087. Z -Boson Searches

1087. Z -Boson Searches
Revised September 2023 by B.A. Dobrescu (FNAL) and S. Willocq (U. Massachusetts).
The Z 0 boson is a massive, electrically-neutral and color-singlet hypothetical particle of spin 1.
This particle is predicted in many extensions of the Standard Model (SM) and has been the objectof extensive phenomenological studies [1].

87.1 Z 0 boson couplings
The couplings of a Z 0 boson to the first-generation fermions are given by

Zµ0 guL uL γ µ uL + gdL dL γ µ dL + guR uR γ µ uR + gdR dR γ µ dR + gνL ν L γ µ νL + geL eL γ µ eL + geR eR γ µ eR ,(87.1)
where u, d, ν, e are the quark and lepton fields in the mass eigenstate basis, and the coefficients
guL , gdL , guR , gdR , gνL , geL , geR are real dimensionless parameters. If the Z 0 couplings to quarks andleptons are generation-independent, then these seven parameters describe the couplings of the Z 0
boson to all SM fermions. More generally, however, the Z 0 couplings to fermions are generationdependent, in which case Eq. (87.1) may be written with generation indices i, j = 1, 2, 3 labelingthe quark and lepton fields, and with the seven coefficients promoted to 3 × 3 Hermitian matrices(e.g., geL ij eiL γ µ ejL , where e2L is the left-handed muon, etc.).
The parameters describing the Z 0 boson interactions with quarks and leptons are subject tosome theoretical constraints. Quantum field theories that include a heavy spin-1 particle are well
behaved at high energies only if that particle is a gauge boson associated with a spontaneously
broken gauge symmetry. Quantum effects preserve the gauge symmetry only if the couplings ofthe gauge boson to fermions satisfy the anomaly equations [2]. Furthermore, the fermion charges
under the new gauge symmetry are constrained by the requirement that the quarks and leptons
get masses from gauge-invariant interactions with the Higgs fields.
The relation between the couplings displayed in Eq. (87.1) and the gauge charges zfLi and zfRiof the fermions f = u, d, ν, e involves the unitary 3 × 3 matrices VfL and VfR that transform thegauge eigenstate fermions fLi and fRi , respectively, into the mass eigenstates. The Z 0 couplings also
depend on the mixings of the new gauge boson in the gauge eigenstate basis (Z̃µ0 ). The main mixings
0 with the hypercharge gauge boson B µ (χ is a dimensionlessare a kinetic mixing (−χ/2)B µν Z̃µνparameter), and a mass mixing δM 2 Z̃ µ Z̃µ0 with the linear combination (Z̃µ ) of neutral bosons that
couples as the SM Z boson [3]. Since both the kinetic and mass mixings shift the mass and couplingsof the Z boson, electroweak measurements impose upper limits on χ and δM 2 /(MZ2 0 − MZ2 ) of theorder of 10−3 [4]. Keeping only linear terms in these two small quantities, the couplings of the
mass-eigenstate Z 0 boson are given by
gfL ij = gz VfLii0 zfL i0



VfL

e
+
0
ij
cW

†

!

sW χMZ2 0 + δM 2 3
 σ −  Qf ,2sW MZ2 0 −MZ2 f(87.2)e Qf ,(87.3)
cW
where gz is the new gauge coupling, Qf is the electric charge of f , e is the electromagnetic gauge
coupling, sW and cW are the sine and cosine of the weak mixing angle, σf3 = +1 for f = u, ν and
σf3 = −1 for f = d, e, andχ MZ2 0 − c2W MZ2 + sW δM 2
=.
(87.4)
MZ2 0 − MZ2

gfR ij = gz VfRii0 zfRi0 VfR

†

i0 j

−

S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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087. Z -Boson Searches

2

The interaction of the Z 0 boson with a pair of W bosons has the form
h 



i





i Wµ− Zν0 −Wν− Zµ0 ∂ µ W +ν+ H.c. + i Wµ+ Wν−−Wν+ Wµ− ∂ µZ 0ν

(87.5)

2 /M 2 [5]. The Z 0 also couples to one SM Higgs boson and one Z
with a coefficient of order MW
Z0boson, Zµ0 Z µ h0 , with a coefficient of order MZ .

