  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.
