Let's assume, we have standard model singlet particle $s$, that mixes after electroweak symmetry breaking with an exotic, vectorlike neutral lepton $N$. The relevant part of the Lagrangian reads

$$ L \supset h^c s N + h s N^c + M N N^c, $$

where $h$ is the standard model higgs and $M$ is a superheavy mass. Moreover, we assume that for some reason there is (at tree level) no Majorana mass term: $ M_s ss$ for the singlet $s$. The tree-level analysis now yields for the singlet $s$ a tiny seesaw type mass: $m_s \approx v_{EW} / M^2 \ll v_{EW}$.

Now, a Majorana mass term for the singlet $s$ will be generically generated at the 1-loop level through a diagram with $N$ in the loop. It was pointed out to me that this 1-loop contribution "*may give rise to a much larger mass for the singlet*". I would like understand how this can happen. I think the relevant diagram looks like this

My naive estimate for this one-loop contribution is $ m_s \approx 1/16 \pi \ m_{EW}^2 /M$, i.e. something comparable to the tree-level estimate, divided by a loop factor, possibly times some logarithm. Thus, while there is possibly some relevant correction due to the logarithm, the consequences do not seem dramatic.

**Is there any other possible correction that I'm missing here? Is there some diagram that potentially leads to a much heavier mass for the singlet $s$?**

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**A relevant analogous scenario**

The situation is similar to the usual seesaw for the left-handed neutrinos $\nu_L$. However, the situation described above is reversed. In the usual seesaw scenario, the left-handed neutrinos $\nu_L$ are light and the singlet $\nu_R$ is heavy. The 1-loop correction to the usual seesaw formula, is discussed in On the importance of the 1-loop finite corrections to seesaw neutrino masses by D. Aristizabal Sierra, Carlos E. Yaguna. (See also, this summary. The relevant diagrams are

and the result is

This result yields a contribution comparable to the result of the tree-level analysis: $ m_{EW}^2 / M$, where $m_{EW}$ denotes the electroweak scale and $M$ a superheavy scale. (In addition the is a potentially enhancing log factor.)