  If neutrinos are Dirac particles, their right-handed partners must be present
in the theory. Once introduced in the Standard Model (SM), the difference
between the baryon number $B$ and the lepton number $L$ can be promoted to a
local $U(1)_{B-L}$ symmetry since the corresponding gauge anomalies can be
canceled by the right-handed neutrinos. Furthermore, the extremely small
neutrino mass can be explained naturally if it is originated from the quantum
correction. In this work, we propose simplest models of radiative Dirac
neutrino mass using only $U(1)_{B-L}$ symmetry, and without introducing
additional fermions and without imposing ad hoc symmetries. In this simple
framework, we provide minimal models where Dirac neutrino mass appears at the
(i) one-loop, (ii) two-loop and (iii) three-loop. By performing systematic
analysis, we show that the minimal one-loop model requires three beyond SM
scalar multiplets, whereas minimal two-loop and three-loop models require five.
The presented two-loop and three-loop Dirac mass models have not appeared in
the literature before.
