Ultralight Dirac neutrinos from possible supergrand scenario

Persistent experimental suggestions about the electron neutrino being an ultralight Dirac particle in the mass range 20 to 55 eV have underlined the need to theoretically generate such a mass naturally, i.e., without any arbitrarily small Yukawa coupling or Higgs-field vacuum expectation value. A mechanism for this is proposed in this paper in terms of a 4×4 neutral-fermion Majorana mass matrix for a single-generation world. The physical eigenstates turn out to be one ultralight and one very heavy Dirac neutrino within each fermion family. A general discussion (including the many-generation case) is given of the necessary and sufficient conditions for the emergence of such ultralight Dirac neutrinos. We also consider the skeleton of an illustrative, though incomplete, SO(10) supersymmetric (SUSY) grand unified theory (GUT) scenario—with a geometric type of hierarchy and some global symmetries—in which the aforesaid mass matrix is likely to arise. The ultralight neutrino Dirac mass is related at the tree level to that of its charge-$\frac{2}{3}$ family member by $m_{\nu }\sim m\left(\frac{2}{3}\right)\frac{M_{\mathrm{SUSY}}}{M_{\mathrm{GUT}}}$ and radiative corrections are shown to be controllably small. Various implications of this result are brought out.