10

86. W -Boson Searches
086. W -Boson Searches
Revised September 10, 2023 by B.A. Dobrescu (FNAL) and S. Willocq (U. Massachusetts).
The W 0 boson is a massive hypothetical particle of spin 1 and electric charge ±1, which is acolor singlet and is predicted in various extensions of the Standard Model (SM).

86.1 W 0 couplings to quarks and leptons
The Lagrangian terms describing the couplings of a W 0+ boson to fermions are given byiWµ0+ h  R√ ui Cqij PR +CqLij PL γ µ dj +ν i C`Rij PR +C`Lij PL γ µ ej .
2

(86.1)

Here, u, d, ν, and e are the SM fermions in the mass eigenstate basis, i, j = 1, 2, 3 label the fermion
generation, and PR,L = (1 ± γ5 )/2. The coefficients CqLij , CqRij , C`Lij , and C`Rij are complex dimensionless parameters. If C`Rij 6= 0, then the ith generation includes a right-handed neutrino. Using
this notation, the SM W couplings are CqL = gVCKM , C`L = g ≈ 0.63 and CqR = C`R = 0.
Unitarity considerations imply that the W 0 boson is associated with a spontaneously-broken
gauge symmetry. This is true even when it is a composite particle (e.g. ρ± -like bound states [1]) if
its mass is much smaller than the compositeness scale, or a Kaluza-Klein mode in theories where
the W boson propagates in extra dimensions [2]. The simplest extension of the electroweak gauge
group that includes a W 0 boson is SU (2)1 × SU (2)2 × U (1), but larger groups are encountered insome theories. A generic property of these gauge theories is that they also include a Z 0 boson [3];the W 0 -to-Z 0 mass ratio is often a free parameter.
A tree-level mass mixing may be induced between the electrically-charged gauge bosons. Upon
diagonalization of their mass matrix, the W -to-Z mass ratio and the couplings of the observed
W boson are shifted from the SM values. Their measurements imply that the mixing angle, θ+ ,between the gauge eigenstates must be smaller than about 10−2 [4]. In certain theories the mixing
is negligible (e.g., due to a new parity [5]), even when the W 0 mass is near the electroweak scale.
Note that SU (2) gauge invariance suppresses the kinetic mixing between the W and W 0 bosons (incontrast to the case of a Z 0 boson [3]).
The W 0 coupling to W Z is fixed by Lorentz and gauge invariances, and to leading order in θ+
is given by [6]ig θ+ i h 0+0+Wµ Wν− Z νµ + Zν W −µν + Z ν W −µ Wνµ+ H.c.,(86.2)cos θW
where W µν ≡ ∂ µ W ν −∂ ν W µ , etc. The θW dependence shown here corrects the one given in Ref. [7],which has been referred to as the Extended Gauge Model by the experimental collaborations. The
W 0 coupling to W h0 , where h0 is the SM Higgs boson, is− ξh gW 0 MW Wµ0+ W µ− h0 + H.c.,(86.3)

where gW 0 is the gauge coupling of the W 0 boson, and the coefficient ξh satisfies ξh ≤ 1 in simple
Higgs sectors [6].
In models based on the “left-right symmetric” gauge group [8], SU (2)L × SU (2)R × U (1)B−L ,the SM fermions that couple to the W boson transform as doublets under SU (2)L while the otherfermions transform as doublets under SU (2)R . Consequently, the W 0 boson couples primarily toright-handed fermions; its coupling to left-handed fermions arises due to the θ+ mixing, so that CqL
is proportional to the CKM matrix and its elements are much smaller than the diagonal elementsof CqR . Generically, CqR does not need to be proportional to VCKM .
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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86. W -Boson Searches

