  The data collected by the LHC collaborations at an energy of 13 TeV indicates
the presence of an excess in the diphoton spectrum that would correspond to a
resonance of a 750 GeV mass. The apparently large production cross section is
nevertheless very difficult to explain in minimal models. We consider the
possibility that the resonance is a pseudoscalar boson $A$ with a two--photon
decay mediated by a charged and uncolored fermion having a mass at the $\frac12
M_A$ threshold and a very small decay width, $\ll 1$ MeV; one can then generate
a large enhancement of the $A\gamma\gamma$ amplitude which explains the excess
without invoking a large multiplicity of particles propagating in the loop,
large electric charges and/or very strong Yukawa couplings. The implications of
such a threshold enhancement are discussed in two explicit scenarios: i) the
Minimal Supersymmetric Standard Model in which the $A$ state is produced via
the top quark mediated gluon fusion process and decays into photons
predominantly through loops of charginos with masses close to $\frac12 M_A$ and
ii) a two Higgs doublet model in which $A$ is again produced by gluon fusion
but decays into photons through loops of vector--like charged heavy leptons. We
also comment on a minimal scenario in which the $A$ state couples only to
photons through a heavy lepton loop and is both produced and decays through
this coupling. In all these scenarios, while the mass of the charged fermion
has to be adjusted to be extremely close to half of the $A$ resonance mass, the
small total widths are naturally obtained if only suppressed three-body decay
channels occur. Finally, the implications of some of these scenarios for dark
matter are discussed.

High Energy Physics - Phenomenology