Neutrino Mass and the SU (2)R Breaking Scale

The neutrino sector in a left-right extension of the Standard Model depends on how SU(2)R is broken. I list all possible scenarios, including the ones where the Majorana νR mass is naturally much smaller than the SU(2)R breaking scale, which is desirable for generating the proper baryon asymmetry of the Universe. The best such choice is identified and discussed. In the Standard Model of particle interactions, the neutrino is part of a left-handed doublet (ν, l)L under SU(2)L × U(1)Y . Whereas the charged lepton must have a righthanded singlet counterpart lR, the singlet νR is not mandatory [because it is trivial under SU(2)L × U(1)Y ] and is absent in the minimal version of the model. On the other hand, its existence is usually assumed so that νL may acquire a naturally small Majorana mass as νR gets a large Majorana mass [again because it is trivial under SU(2)L × U(1)Y ] in the famous canonical seesaw mechanism [1, 2]. Where does νR come from? and what is the magnitude of its Majorana mass? The simplest answer [2] is that U(1)Y is actually a remnant of SU(2)R × U(1)B−L under which (ν, l)R is a doublet, and the large Majorana νR mass comes from the vacuum expectation value (vev) of a scalar SU(2)R triplet, which also breaks SU(2)R × U(1)B−L to U(1)Y . This scenario has dominated the thinking on neutrino mass for over 20 years, but it is not the only possibility, even if the existence of νR is conceded. (Mechanisms without νR are also possible and just as natural [3].) It may not even be the best possibility as far as leptogenesis [4] is concerned, because the SU(2)R gauge interactions will tend to diminish the νR number density in the early Universe. Under SU(3)C × SU(2)L × SU(2)R × U(1)B−L, the quarks and leptons transform as: qL = (u, d)L ∼ (3, 2, 1, 1/3), (1) qR = (u, d)R ∼ (3, 1, 2, 1/3), (2) lL = (ν, e)L ∼ (1, 2, 1,−1), (3) lR = (ν, e)R ∼ (1, 1, 2,−1), (4) where the electric charge is given by Q = I3L + I3R + 1 2 (B − L). (5) To break SU(2)R × U(1)B−L to U(1)Y , there are two possibilities. One is to use the scalar