410
22. The GSW Gauge Theory of Electroweak Interactions
1963, Kobayashi and Maskawa 1973), originally introduced by Kobayashi
and Maskawa in the context of their three-generation extension of the thendeveloping Standard Model, in order to provide room for CP violation within
the SU(2) × U(1) gauge theory framework. The interaction (22.160) then has
the form
g
− √ ˆ ¯ μ ˆ ′
¯ μ
¯
ˆ
W μ [u ˆ L γ d L + c ˆ L γ s ˆ
′
L + t ˆ L γ
μ b
′
L ] + h.c.,
(22.162)
2
where
(
) (
) (
)
ˆ
d
′
ˆ
L
V ud V us V ub
d L
( s ˆ
′ ) = ( V cd V cs V cb ) ( s )
L
ˆ L
,
(22.163)
ˆ b
V td V ts V tb
ˆ
L
′
b L
with the phenomenology described in the previous chapter.
An analysis similar to the above can be carried out in the leptonic sector.
We would then have leptonic flavour mixing in charged current processes,
via the leptonic analogue of the CKM matrix, namely the PMNS matrix
(Pontecorvo 1957, 1958, 1967; Maki, Nakagawa and Sakata 1962); this is
the matrix whose elements are probed in neutrino oscillations, as we saw in
chapter 21.
22.6 Higher-order corrections
The Z
0 mass
M Z = 91.1876 ± 0.0021 GeV
(22.164)
has been determined from the Z-lineshape scan at LEP1 (Schael et al. 2006).
The W mass is (Nakamura et al. 2010)
M W = 80.399 ± 0.023 GeV.
(22.165)
The asymmetry parameter A e (see (22.100)) is (Abe et al. (2000))
A e = 0.15138 ± 0.00216
(22.166)
from measurements at SLD. These are just three examples from the table
of 36 observables listed in the review of the electroweak model by Erler and
Langacker in Nakamura et al. (2010). Such remarkable precision is a triumph of machine design and experimental art – and it is the reason why we
need a renormalizable electroweak theory. The overall fit to the data, including higher-order corrections, is generally very good, as quoted by Erler and
Langacker with χ
2 /d.o.f = 43.0/44. One of the few discrepancies is a 2.7σ de(0,b)
viation in the Z-pole forward-backward asymmetry A FB from LEP1; another
is a 2.5σ deviation in the muon anomalous magnetic moment, g μ − 2. This
strong numerical consistency lends impressive support to the belief that we
22. The GSW Gauge Theory of Electroweak Interactions
1963, Kobayashi and Maskawa 1973), originally introduced by Kobayashi
and Maskawa in the context of their three-generation extension of the thendeveloping Standard Model, in order to provide room for CP violation within
the SU(2) × U(1) gauge theory framework. The interaction (22.160) then has
the form
g
− √ ˆ ¯ μ ˆ ′
¯ μ
¯
ˆ
W μ [u ˆ L γ d L + c ˆ L γ s ˆ
′
L + t ˆ L γ
μ b
′
L ] + h.c.,
(22.162)
2
where
(
) (
) (
)
ˆ
d
′
ˆ
L
V ud V us V ub
d L
( s ˆ
′ ) = ( V cd V cs V cb ) ( s )
L
ˆ L
,
(22.163)
ˆ b
V td V ts V tb
ˆ
L
′
b L
with the phenomenology described in the previous chapter.
An analysis similar to the above can be carried out in the leptonic sector.
We would then have leptonic flavour mixing in charged current processes,
via the leptonic analogue of the CKM matrix, namely the PMNS matrix
(Pontecorvo 1957, 1958, 1967; Maki, Nakagawa and Sakata 1962); this is
the matrix whose elements are probed in neutrino oscillations, as we saw in
chapter 21.
22.6 Higher-order corrections
The Z
0 mass
M Z = 91.1876 ± 0.0021 GeV
(22.164)
has been determined from the Z-lineshape scan at LEP1 (Schael et al. 2006).
The W mass is (Nakamura et al. 2010)
M W = 80.399 ± 0.023 GeV.
(22.165)
The asymmetry parameter A e (see (22.100)) is (Abe et al. (2000))
A e = 0.15138 ± 0.00216
(22.166)
from measurements at SLD. These are just three examples from the table
of 36 observables listed in the review of the electroweak model by Erler and
Langacker in Nakamura et al. (2010). Such remarkable precision is a triumph of machine design and experimental art – and it is the reason why we
need a renormalizable electroweak theory. The overall fit to the data, including higher-order corrections, is generally very good, as quoted by Erler and
Langacker with χ
2 /d.o.f = 43.0/44. One of the few discrepancies is a 2.7σ de(0,b)
viation in the Z-pole forward-backward asymmetry A FB from LEP1; another
is a 2.5σ deviation in the muon anomalous magnetic moment, g μ − 2. This
strong numerical consistency lends impressive support to the belief that we