Pictures Paths Particles Processes

November 7, 2013 247
where we must realize that the Dirac unit matrix is involved 25 . For the process
UU → W W we then have a fourth available diagram :
which contributes to the amplitude the amount
M 4 = −i¯h g UUH g WWH v(p 1 )u(p 2 )
In the fully longitudinal case we therefore have
1
s − m H
2 (ɛ +.ɛ − ) . (9.111)
M 4 ⌋ =
− i¯h g UUHg WWH
2m W
2
v(p 1 )u(p 2 ) + · · · , (9.112)
and the following requirement on g UUH is obtained :
or
Q W 2 m U
4s W
2
+ ¯h g UUHg WWH
2m W
2
= 0 , (9.113)
g UUH = − Q W m U
. (9.114)
2s W m W
This discussion can of course be applied to any fermion type 26 , and we find the
general Feynman rule
f
f
H
↔
ī h
e
2s W
m f
m W
1
9.4.5 Higgs self-interactions
The triple H coupling
There remains the issue of possible self-interactions of the Higgs particle. To
this end we examine not a 2 → 2 but a 2 → 3 process, namely
Z(p 1 , ɛ 1 ) Z(p 2 , ɛ 2 ) → Z(p 3 , ɛ 3 ) Z(p 4 , ɛ 4 ) H(p 5 ) .
At the tree level, this process is described by 21 Feynman diagrams provided we
allow for three-point couplings between H’s. These belong to one of the three
25 In fact, the observation that the nonsafe part in this process is proportional to vu is the
strongest argument in favour of a scalar Higgs.
26 Note that for D-type fermions, a D has opposite sign ; but also the W + and W − are
interchanged in the first diagram.