  Low energy observables involving the Standard Model fermions which are
chirality-violating, such as anomalous electromagnetic moments, necessarily
involve an insertion of the Higgs in order to maintain $SU(2) \times U(1)$
gauge invariance. As the result, the properties of the Higgs boson measured at
the LHC impact our understanding of the associated low-energy quantities. We
illustrate this feature with a discussion of the electromagnetic moments of the
$\tau$-lepton, as probed by the rare decay $H \rightarrow \tau^+ \tau^-
\gamma$. We assess the feasibility of measuring this decay at the LHC, and show
that the current bounds from lower energy measurements imply that $13~\rm{TeV}$
running is very likely to improve our understanding of new physics contributing
to the anomalous magnetic moment of the tau.
