See-saw and supersymmetry or exact R-parity

SO(10) theory of R-parity and neutrino mass

“…We showed that at the large scale 16 = ν c = 0 and so R-parity is conserved. Next, as in any theory based on the renormalizable see-saw mechanism [5], one can show that ν = 0 too. This is valid at all energies all the way to the electroweak scale and below (of course one has to assume ν = 0 at high scale, as with other fields that break the SM symmetry).…”

“…Further, as we emphasized in [5], the exact form of the see-saw is rather model dependent in supersymmetric SO(10) theories. The canonical form for the see-saw for our model is spoiled by effective non-renormalizable terms in the superpotential of the form…”

“…This is a fundamental result which guarantees the stability of the lightest supersymmetric partner (LSP), an ideal candidate for the dark matter of the universe. This is true of any renormalizable theory of the see-saw mechanism based on the spontaneous breaking of B−L symmetry [5].…”

“…Second, supersymmetry helps us not to have uncontrollable VEVs from the left-handed triplet VEVs, and indeed the supersymmetry breaking effects are negligible for such high M R [5].…”

“…For example, this is what happens if the Dimopoulos-Wilczek mechanism [17] is employed to solve the doublet-triplet splitting problem. Let us briefly repeat the argument [5]. As mentioned above, the form (23) is obtained from the terms (H is the 10-dimensional Higgs)…”