Photons are massless, therefore, in the Standard Model, the
Higgs boson does not couple directly to photons. Instead, the
decay of the Higgs into 2 photons is a loop mediated process. It
happens to be dominated by two contributions: one, larger, from
the W boson, and the other, 5 times smaller, from the top quark.
Incidentally, these two contributions enter with opposite signs
(in fact it's not quite an accident but a consequence of the
theorem that links these contributions to the electromagnetic
beta function). The other known charged particles are expected
to contribute much less because their coupling to the Higgs is
much smaller. Now it is clear what tricks can be played to pump
up the Higgs decay width into photons: - Increase the Higgs
couplings to W bosons. But then one needs to explain why no
excess in the WW channel has been observed. - Decrease the Higgs
coupling to the top quark. But then the Higgs production rate
would be decreased as well, and one needs to cook up new
production channels. - Intr