multiplications. These results have a str aightforward application for propagation in matter. We also comment on the (mathematical) relation with neutrino oscillations.