What are ordinary mass-terms (of neutrinos)?

Question

When reading the introduction to Sterile neutrino hot, warm, and cold dark matter I came across the following definition of sterile neutrinos:

We can define sterile neutrinos generically as spin-$\frac{1}{2}$, $SU(2)$-singlet particles which interact with the standard $SU(2)$-doublet (“active”) neutrinos $\nu_e$, $\nu_\mu$, and $\nu_\tau$, solely via ordinary mass terms.

What is the meaning of ordinary mass terms?

Is it simply the mass terms of SM particles, in this case "active" neutrinos? Meaning that the mass of sterile neutrinos can be written in terms of the mass terms of $\nu_e$, $\nu_\mu$, and $\nu_\tau$?

Or is there another meaning I am not understanding?

Answer 1

What is the meaning of ordinary mass terms?

The "ordinary mass terms" in the quoted paper (see-saw mechanism) would stand for Dirac mass terms, which couple active left-handed neutrinos $\nu_L$ (the isospin "up" part of the electroweak $SU(2)$ left-handed neutrino-electron doublets) to the sterile right-handed neutrinos $\nu_R$ (as $SU(2)$-singlets): $$ m (\bar{\nu}_L\nu_R + \bar{\nu}_R\nu_L). $$

The "non-ordinary mass terms" would mean Majorana mass terms, which couple the sterile right-handed neutrino $\nu_R$ to the charge-conjugate of itself $\nu^c_R$: $$ M \bar{\nu}_R\nu^c_R. $$

The "ordinary" Dirac mass $m$ is of the eletroweak symmetry breaking scale, while the "non-ordinary" Majorana mass $M$ is of the much higher see-saw (or grand unification) scale . In the usual scheme of the sea-saw model, the tiny neutrino mass is the resultant effective mass $m_{\nu}$ with scale: $$ m_{\nu}\sim \frac{m^2}{M}. $$

Answer 2

I am understanding the "ordinary" in "ordinary mass terms" as a way for the author to emphasize the fact that the mass term coupling does not come from a renormalization effect for some other interaction or that it does not arise due to symmetry breaking. And that the coupling itself comes from a type of mixing resembling the PMNS matrix, which mixes the masses of the active and sterile neutrinos.