fixed conjugations in 1-loop mass matrices for leptons

[wkotlarski]

According to @vytautasdudenas, those self energies should be conjugated. Working hypothesis: this is also what SPheno does.

[Expander]

Is there some paper or book for reference?

[wkotlarski]

First, is there a reference where does this eq.

"const " <> selfEnergyMatrixCType <> " delta_M(- self_energy_PR * M_tree " <>
"- M_tree * self_energy_PL - self_energy_1);\n";

come from? :) They all kind of look like from the BPMZ. We are afraid that SARAH does not follow this convention and therefore the self energies have to be conjugated before substituting to formulas from the BPMZ.

[Expander]

Yes, they are taken from PBMZ and I assumed that SARAH uses this convention (which may be a false assumption).

Another reference I've found is the SARAH manual sections E.2.2.0.1 and E.2.3. The equation from above seems to be (E.103). There is a $^+$ at the self energies, which could mean adjoint, $\Sigma^+ = (\Sigma^T)^\ast$, or just complex conjugate, $\Sigma^+ = \Sigma^\ast$. So, it seams at least that you've found a bug in FS. :) But I'm not sure whether your proposed fix is correct, because it could be that we need to use .adjoint(), not .conjugate().

[wkotlarski]

I'm not sure if + means anything at all. Like in D. 30 of BPMZ, maybe + just means a self-energy of a complex field. @vytautasdudenas, if you compare eq. E.103 of SARAH manual with those in points E.2.2.0.1 therein, do they look correct?

What I was thinking about, is that D. 30 has a right coupling conj, and left one un-conj. While in E.2.2.0.1 it's the opposite.