Next: Fermionic decays
Up: Higgs decays
Previous: Higgs decays
Starting from the Feynman rule for the HZZ vertex [7] in
fig. 2.7 the partial Higgs width
can be
calculated. The matrix element is

i M _{H ZZ} = igg_{}
 (27)

with
, the polarisation vectors of the two Z
bosons with polarisation indices
, .
Figure 2.7:
The decay of a Higgs boson to two Z^{ 0} bosons with
four momentum p , q and the Feynman rule for the vertex.

For the twobody decay to two equal mass particles the differential
decay rate [16] is given as
where n is the number of identical final state particles of type
k . The squared matrix element can from (2.41) be
written as

M ^{2} = 2g_{}g_{}
 (28)

The summation over the three polarisation states of the massive Z
bosons [16] is
which is just the Lorentz covariant generalisation of having three
orthonormal polarisation vectors e _{} in the rest frame
of the Z where

e ^{i}_{}e ^{j}_{} = .
 (30)

The squared matrix element (2.45) can now be
simplified as
The decay rate can be written as
The width of the Higgs decaying to W^{ +}W^{ } is the same as the
calculation above, except that the two decay particles are not equal
leading to a factor two larger result from (2.44). In a notation
with scaling variables the results can be given as
where

x_{Z} = 4, x_{W} = 4.
 (31)

It is the longitudinal polarisation that is responsible for the second
part of the sum in (2.46) and by following this part
onwards to (2.60) it is seen that the transverse
polarisation only enters with powers of x_{Z}/x_{W} or higher.
At high Higgs masses the Higgs coupling to vector mesons is thus
totally dominated by the longitudinal vector boson states.
Next: Fermionic decays
Up: Higgs decays
Previous: Higgs decays
Ulrik Egede
1/8/1998