87.2 Z 0 models
A simple origin of a Z 0 boson is a new U (1)0 gauge symmetry. In that case, the matricial
equalities zuL = zdL and zνL = zeL are required by the SM SU (2)W gauge symmetry. Given that theU (1)0 interaction is not asymptotically free, the theory may be well-behaved at high energies (e.g.,
by embedding U (1)0 in a non-Abelian gauge group) only if the charges are commensurate numbers,
i.e. any ratio of charges is a rational number. Satisfying the anomaly equations [6] with rational
numbers is highly nontrivial, and typically new fermions charged under U (1)0 are necessary.
If the couplings are generation-independent (VfL,R are then unit matrices in Eq. (87.2)) and themixings of Z̃ 0 are negligible, then there are five commensurate couplings: guR , gdR , geR , gqL (q = uor d), glL (l = ν or e). Four sets of charges are displayed in Table 87.1, each of them spannedby a free parameter x [6]. The first set, labeled B − xL, has charges proportional to the baryon
number minus x times the lepton number. These charges allow all SM Yukawa couplings to the
Higgs doublet which is neutral under U (1)B−xL , so that there is no tree-level Z̃ − Z̃ 0 mixing. For
x = 1 one recovers the U (1)B−L group, which is non-anomalous in the presence of one “righthanded neutrino” (a chiral fermion that is a singlet under the SM gauge group) per generation.
For x 6= 1, it is necessary to include some fermions that are vectorlike (i.e. their mass terms aregauge invariant) with respect to the electroweak gauge group and chiral with respect to U (1)B−xL .
In the particular cases x = 0 or x  1, the Z 0 is leptophobic or quark-phobic, respectively.
The second set, U (1)10+x5̄ , has charges that commute with the representations of the SU (5)grand unified group. Here x is related to the mixing angle between the two U (1) bosons encounteredin the E6 → SU (5) × U (1) × U (1) symmetry breaking patterns of grand unified theories [1,7]. With
these charges, two Higgs doublets are typically required to generate masses for both up- and downtype fermions. This set leads to Z̃ − Z̃ 0 mass mixing at tree level, such that for a Z 0 mass close
to the electroweak scale, the measurements at the Z-pole require some fine tuning between the
charges and VEVs of the two Higgs doublets. Vectorlike quarks charged under the electroweak
gauge group are required (except for x = −3) to make this set anomaly free. The particular cases
x = −3, 1, −1/2 are usually labeled U (1)χ , U (1)ψ , and U (1)η , respectively. Under the third set,
U (1)d−xu , the weak-doublet quarks are neutral, and the ratio of uR and dR charges is −x. For
x = 1, this is the “right-handed” group U (1)R . For x = 0, the charges are those of the E6 -inspired
U (1)I group, which requires new quarks and leptons. Other generation-independent sets of U (1)0charges are given in Ref. [8].
In the absence of new fermions charged under the SM group, the most general generationindependent charge assignment is U (1)q+xu , which is a linear combination of hypercharge and
B − L. Many other anomaly-free solutions exist if generation-dependent charges are allowed. An
example is B − xLe − yLµ + (y − 3)Lτ , with x, y free parameters. This allows all fermion masses
to be generated by Yukawa couplings to a single Higgs doublet, without inducing tree-level flavorchanging neutral current (FCNC) processes. There are also lepton-flavor dependent charges thatallow neutrino masses to arise only from operators of high dimensionality [9].
If the SU (2)W -doublet quarks have generation-dependent U (1)0 charges, then the mass eigenstate quarks have flavor off-diagonal couplings to the Z 0 boson (see Eq. (87.1), and note that
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087. Z -Boson Searches

