Small and calculable Dirac neutrino mass

We present an extension of the left-right-symmetric model by including extra singlet quarks and leptons, which leads to calculable ${\mathrm{W}}_{\mathrm{L}}$-${\mathrm{W}}_{\mathrm{R}}$ mixing and an ultralight Dirac mass for the neutrino. For a ${\mathrm{W}}_{\mathrm{R}}$ mass in the tera-electron-volt range, the neutrino masses can be in the right range to explain the solar neutrino puzzle via the Mikheyev-Smirnov-Wolfenstein oscillation amplification mechanism. Crucial for our results is a ‘‘see-saw’’-type mechanism for the smallness of the d-quark masses.