  We consider a rather minimal extension of the Standard Model involving just
one extra particle, namely a single $SU(2)_L$ singlet scalar $S^{++}$ and its
antiparticle $S^{--}$. We propose a model independent effective operator, which
yields an effective coupling of $S^{\pm \pm}$ to pairs of same sign weak gauge
bosons, $W^{\pm} W^{\pm}$. We also allow tree-level couplings of $S^{\pm \pm}$
to pairs of same sign right-handed charged leptons $l^{\pm}_Rl'^{\pm}_R$ of the
same or different flavour. We calculate explicitly the resulting two-loop
diagrams in the effective theory responsible for neutrino mass and mixing. We
propose sets of benchmark points for various $S^{\pm \pm}$ masses and couplings
which can yield successful neutrino masses and mixing, consistent with limits
on charged lepton flavour violation (LFV) and neutrinoless double beta decay.
We discuss the prospects for $S^{\pm \pm}$ discovery at the LHC, for these
benchmark points, including single and pair production and decay into same sign
leptons plus jets and missing energy. The model represents a minimal example of
the complementarity between neutrino physics (including LFV) and the LHC,
involving just one new particle, the $S^{\pm \pm}$.
