Why can't we add a majorana mass type term in general Lagrangian?
I mean when we write a Lagrangian, we usually write it in Dirac representation. But when it is about seesaw mechanism or about neutrinos we write a Majorana mass term in the Lagrangian as well. Why is it so?
There are at least two simple ways. If you include a triplet Higgs T then it is possible to write Yukawa coupling LLT which will contain the left handed Majorana mass term ν̅L νLc or, otherwise, if you include any singlet fermion such as a right handed neutrino field, then you can also write ν̅R νRc ; in both the cases, however, you have to go beyond the standard model.
Neutrino-less double beta decay experiments search for left handed Majorana mass of the neutrino. If a positive result comes out in these experiments then it will make a signal for new physics beyond the standard model.
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