3

Table 87.1: Examples of generation-independent U (1)0 charges for quarks
and leptons. The parameter x is an arbitrary rational number. Gauge
anomaly cancellation requires certain new fermions [6].

fermion(uL , dL )U (1)B−xL
1/3

U (1)10+x5̄
1/3

U (1)d−xu0

U (1)q+xu
1/3

uR

1/3

−1/3

−x/3

x/3

dR

1/3

−x/3

1/3

(2 − x)/3(νL , eL )

−x

x/3

(−1 + x)/3

−1

eR

−x

−1/3

x/3

−(2 + x)/3†

VuL VdL is the CKM matrix). These are severely constrained by measurements of FCNC processes, which in this case are mediated at tree-level by Z 0 boson exchange [10]. The constraints
are relaxed if the first and second generation charges are the same, although they are increasingly
tightened by the measurements of B meson properties [11]. If only the SU (2)W -singlet quarks
have generation-dependent U (1)0 charges, there is more freedom in adjusting the flavor off-diagonal
R matrices are not observable in the SM.
couplings because the Vu,dThe anomaly equations for U (1)0 could be circumvented only if there is an axion with certain
dimension-5 couplings to the gauge bosons. However, such a scenario violates unitarity unless thequantum field theory description breaks down at a scale near MZ 0 [12]. It is possible, though,that the SM fermions are not charged under the U (1)0 , but have mass mixing with some vectorlike
fermions which are charged under U (1)0 , implying that the physical fermions have couplings to theZ 0 [13]. For example, if the only SM quarks that have large mixings with some vectorlike quarks are
the b quarks, then the only currently known particles that couple to the Z 0 would be the physicalb quarks.
Z 0 bosons may also arise from larger gauge groups. These may extend the electroweak group,as in SU (2) × SU (2) × U (1), or may embed the electroweak group, as in SU (3)W × U (1) [14]. If thelarger group is spontaneously broken down to SU (2)W ×U (1)Y ×U (1)0 at a scale v?  MZ 0 /gz , thenthe above discussion applies up to corrections of order MZ2 0 /(gz v? )2 . For v? ∼ MZ 0 /gz , additional
gauge bosons have masses comparable to MZ 0 , including at least a W 0 boson [14]. If the larger
gauge group breaks together with the electroweak symmetry directly to the electromagnetic U (1)em ,then the left-handed fermion charges are no longer correlated (zuL 6= zdL , zνL 6= zeL ) and a Z 0 W + W −coupling is induced.
If the electroweak gauge bosons propagate in extra dimensions, then their Kaluza-Klein (KK)
excitations include a series of Z 0 boson pairs. Each of these pairs can be associated with a different
SU (2) × U (1) gauge group in four dimensions. The properties of the KK particles depend strongly
on the extra dimensional theory [15]. For example, in universal extra dimensions there is a paritythat forces all couplings of Eq. (87.1) to vanish in the case of the lightest KK bosons, whileallowing couplings to pairs of fermions involving a SM and a heavy vectorlike fermion. There arealso 4-dimensional gauge theories (e.g. little Higgs with T parity) with Z 0 bosons exhibiting similar
properties. By contrast, in a warped extra dimension, the couplings of Eq. (87.1) may be sizable
even when SM fields propagate along the extra dimension.
Z 0 bosons may also be composite particles. For example, in confining gauge theories [16], theρ-like bound state is a spin-1 boson that may be interpreted as arising from a spontaneously broken
gauge symmetry [17].

