Diagonalization of Coupled Scalars and its Application to the Supersymmetric Neutral Higgs Sector

Abstract

We introduce a momentum dependent mixing angle $α(p^2)$ which allow us to diagonalize at any external momentum $p$ the one-loop corrected inverse propagator matrix of two coupled scalar fields while keeping the full momentum dependence in the self energies. We compare this method with more traditional techniques applied to the diagonalization of coupled scalars at the one-loop level. This method is applied to the CP-even Higgs sector of the Minimal Supersymmetric Model, defining the momentum dependent mixing angle $α(p^2)$, and calculating the two CP-even Higgs masses and the mixing angle at these two scales. We compare the results obtained in this way with alternative techniques. We make explicit the relation between $α(p^2)$ and the running mixing angle. We find differences between the mixing angle calculated with our method and the one calculated with more traditional methods, and these differences are relevant for Higgs searches at LEP2.