  The canonical type-I seesaw model with three heavy Majorana neutrinos is one
of the most natural extensions of the standard model (SM) to accommodate tiny
Majorana masses of three ordinary neutrinos. At low-energy scales, Majorana
neutrino masses and unitarity violation of lepton flavor mixing have been
extensively discussed in the literature, which are respectively generated by
the unique dimension-five Weinberg operator and one dimension-six operator in
the seesaw effective field theory (SEFT) with the tree-level matching. In this
work, we clarify that a self-consistent calculation of radiative decays of
charged leptons $\beta^- \to \alpha^- + \gamma$ requires the SEFT with one-loop
matching, where new six-dimensional operators emerge and make important
contributions. For the first time, the Wilson coefficients of all the relevant
six-dimensional operators are computed by carrying out the one-loop matching
between the effective theory and full seesaw model, and applied to calculate
the total rates of radiative decays of charged leptons.