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4087. Z -Boson Searches

87.3 Non-resonant Z 0 signatures at colliders
In the presence of the couplings shown in Eq. (87.1), the Z 0 boson may be produced in the schannel at colliders, and would decay to pairs of fermions. The decay width into a pair of electrons
is given by  2  2  M 0
ZΓ Z 0 → e+ e− ' geL + geR,(87.6)
24π
where small corrections from electroweak loops are not included. The decay width into q q̄ is similar,
except for an additional color factor of 3, QCD radiative corrections, and fermion mass corrections.
Thus, one may compute the Z 0 branching fractions in terms of the couplings of Eq. (87.1). However,other decay channels, such as W W or a pair of new particles, could have large widths and need tobe added to the total decay width.
As mentioned above, there are theories in which the Z 0 couplings are controlled by a discrete
symmetry that forbids decays into a pair of SM particles. Typically, such theories involve several
new particles, which may be produced only in pairs and undergo cascade decays through Z 0 bosons,leading to signals involving missing transverse momentum. Given that the cascade decays dependon the properties of new particles other than the Z 0 boson (see, e.g. Ref. [18]), this case is notdiscussed further here.
The Z 0 contribution to the cross sections for e+ e− → f f¯ proceeds through an s-channel Z 0√
exchange (when f = e, there are also t- and u-channel exchanges). For MZ 0 < s, the Z 0 appears
as an f f¯ resonance in the radiative return process where photon emission tunes the effective centerof-mass energy to MZ 0 . The agreement between the LEP-II measurements and the SM predictions
implies that either the Z 0 couplings are smaller than or of order 10−2 , or else MZ 0 is above 209
GeV, the maximum energy of LEP-II. In the latter case, the Z 0 exchange may be approximated up
to corrections of order s/MZ2 0 by the contact interactions
h

 ih

 i
gz2
L
R
¯γ µ z L PL + z R PR f ,
ēγ
z
P
+
z
P
e
f
µ
L
R
e
e
f
f
MZ2 0 − s(87.7)

where PL,R are chirality projection operators, and the relation between Z 0 couplings and charges(see Eq. (87.2) in the limit where the mass and kinetic mixings are neglected) is used, assuming
generation-independent charges. The four LEP collaborations have set limits on the coefficientsof such operators for all possible chiral structures and for various combinations of fermions [19].
Thus, one may derive bounds on (MZ 0 /gz )|zeL zfL |−1/2 and the analogous combinations of LR, RL
and RR charges, which are typically on the order of a few TeV. LEP-II limits were derived [6] on
the four sets of charges shown in Table 87.1.
Somewhat stronger bounds can be set on MZ 0 /gz for specific sets of Z 0 couplings if the effects
of several operators (87.7) are combined. Dedicated analyses by the LEP collaborations have set
limits on Z 0 bosons for particular values of the gauge coupling (see section 3.5 of Ref. [19]). For
example, MZSSM > 1.76 TeV for a “sequential” Z 0 of same couplings as the SM Z boson, while
MZχ > 0.785 TeV for the Z 0 associated with U (1)χ assuming a unification condition for the gauge
coupling.

87.4 Searches at hadron colliders
Z 0 bosons with couplings to quarks (see Eq. (87.1)) may be produced at hadron colliders inthe s-channel and would show up as resonances in the invariant mass distribution of the decay
products. The cross section for producing a Z 0 boson at the LHC, which then decays to some f f¯
final state, takes the form [20]
π X f (87.8)σ pp → Z 0 X → f f¯X 'cq wq s, MZ2 0
6s q
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087. Z -Boson Searches
140 fb-1 (13 TeV, µµ)
102

ATLAS

s = 13 TeV, 139 fb([σ⋅B] Z' / [σ⋅B] Z) × 1928 [pb]σfid × B [fb]5

-1

X → ee101

10−1Observed limit at Γ/m = 6%
Expected limit at Γ/m = 6%
Γ/m = 1.2%
Γ/m = 0.5%

−2

10

3×102

103

Z'χ model
Z'ψ model

1

CMS

Obs. 95% CL limit
Exp. 95% CL limit, median

10−1

width

10−2

0.6%

3%

5%

10%

Z'SSM (width 2.97%)

10−3

Z'Ψ (width 0.53%)

−4

10

10−5

2×103 3×103

1000

2000

mX [GeV]

3000

4000

5000
m [GeV]

