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\gammaHℓ‾ℓγ
operators which are first generated only at dimension-eight in the
SMEFT.