RGEs for REAL and COMPLEX SCALARS

[jaburico]

Hi all, thanks for everything. I extended the SM by a scalar field in two ways. By a complex and by a real scalar fields. However, after analyzing the beta function of both of them, they are identical. However, theoretically, there are differences between beta functions of quartic couplings if they are real or scalr fields, right? So, what happened? SARAH do not differentiate real and complex scalars in such matter? What I can do in order to create a differentiation between them?
Obs:
the difference between real and complex field to me is simply defining the function as

vs + Rs or vs + Rs + I*Is

and including (or not) a new particle to the mixing with Ah field.

best,
J P Pinheiro.

[MDGoodsell]

A complex field is just two real fields. The differences in the RGEs will appear only from counting or from selection rules (complex fields require additional symmetries). SARAH knows perfectly well how to treat both (in the RGEs, this is often by making the decomposition of complex into two real). But what do you want to see? If you have just added a neutral scalar to the SM, there is indeed not much difference in the RGEs between a complex scalar, and a real scalar having a Z2 symmetry (up to coupling definitions and possible factors of 2).