Figure 87.1: Upper limits on the cross section for Z 0 production times the branching fractionfor Z 0 → e+ e− (left panel, set by ATLAS [22]) or Z 0 → µ+ µ− (right panel, set by CMS [23]) asa function of MZ 0 . The lines labeled by Zψ0 and Zχ0 are theoretical predictions for the U (1)10+x5̄
models in Table 87.1 with x = −3 and x = +1, respectively, for gz fixed by an E6 unification0
condition. The ZSSM
line corresponds to Z 0 couplings equal to those of the Z boson.
for flavor-diagonal couplings to quarks. Here, we have neglected the interference with the SM
contribution to f f¯ production, which is a good approximation for a narrow Z 0 resonance (deviations
from the narrow width approximation are discussed in Ref. [21]). The coefficients
cfq =



gqL

2

+



gqR

2 

B(Z 0 → f f¯)(87.9)

contain all the dependence on the Z 0 couplings, while the functions wq include all the information
about parton distributions and QCD corrections [6, 8]. This factorization holds exactly to NLO
and the deviations from it induced at NNLO are very small. Note that the wu and wd functions
are substantially larger than the wq functions for the other quarks. Eq. (87.8) also applies to theTevatron, except for changing the pp initial state to pp̄, which implies that the wq (s, MZ2 0 ) functions
are replaced by some other functions w̄q ((1.96 TeV)2 , MZ2 0 ).
It is common to present results of Z 0 searches as limits on the cross section versus MZ 0 (see forexample Fig. 87.1). An alternative is to plot exclusion curves for fixed MZ 0 values in the cfu − cfd
planes, allowing a simple derivation of the mass limit within any Z 0 model. CMS upper limits inthe c`u − c`d plane (` = e or µ) for different MZ 0 are shown in Ref. [23] (for Tevatron limits, see
Refs. [8, 24]).
The discovery of a dilepton resonance at the LHC would determine the Z 0 mass and width. A
measurement of the total cross section would define a band in the c`u − c`d plane. Angular distributions can be used to measure several combinations of Z 0 parameters (angular distributions wereused in Ref. [25] to improve the Tevatron sensitivity). Even though the original quark direction
in a pp collider is unknown, the leptonic forward-backward asymmetry A`FB can be extracted fromthe kinematics of the dilepton system, and is sensitive to parity-violating couplings. A fit to theZ 0 rapidity distribution can distinguish between the couplings to up and down quarks. These measurements, combined with off-peak observables, have the potential to differentiate among various
Z 0 models [26]. In some cases, A`FB may provide discovery sensitivity that is competitive with themass distribution [27]. The spin of the Z 0 boson may be determined from angular distributions [28].
Searches for Z 0 decays into e+ e− and µ+ µ− by the ATLAS and CMS collaborations [22, 23]
have set 95% C.L. upper cross-section limits as low as 0.02 fb (see Fig. 87.1), with the mass lower
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087. Z -Boson Searches

6g'q

CMS Preliminary

LHCP 2020

ΓZ' / MZ' < ~100%

ATLAS Boosted Dijet, 13 TeV[arXiv:1801.08769]

CMS Dijet χ, 13 TeV[arXiv:1803.08030]

ATLAS Dijet+ISR γ , 13 TeV[arXiv:1901.10917]

ΓZ' / MZ' < ~30%

ATLAS Dijet TLA, 13 TeV[arXiv:1804.03496]

ΓZ' / MZ' = 10%

CMS Broad Dijet, 13 TeV[arXiv:1806.00843]

ATLAS Dijet, 13 TeV[arXiv:1910.08447]

ΓZ' / MZ' = 5%

ΓZ' / MZ' < ~10%

CMS Dijet b tagged, 8 TeV[arXiv:1802.06149]

CMS Dijet, 8 TeV[arXiv:1604.08907]

CMS Dijet Scouting '16, 13 TeV[arXiv:1806.00843]

CMS Dijet, 13 TeV[arXiv:1911.03947]

CMS Boosted Dijet, 13 TeV[arXiv:1909.04114]

CMS Dijet+ISR jet, 13 TeV[arXiv:1911.03761]

