3 The Standard Model of Electroweak Interactions
63
3.11 Electroweak Precision Tests in the SM and Beyond
For the analysis of electroweak data in the SM one starts from the input parameters:
as is the case in any renormalizable theory, masses and couplings have to be
specified from outside. One can trade one parameter for another and this freedom is
used to select the best measured ones as input parameters. Some of them, α, G F and
m Z , are very precisely known, as we have seen, some other ones, m f light , m t and
α s (m Z ) are less well determined while m H is largely unknown. Among the light
fermions, the quark masses are badly known, but fortunately, for the calculation
of radiative corrections, they can be replaced by α(m Z ), the value of the QED
running coupling at the Z mass scale. The value of the hadronic contribution to
the running, embodied in the value of
(5)
had (m 2
Z ) (see Table 3.1, [8] ) is obtained
through dispersion relations from the data on e + e − → hadrons at moderate centreof-mass energies. From the input parameters one computes the radiative corrections
to a sufficient precision to match the experimental accuracy. Then one compares the
theoretical predictions with the data for the numerous observables which have been
measured [45], checks the consistency of the theory and derives constraints on m t ,
α s (m Z ) and m H . A detailed discussion of all experimental aspects of precision tests
of the EW theory is presented in Chap. 6.
The basic tree level relations:
g 2
8m 2
W
=
G F
√
2
,
g
2 sin
2 θ W = e
2
= 4πα
(3.97)
can be combined into
sin
2 θ W =
πα
√
2G F m 2
W
(3.98)
Always at tree level, a different definition of sin 2 θ W is from the gauge boson
masses:
m 2
W
m 2
Z cos 2 θ W
= ρ 0 = 1 ⇒ sin
2 θ W = 1 −
m 2
W
m 2
Z
(3.99)
where ρ 0 = 1 assuming that there are only Higgs doublets. The last two relations
can be put into the convenient form
(1 −
m 2
W
m 2
Z
)
m 2
W
m 2
Z
=
πα
√
2G F m 2
Z
(3.100)
63
3.11 Electroweak Precision Tests in the SM and Beyond
For the analysis of electroweak data in the SM one starts from the input parameters:
as is the case in any renormalizable theory, masses and couplings have to be
specified from outside. One can trade one parameter for another and this freedom is
used to select the best measured ones as input parameters. Some of them, α, G F and
m Z , are very precisely known, as we have seen, some other ones, m f light , m t and
α s (m Z ) are less well determined while m H is largely unknown. Among the light
fermions, the quark masses are badly known, but fortunately, for the calculation
of radiative corrections, they can be replaced by α(m Z ), the value of the QED
running coupling at the Z mass scale. The value of the hadronic contribution to
the running, embodied in the value of
(5)
had (m 2
Z ) (see Table 3.1, [8] ) is obtained
through dispersion relations from the data on e + e − → hadrons at moderate centreof-mass energies. From the input parameters one computes the radiative corrections
to a sufficient precision to match the experimental accuracy. Then one compares the
theoretical predictions with the data for the numerous observables which have been
measured [45], checks the consistency of the theory and derives constraints on m t ,
α s (m Z ) and m H . A detailed discussion of all experimental aspects of precision tests
of the EW theory is presented in Chap. 6.
The basic tree level relations:
g 2
8m 2
W
=
G F
√
2
,
g
2 sin
2 θ W = e
2
= 4πα
(3.97)
can be combined into
sin
2 θ W =
πα
√
2G F m 2
W
(3.98)
Always at tree level, a different definition of sin 2 θ W is from the gauge boson
masses:
m 2
W
m 2
Z cos 2 θ W
= ρ 0 = 1 ⇒ sin
2 θ W = 1 −
m 2
W
m 2
Z
(3.99)
where ρ 0 = 1 assuming that there are only Higgs doublets. The last two relations
can be put into the convenient form
(1 −
m 2
W
m 2
Z
)
m 2
W
m 2
Z
=
πα
√
2G F m 2
Z
(3.100)