  The one-loop contribution of scalar and vector leptoquarks (LQs) to the
electromagnetic properties (NEPs) of massive Dirac neutrinos is presented via
an effective Lagrangian approach, with emphasis on the effective neutrino
charge radius (NCR), which has never been calculated and is obtained by the
background field formalism in a Yang-Mills-like scenario for gauge LQs.
Analytical results for nonzero neutrino mass are presented in terms of both
Feynman-parameter integrals and Passarino-Veltman scalar functions, which can
be useful to obtain the NEPs of heavy neutrinos, out of which approximate
expressions are obtained for light neutrinos. For the numerical analysis we
concentrate on the only renormalizable scalar and vector LQ representations
that do not need extra symmetries to forbid tree-level proton decay.
Constraints on the parameter space consistent with current experimental data
are then discussed and it is found that the LQ representations
$\widetilde{R}_2$ and $U_1$ could yield the largest contributions to the NEPs
provided that they have couplings to both left- and right-handed neutrinos of
the order of $O(1)$. For a LQ mass of $1.5$ TeV, the magnetic dipole moment
(MDM) of the tau neutrino can be of the order of $10^{-9}$ $\mu_B$, whereas its
neutrino electric dipole moment (EDM) can reach values as high as
$10^{-20}$-$10^{-19}$ ecm. On the other hand, the NCR can reach values up to
$10^{-35}$ cm$^2$ regardless of the neutrino flavor and even in the absence of
right-handed neutrinos. In the latter scenario, the EDM vanishes and the
contribution to neutrino MDM would be negligible, of the order of $10^{-14}$
$\mu_B$ for the tau neutrino, whereas those for the muon and electron neutrinos
would be about two and seven orders of magnitude smaller, respectively. Our
estimates could be severely suppressed due to a possible suppression of the LQ
coupling constants.
