  We study a Dirac neutrino mass model of Davidson and Logan. In the model, the
smallness of the neutrino mass is originated from the small vacuum expectation
value of the second Higgs of two Higgs doublets. We study the one loop
effective potential of the Higgs sector and examine how the small vacuum
expectation is stable under the radiative correction. By deriving formulae of
the radiative correction, we numerically study how large the one loop
correction is and show how it depends on the quadratic mass terms and quartic
couplings of the Higgs potential. The correction changes depending on the
various scenarios for extra Higgs mass spectrum.
