  We present the three-body decay of the Higgs boson into two leptons and a
photon to dimension-eight in the Standard Model Effective Field Theory (SMEFT).
In order to obtain this result we interfere the full one-loop Standard Model
result with the tree-level result in the SMEFT. This is the first calculation
of the partial width of the Higgs boson into two leptons and a photon in the
SMEFT to incorporate the full one-loop dependence for the Standard Model as
well as the full tree level dimension-eight dependence in the SMEFT. We find
that this channel can aid in distinguishing strongly interacting and weakly
interacting UV completions of the SMEFT under standard assumptions. We also
find that this channel presents the opportunity to distinguish different
operator Classes within the SMEFT, potentially including contact
$H\bar\ell\ell\gamma$ operators which are first generated only at
dimension-eight in the SMEFT.
