Pictures Paths Particles Processes

November 7, 2013 241
certainly cannot be a fermion ; if it were a vector particle, its propagator would
contain unwanted higher powers of the energy E, the W W H and ZZH would
presumably be of Yang-Mills type hence also E-dependent. The vertices given
above are essentially the only ones possible for the interactions between two
vectors and a scalar if we want them to be energy-independent. Note that g WWH
and g ZZH may both be expected to contain a mass, that is, they are of dimension
L −1 / √¯h. The assumption that there is just one type of neutral scalar involved
is, of course, based on nothing but a prejudice in favour of simplicity. Finally,
at high energy all contributions from m H end up in safe terms, and we do not
expect to glean any information on the Higgs mass from our considerations.
W W → W W scattering
Another four-boson scattering process of interest is
W + (p 1 , ɛ 1 )W + (p 2 , ɛ 2 ) → W + (p 3 , ɛ 3 )W + (p 4 , ɛ 4 )
for which we have five purely vector-boson diagrams :
1
2
γ,Ζ
4
3
1
γ,Ζ
4 1
2 3
2
3
4
whose contributions can be conviently written as
M 1 = −i¯h Y (p 3 , ɛ 3 ; −p 1 , ɛ 1 ; p 1 − p 3 , µ)
(
2 −g µν
× Q W
(p 1 − p 3 ) 2 + g 2 −gµν + (p 1 − p 3 ) µ (p 1 − p 3 ) ν )
2
/m W
WWZ
(p 1 − p 3 ) 2 − m
2 Z
× Y (p 4 , ɛ 4 ; −p 2 , ɛ 2 ; p 2 − p 4 , ν) ,
M 2 = M 1 ⌋ p3,ɛ 3 ↔ p 4,ɛ 4
,
M 3 = i¯h Q 2
W
s
2 X(ɛ 3, ɛ 4 , ɛ 1 , ɛ 2 ) . (9.87)
W
By the same methods as used in the previous section we arrive at
⎥ ⎥⎥⎦ 3∑
M j
L
j=1
= i¯h E2 Q W
2
m W4 s W
2
(
−4mW 2 + 3m Z 2 c W
2 ) + · · · (9.88)
The Higgs hypothesis now provides for two additional diagrams :
1
2
H
4
3
1
2
H
3
4