For a fermion singlet “Psi” with hypercharge Y = 0, it seems that CheckModel does not take terms involving conj[Psi] into account. For example, when I add such a fermion to the Standard Model (built-in model “SM”):
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FermionFields[[6]] = {Psi, 1, psi 0, 1, 1};
I get the following result when running CheckModel:
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…
Checking for additional terms in the potential
{C[Psi],C[Psi,Psi],C[H,l,Psi],C[Psi,conj[H],conj[l]]}
! PossibleTerms::NonSUSY: The following terms are not present in the potential but allowed by gauge invariance: {{Psi},{Psi,Psi},{H,l,Psi},{Psi,conj[H],conj[l]}}.
…
Now, the terms {Psi} and {Psi,conj[H],conj[l]} obviously shouldn’t be there (but are listed because there is
no check for Lorentz invariance). But for {Psi,Psi} and {H,l,Psi}, I would have expected that their Hermitian conjugates should also be reported as missing. That is, I think CheckModel should also list {conj[Psi],conj[Psi]} and {conj[H],conj[l],conj[Psi]} as missing terms!