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10. Electroweak model and constraints on new physics
1
10. ELECTROWEAK MODEL AND
CONSTRAINTS ON NEW PHYSICS
Revised November 2009 by J. Erler (U. Mexico) and P. Langacker (Institute for Advanced
Study).
10.1
Introduction
10.2
Renormalization and radiative corrections
10.3
Low energy electroweak observables
10.4
W
and
Z
boson physics
10.5
Precision ﬂavor physics
10.6
Experimental results
10.7
Constraints on new physics
10.1. Introduction
The standard electroweak model (SM) is based on the gauge group [1] SU(2)
×
U(1),
with gauge bosons
W
i
μ
,
i
=1
,
2
,
3,
and
B
μ
for the SU(2) and U(1) fac
tors,
respectively,
and the corresponding gauge coupling constants
g
and
g
±
.
The lefthanded fermion Felds of the
i
th
fermion family transform as doublets
Ψ
i
=
µ
ν
i
±
−
i
¶
and
µ
u
i
d
±
i
¶
under SU(2), where
d
±
i
≡
∑
j
V
ij
d
j
,and
V
is the Cabibbo
KobayashiMaskawa mixing matrix. (Constraints on
V
and tests of universality are
d
i
s
cu
s
s
edinR
e
f
.2andinth
eS
e
c
t
i
onon“Th
eCKMQu
a
rk
M
ix
in
gM
a
t
r
”
.Th
e
extension of the formalism to allow an analogous leptonic mixing matrix is discussed in
the Section on “Neutrino Mass, Mixing, and ±lavor Change”.) The righthanded Felds
are SU(2) singlets. In the minimal model there are three fermion families and a single
complex Higgs doublet
φ
≡
³
φ
+
φ
0
´
which is introduced for mass generation.
After spontaneous symmetry breaking the Lagrangian for the fermion Felds,
ψ
i
,is
L
F
=
X
i
ψ
i
µ
i
±
∂
−
m
i
−
gm
i
H
2
M
W
¶
ψ
i
−
g
2
√
2
X
i
Ψ
i
γ
μ
(1
−
γ
5
)(
T
+
W
+
μ
+
T
−
W
−
μ
)Ψ
i
−
e
X
i
q
i
ψ
i
γ
μ
ψ
i
A
μ
−
g
2cos
θ
W
X
i
ψ
i
γ
μ
(
g
i
V
−
g
i
A
γ
5
)
ψ
i
Z
μ
.
(10
.
1)
θ
W
≡
tan
−
1
(
g
±
/g
) is the weak angle;
e
=
g
sin
θ
W
is the positron electric charge; and
A
≡
B
cos
θ
W
+
W
3
sin
θ
W
is the (massless) photon Feld.
W
²
≡
(
W
1
∓
iW
2
)
/
√
2and
Z
≡−
B
sin
θ
W
+
W
3
cos
θ
W
are the massive charged and neutral weak boson Felds,
K. Nakamura
et al.
,JPG
37
, 075021 (2010) (http://pdg.lbl.gov)
July 30, 2010
14:36
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10. Electroweak model and constraints on new physics
respectively.
T
+
and
T
−
are the weak isospin raising and lowering operators. The vector
and axialvector couplings are
g
i
V
≡
t
3
L
(
i
)
−
2
q
i
sin
2
θ
W
,
(10
.
2
a
)
g
i
A
≡
t
3
L
(
i
)
,
(10
.
2
b
)
where
t
3
L
(
i
) is the weak isospin of fermion
i
(+1
/
2for
u
i
and
ν
i
;
−
1
/
d
i
and
e
i
)and
q
i
is the charge of
ψ
i
in units of
e
.
The second term in
L
F
represents the chargedcurrent weak interaction [3,4].
For
example, the coupling of a
W
to an electron and a neutrino is
−
e
2
√
2sin
θ
W
h
W
−
μ
eγ
μ
(1
−
γ
5
)
ν
+
W
+
μ
νγ
μ
(1
−
γ
5
)
e
i
.
(10
.
3)
For momenta small compared to
M
W
, this term gives rise to the e±ective fourfermion
interaction with the Fermi constant given (at tree level,
i.e.
, lowest order in perturbation
theory) by
G
F
/
√
2=
g
2
/
8
M
2
W
.
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This note was uploaded on 06/07/2011 for the course PHYS 4132 taught by Professor Kutter during the Spring '11 term at University of Florida.
 Spring '11
 Kutter
 Physics, The Land

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