Loop-level corrections to the neutrino mass

[ryanwilk]

Hi,

Quick question. In the SM, why can't we have loop-level interactions that give neutrinos their small masses?
(It seems like we must also have Majorana neutrinos)Thanks.

 

[Parlyne]

Giving neutrinos a Dirac mass requires there to be right-handed neutrinos and giving them Majorana masses requires a source of explicit lepton number violation. The standard model has neither of these*; so, it can't generate any sort of neutrino masses.

*Well, strictly, the SM does have non-perturbative lepton number violation; but, only with a compensating violation of baryon number that leaves B-L conserved. Majorana mass requires that this be broken as well.