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 mixing angle that uses the (unpinched) scalar two-point function evaluated at a particular value of the external momentum [p_*^2=(M_1^2+M_2^2)/2, where M_{1,2} are the masses of the mixed particles] computed in 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 Feynman gauge. An arbitrariness of the pinch technique for scalar particles is also discussed.