  We compute the one-loop running of the dimension-six CP-even Higgs operators
in the Standard Model effective field theory involving the right-handed
component of the would-be Dirac neutrinos. We discuss the implications of a
large Dirac neutrino magnetic dipole moment. In particular, we demonstrate that
a neutrino magnetic moment explaining the recent XENON1T excess induces Higgs
and $Z$ invisible decays with branching ratios in the range $[10^{-18},
10^{-12}]$. These numbers are unfortunately beyond the reach of current and
near future facilities.
