Complex masses for Dirac and Weyl spinors I'm trying understand how to rotate Dirac fields to absorb complex phases in masses. I have a few related questions:


*

*With Weyl spinors, I understand, $$ \mathcal{L} = \text{kinetic} +
    |M|e^{i\theta}\xi\chi + \textrm{h.c.} $$ The phase removed by separate
left- and right-handed rotations, e.g. $\xi \to e^{-i\theta/2}\xi$
and $\chi \to e^{-i\theta/2}\chi$. These phases cancel in the
kinetic terms.
Is it correct that with Dirac spinors, $$ \mathcal{L} = \bar\psi
    |M|e^{i\theta\gamma_5} \psi = \text{Re}(M)\bar\psi\psi
    +i\text{Im}(M)\bar\psi\gamma_5\psi $$ and the phase is removed by $\psi \to e^{-i\theta\gamma_5/2}\psi$? The appearance of the
$\gamma_5$ in the phase troubles me a little - I suppose this is
telling us that Weyl spinors are a more suitable basis than Dirac
spinors?

*If the field is Majorana, $\xi = \chi$, and the field can still
absorb a phase? I think I must be making a trivial mistake. 
For example, Majorana neutrino fields cannot absorb phases, leading to extra CP violation.
And in SUSY, the gaugino Majorana soft-breaking
masses are e.g. $M_1e^{i\theta}$. Can their phases be re-absorbed via a field redefinition? I don't think they can. So I must have a mistake.
 A: Having looked at a few more sources, I think I know the answer now, but please do correct me if I'm wrong.
For 1., I still find the appearance of the $\gamma_5$ matrix in Dirac spinor description surprising. I suppose the resolution is that the Weyl spinors are a more intuitive description in some cases.
For 2., I think the source of my confusion is some ambiguous statements in the literature. I've heard that Majorana fields "cannot absorb a phase," which I've misunderstood to mean cannot absorb a phase from a complex mass term, whereas it means that Majorana fields must be singlets in the fundamental representation/must have no non-zero quantum numbers, because the symmetry would violate the Majorana condition itself. 
The statement that Majorana fields cannot absorb phases from complex masses is true only in certain circumstances, namely, if there are interaction terms in the Lagrangian which are not invariant under the field redefinition. In the case of the Majorana neutrinos, because one no longer has the freedom to rotate right-handed fields only to avoid complications with left-handed weak interactions, fewer phases can be absorbed.
For the gauginos, I think there are F-terms, which prevent the total removal of the phases, leaving physical phases e.g. $\text{Arg}(M_i \mu)$.
