other part is the left-handed charged lepton as it is present in the minimal standard model with neutrino masses omitted, and let be a postulated right-handed neutrino Weyl spinor which is a singlet under weak isospin – i.e. a neutrino that fails to interact weakly, such as a sterile neutrino. There are now three ways to form Lorentz covariant mass terms, giving either and their complex conjugates, which can be written as a quadratic form, Since the right-handed neutrino spinor is uncharged under all standard model gauge symmetries, is a free parameter which can in principle take any arbitrary value. The parameter is forbidden by electroweak gauge symmetry, and can only appear after the symmetry has been spontaneous broken by a Higgs mechanism, like the Dirac masses of the charged leptons. In particular, since has weak isospin like the Higgs field , and has weak isospin 0, the mass parameter can be generated from Yukawa interactions with the Higgs field, in the conventional standard model fashion, This means that is naturally of the order of the vacuum expectation value of the standard model Higgs field, the vacuum expectation value (VEV) if the dimensionless Yukawa coupling is of order . It can be chosen smaller consistently, but extreme values can make the model nonperturbative. The parameter on the other hand, is forbidden, since no renormalizable singlet under weak hypercharge and isospin can be formed using these doublet components – only a nonrenormalizable, dimension 5 term is allowed. This is the origin of the pattern and hierarchy of scales of the mass matrix within the "Type 1" seesaw mechanism. The large size of can be motivated in the context of grand unification. In such models, enlarged gauge symmetries may be present, which initially force in the unbroken phase, but generate a large, non-vanishing value around the scale of their spontaneous symmetry breaking. So given a mass one has A huge scale has thus induced a dramatically small neutrino mass for the eigenvector See also Majoron Spinor Footnotes References External links Neutrinos Physics beyond the Standard Model