CMS Boosted Dijet+γ , 13 TeV[arXiv:1905.10331]

CDF Run1[arXiv:hep-ex/9702004]

ΓZ' / MZ' < ~5%

CDF Run2[arXiv:0812.4036]

CMS tt, 13 TeV[arXiv:1810.05905]

ΓZ' / MZ' = 100%
ΓZ' / MZ' = 50%

1

ΓZ' / MZ' = 30%

10−1

Z'→qq
8 10

95% CL exclusions

20 30

100

200

1000 2000

MZ' [GeV]

UA2[Nucl. Phys. B 400, 3 (1993)]
Z width (all ΓZ'/MZ')[arXiv:1404.3947]

Υ width (all Γ /MZ')Z'[arXiv:1404.3947]

Figure 87.2: Upper limits on the Z 0 coupling to quarks as a function of MZ 0 based on various
searches performed by the ATLAS, CMS, CDF, and UA2 experiments [38].
limits in specific models as high as 4.9 TeV in a single channel. Cross section limits in the dimuon
channel for low mass regions, below 200 GeV but not near the Z mass, have been set at the LHC
by CMS [29, 30] and LHCb [31].
The Z 0 → τ + τ − decay has been searched for by ATLAS with 36 fb−1 of 13 TeV data [32], anda limit MZ 0 > 2.4 TeV has been set in the case of a sequential Z 0 . Limits on heavy scalars in theτ + τ − final state, set by ATLAS [33] and CMS [34] with the full Run 2 datasets, can be recast
into limits on Z 0 . Limits in the flavor-violating leptonic final states have also been reported by
ATLAS [35] and CMS [36] at 13 TeV, for resonances in the e± µ∓ , e± τ ∓ and µ± τ ∓ channels.
Final states with higher background, jj, bb̄ and tt̄, are also important as they probe various
combinations of Z 0 couplings to quarks. Besides the improved sensitivity at masses of several TeV,
the LHC searches in the dijet channel have been also extended to masses as low as 10 GeV, throughthe use of new techniques involving boosted topologies and initial state radiation [37]. Limits fromsuch Z 0 searches in hadronic final states are summarized in Fig. 87.2.
Searches for the Z 0 → bb̄ decay have been performed for two production mechanisms. ATLAS [39] and CMS [40] searched for bb̄ resonances using the full Run 2 datasets, setting limits
under the assumption that the Z 0 boson couples to light quarks and thus is produced in the schannel. The CMS upper limit on the cross-section times the Z 0 → bb̄ branching fraction decreases
from 40 fb at MZ 0 = 1.8 TeV to 0.4 fb at MZ 0 = 8 TeV. The ATLAS search covered the 1.3 TeV –0
5 TeV mass range, setting a lower mass limit of 2.7 TeV for the ZSSM
. Independent of any other0
couplings, if the Z couples to the b quark, then it can be produced in association with a bb̄ pair,
and it decays to a second bb̄ pair, which forms a resonance. The cross-section limit for that process,set by ATLAS [41] with 103 fb−1 of 13 TeV data, is between 0.1 and 0.2 pb for MZ 0 in the 1.3 – 3
TeV range. For a vector coupling gb of Z 0 to b quarks, i.e, gdL 33 = gdR 33 = gb using the notation of
Eq. (87.1), the limit is MZ 0 > 1.45 TeV when gb = 1.
Another search that depends on the Z 0 couplings to the b quark for production (more precisely,
for a bb̄, sb̄ or bs̄ initial state) was performed by CMS [42], under the assumption that the Z 0 boson
decays into a muon pair. Searches for the Z 0 → tt̄ decay are discussed in Ref. [16].
Heavy resonances decaying into Zh0 with Z → `+ `− , ν ν̄ or q q̄ and h0 → bb̄ have been studied
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7087. Z -Boson Searches

