Scale- and gauge-independent mixing angles for scalar particles

The existing definitions of mixing angles (one-loop radiatively corrected and renormalization-scale independent) for scalar particles turn out to be gauge dependent when used in gauge theories. We show that a scale- and gauge-independent mixing angle can be obtained if the scalar self-energy is improved by the pinch technique, and give two relevant examples in the minimal supersymmetric standard model: the mixing of CP-even Higgs scalars and of top squarks. We also show that the recently proposed definition of a mixing angle that uses the (unpinched) scalar two-point function evaluated at a particular value of the external momentum [p*2=(M12+M22)/2, where M1,2 are the masses of the mixed particles] computed in the Feynman gauge coincides with the gauge-invariant pinched result. In alternative definitions (e.g., in the on-shell scheme), the improved Higgs mixing angle is different from that in the Feynman gauge. Some freedom in the pinch technique for scalar-scalar-gauge couplings is also discussed