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Since the photon is massless there is no coupling between the standard
model Higgs and the photon. However, the decay is possible through
loop processes with either fermions or bosons in the loop. For an
extended Higgs sector charged scalars can also enter. Feynman
diagrams for the lowest order processes are shown in
fig. 2.9.
Figure 2.9:
Feynman diagrams in the Standard Model for the Higgs
decay to two photons in lowest order.

The calculation of the matrix element for the decay is rather
complicated and involves dimensional regularisation of the infinities
arising from the loop. The end result for the squared matrix element
is [20]

M ^{2} = 2,
 (34)

with the sum over all scalars, fermions and bosons in the loop with
charge e_{i} and colour factor N_{c} (3 for quarks else 1). The factor
F is given as
The term
F_{fermion} disappears for small which means
that light quarks and leptons are insignificant. The only fermion
participating is the top quark. For bosons the loop only contains the
charged W.
The F parameters for the top and W contributions scaled with the
colour factor are plotted in fig. 2.10 for the Higgs
mass range where the decay is of interest. It can be seen how the
fermion and boson loops have opposite signs but with the W loop
dominating. Adding a fourth family with the lepton and the two quarks
having masses above 500 GeV will give a near cancellation in the
matrix element. A possible scalar particle in the loop will only have
a small influence following (2.74).
Figure:
The contribution from the W and top quark loop to the
matrix element in the
H decay. The sum of the two and the
influence of adding a 4th heavy family (
l',',b',t')
is also shown.

The width of the
H decay channel is now easily obtained using
(2.42) and performing the trivial angular
integration. The result is
which always gives a branching ratio below 0.3% due to the much
larger width of the
H b decay. The two photon signature is, however,
clean and as will be seen in section 2.6.1 an
important decay channel at the LHC. Adding a fourth family will reduce
the branching ratio by more than a factor 8 if the Higgs mass is below
140 GeV.
The radiative corrections to the
H decay width are relatively
simple as they only affect the top quark loop and neither the W loop
nor the final state photons. The corrections are below
3% [21] and thus of limited importance.
Next: Two gluon decay
Up: Higgs decays
Previous: Fermionic decays
Ulrik Egede
1/8/1998