Radiative seesaw: a case for split supersymmetry

We revive Witten's mechanism for the radiative seesaw induced neutrino masses in SO(10) grand unified theory. We propose its extension to charged fermion masses as a possible cure for wrong tree level mass relations. We offer two simple realizations that can produce a realistic fermionic spectrum. The first one requires two 10-dimensional Higgses in the Yukawa sector and utilizes radiative effects for charged fermion masses. The second one trades one 10- for a 120-dimensional Higgs and leads to the SO(10) theory with less parameters in the Yukawa sector. The mechanism works only if supersymmetry is broken at the GUT scale while gauginos and higgsinos remain at TeV. This provides a strong rationale for the so-called split supersymmetry.