  In this paper we present general formulae for the calculation of LFV Higgs
decays $H_r \to l_a l_b$ at one-loop, with $H_r$ being part of the Higgs
spectrum of a generic multi-scalar extension of the Standard Model (SM) with
neutrino masses. We develop a method based on a classification of the particles
appearing in the loop diagrams (scalars, fermions and vectors), and by
identifying the corresponding couplings, we are able to present compact
expressions for the form factors involved in the amplitudes. Our results are
applicable to models where Flavor Changing Neutral Currents (FCNC) are
forbidden at tree-level, but change of flavor is induced by charged currents.
Then, as applications of our formalism, we evaluate the branching ratio for the
mode $h \to l_a l_b$, for two specific models: the See-Saw Type I-$\nu$SM and
the Scotogenic model (here $h = H_1$ corresponds to the SM-like Higgs boson);
we find that the largest branching ratio for SM-like Higgs $h$ boson within the
$\nu$SM is of the order $\mathcal{BR}(h\to \mu \tau)\simeq 10^{-12}$, while for
the Scotogenic model we find $\mathcal{BR}(h\to l_a l_b)\lesssim 10^{-9}$,
which satisfy the latest experimental LHC results.

High Energy Physics - Phenomenology