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–1–
Z
±
BOSON SEARCHES
Revised September 2009 by M.C. Chen (UC Irvine) and
B.A. Dobrescu (Fermilab).
The
Z
±
boson is a hypothetical massive, electricallyneutral
and colorsinglet particle of spin 1. This particle is predicted
in many extensions of the standard model, and has been the
object of extensive phenomenological studies [1].
Z
±
couplings to quarks and leptons.
The couplings of a
Z
±
boson to the ±rstgeneration fermions are given by
Z
±
μ
(
g
L
u
u
L
γ
μ
u
L
+
g
L
d
d
L
γ
μ
d
L
+
g
R
u
u
R
γ
μ
u
R
+
g
R
d
d
R
γ
μ
d
R
+
g
L
ν
ν
L
γ
μ
ν
L
+
g
L
e
e
L
γ
μ
e
L
+
g
R
e
e
R
γ
μ
e
R
)
,
(1)
where
u, d, ν
and
e
are the quark and lepton ±elds in the
mass eigenstate basis, and the coeﬃcients
g
L
u
,
g
L
d
,
g
R
u
,
g
R
d
,
g
L
ν
,
g
L
e
,
g
R
e
are real dimensionless parameters. If the
Z
±
couplings to
quarks and leptons are generationindependent, then these seven
parameters describe the couplings of the
Z
±
to all standard
model fermions. More generally, however, the
Z
±
couplings to
fermions are generationdependent, in which case Eq. (1) may
be written with some generation indices
i, j
=1
,
2
,
3 labelling
the quark and lepton ±elds, and with the seven coeﬃcients
promoted to 3
×
3 Hermitian matrices.
These parameters describing the
Z
±
interactions with quarks
and leptons are subject to some theoretical constraints. Quan
tum ±eld theories that include a heavy spin1 particle are well
behaved at high energies only if that particle is a gauge bo
son associated with a spontaneously broken gauge symmetry.
Quantum e²ects preserve the gauge symmetry only if the cou
plings of the gauge boson to fermions satisfy a certain set of
equations called anomaly cancellation conditions. Furthermore,
the fermion charges under the new gauge symmetry are con
strained by the requirement that the quarks and leptons get
masses from gaugeinvariant interactions with Higgs doublets
or whatever else breaks the electroweak symmetry.
The relation between the couplings displayed in Eq. (1)
and the gauge charges
z
L
f
i
and
z
R
f
i
of the fermions
f
=
u, d, ν, e
CITATION: K. Nakamura
et al.
(Particle Data Group), JPG
37
, 075021 (2010) (URL: http://pdg.lbl.gov)
July 30, 2010
14:34
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involves the unitary 3
×
3 matrices
V
L
f
and
V
R
f
that transform
the gauge eigenstate fermions
f
Li
and
f
Ri
, respectively, into the
mass eigenstate ones. In addition, the
Z
±
couplings are modiFed
if the new gauge boson
˜
Z
±
μ
(in the gauge eigenstate basis)
has a kinetic mixing (
−
χ/
2)
B
μν
˜
Z
±
μν
with the hypercharge
gauge boson
B
μ
, or a mass mixing
δM
2
˜
Z
μ
˜
Z
±
μ
with the linear
combination (
˜
Z
μ
) of neutral bosons which has same couplings
as the
Z
0
in the standard model [2].
Both the kinetic and
mass mixings shift the mass and couplings of the
Z
boson, such
that the electroweak measurements impose upper limits on
χ
and
2
/
(
M
2
Z
±
−
M
2
Z
) of the order of 10
−
3
[3].
Keeping only
linear terms in these two small quantities, the couplings of the
masseigenstate
Z
±
boson are given by
g
L
f
=
g
z
V
L
f
z
L
f
(
V
L
f
)
†
+
e
c
W
Ã
s
W
χM
2
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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
 Mass

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