by ATLAS [43, 44] and CMS [45, 46] using the full 13 TeV dataset. CMS also searched for Z 0
bosons in the q q̄τ τ final state [47]. The most stringent constraint on Z 0 production in the context
of the Heavy Vector Triplet (HVT) model weakly-coupled scenario A [48] is set in the semi-leptonic
channel, with a mass lower limit of 3.5 TeV [45].
Searches for a Z 0 boson lighter than the SM Z and which couples to leptons have been performedin the 4-lepton final state. ATLAS [49] and CMS [50] focused on the Z decays into a muon pairfollowed by the radiation of a narrow Z 0 boson which decays itself into a muon pair. A related
CMS search [51] for Z decays into four leptons, but without requiring that a pair of leptons form
a narrow resonance, was used to set limits on Z 0 couplings to electrons or muons as a function ofmass, which are relevant for large widths. ATLAS [52] considered the h0 → ZZ 0 and h0 → Z 0 Z 0
processes followed by the leptonic decays of both spin-1 bosons.
The pp → Z 0 X → W + W − X process has also been searched for at the LHC. The channel where
the Z 0 boson is produced through its couplings to quarks, and the W bosons decay hadronically, hasbeen explored using boosted techniques to analyze the 13 TeV data [46, 53–55] with a mass lower
limit of 3.5 TeV in the HVT model A [54]. A search in the eνµν final state sets cross-section limits
at lower Z 0 mass [56]. The Z 0 boson may also be produced through its couplings to W bosons [57],which has been explored with the use of forward jets consistent with a vector boson fusion event
topology [46, 54, 55]. The latter process provides a test of fermiophobic Z 0 models.
At the Tevatron, the CDF and DØ collaborations have searched for Z 0 bosons in the e+ e− [58],+µ µ− [59], e± µ∓ [60], τ + τ − [61], tt̄ [62], jj [63] and W + W − [64] final states. These limits havebeen mostly superseded by the LHC results.

87.5 Low-energy constraints
Z 0 boson properties are also constrained by a variety of low-energy experiments [65]. Polarized
electron-nucleon scattering and atomic parity violation are sensitive to electron-quark contact interactions, which get contributions from Z 0 exchange that can be expressed in terms of the couplings
introduced in Eq. (87.1) and MZ0 . Further corrections to the electron-quark contact interactions
are induced in the presence of Z̃ − Z̃ 0 mixing because of the shifts in the Z couplings to quarks andleptons [3]. Deep-inelastic neutrino-nucleon scattering is similarly affected by Z 0 bosons. Other
low-energy observables are discussed in [4]. Viable models with Z 0 bosons much lighter than the
Z boson have been constructed, despite many additional experimental constraints [66]. Limits on
the Z 0 coupling to leptons in the mass range 0.02–10.2 GeV have been set in e+ e− collisions by
BaBar [67], assuming a dark photon, i.e., a Z 0 boson whose couplings arise only from the kinetic
mixing with the hypercharge gauge boson.
In some models, the lower limits on MZ 0 set by low-energy data are above 1 TeV. For example,
MZχ > 1.1 TeV and MZη > 0.43 TeV assuming that the Higgs sectors consist of electroweak
doublets and singlets only [4], while the gauge coupling is fixed by an SO(10) unification condition
for U (1)χ and U (1)η . For more general models, see Refs. [1, 6, 68]. The mass bounds from direct
searches at the LHC [22, 23] exceed the electroweak constraints by a factor of three or more forthe models mentioned here. This conclusion could change if the collider bounds are weakened byexotic decay channels [69].
Although the LHC data are most constraining for many Z 0 models, one should be careful inassessing the relative reach of various experiments given the freedom in Z 0 couplings. For example,a Z 0 coupled to B − yLµ + (y − 3)Lτ has implications for the muon g − 2, neutrino oscillations orτ decays, and would be hard to see in processes involving first-generation fermions. Moreover, thecombination of LHC searches and low-energy measurements could allow a precise determination of
the Z 0 parameters [70].
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8087. Z -Boson Searches

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[4] J. Erler et al., JHEP 08, 017 (2009), [arXiv:0906.2435].
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