2

There are many other models based on the SU (2)1 × SU (2)2 × U (1) gauge symmetry. In the“alternate left-right” model [9], all the couplings shown in Eq. (86.1) vanish, but there are some
new fermions such that the W 0 boson couples to pairs involving a SM fermion and a new fermion.
In the “ununified SM” [10], the left-handed quarks are doublets under one SU (2), and the lefthanded leptons are doublets under a different SU (2), leading to a mostly leptophobic W 0 boson:
C`Lij  CqLij and C`Rij = CqRij = 0. Fermions of different generations may also transform as doublets
under different SU (2) gauge groups [11]. In particular, the couplings to third generation quarks
may be enhanced [12].
It is also possible that the W 0 couplings to SM fermions are highly suppressed. For example, if
the quarks and leptons are singlets under one SU (2) [13], then the couplings are proportional to
the tiny mixing angle θ+ . Similar suppressions may arise if some vectorlike fermions mix with the
SM fermions [14].
Gauge groups that embed the electroweak symmetry, such as SU (3)W ×U (1) or SU (4)W ×U (1),also include one or more W 0 bosons [15].

86.2 Collider searches
At hadron colliders, W 0 bosons can be detected through resonant pair production of fermions(f and f 0 ) or electroweak bosons with a net electric charge equal to ±1. When W 0 has a widthmuch smaller than its mass (ΓW 0 /MW 0 . 7%), the contribution of the s-channel W 0 exchange tothe total rate for pp → f f¯0 X, where X is any final state, may be approximated by the branching
fraction B(W 0 → f f¯0 ) times the production cross section [16], which may be written as
σ pp → W 0 X 'iπ Xh L 2
2(Cqij) +(CqRij)2 wij MW
0 /s, MW 0 .
6s i,j(86.4)

The functions wij include the information about proton structure, and are given to leading orderin αs by




Z 1 
dx
z
z
ui (x, µ) dj, µ + ui(x, µ) dj,µ ,(86.5)wij (z, µ) =xxz x
where ui (x, µ) and di (x, µ) are the parton distributions inside the proton at the factorization scaleµ and parton momentum fraction x for the up- and down-type quarks of the ith generation, respectively. QCD corrections to W 0 production are sizable (they also include quark-gluon initial states),
but preserve the above factorization of couplings at next-to-leading order [17].
The most commonly studied W 0 signal consists of a high-momentum electron or muon andlarge missing transverse momentum. The signal transverse mass distribution forms a Jacobianpeak with its endpoint at MW 0 (see Fig. 1 (top) of Ref. [18]). Given that the branching fractions forW 0 → eν and W 0 → µν could be very different, the results in these channels should be presented
separately. Searches in these channels often implicitly assume that the left-handed couplings vanish(no interference between W and W 0 ), and that the right-handed neutrino is light compared to theW 0 boson and escapes the detector. An example of parameter values that satisfy these assumptions
is CqR = gVCKM , C`R = g, CqL = C`L = 0, which define a model that preserves lepton universality
and predicts the same total cross section as the Sequential SM used in many W 0 searches. However,
if a W 0 boson were discovered and the final state fermions have left-handed helicity, then the effectsof W − W 0 interference could be observed [19], providing information about the W 0 couplings. The
effects of the W 0 width on interference are discussed in Ref. [20].
In the eν channel, the ATLAS and CMS collaborations set limits on the W 0 production crosssection times branching fraction σ × B (and thus indirectly on the W 0 couplings). These limits√
are set for MW 0 in the 0.15 − 7 TeV range and are based on approximately 140 fb−1 at s = 13
TeV [18,21], with the most stringent limits reproduced in Fig. 86.1. ATLAS sets the strongest mass
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086. W -Boson Searches

3σ(pp→W’→eν) [pb]limit MW 0 > 6.0 TeV in the Sequential SM (all limits in this mini-review are at the 95% CL). The
coupling limits are much weaker for MW 0 < 150 GeV, a range last explored with the Tevatron at√
s = 1.8 TeV [22].
In the µν channel, ATLAS and CMS set rate limits for MW 0 in the 0.15 − 7 TeV range [18, 21],with the strongest mass lower limit of 5.6 TeV in the Sequential SM set by CMS [21] using 138 fb−1√of s = 13 TeV data, as shown in Fig. 86.1. When combined with the eν channel assuming lepton√
universality, the upper limit on the s = 13 TeV cross section times branching fraction to `ν varies
between 0.05 and 2.1 fb for MW 0 values between 1 and 6 TeV [18]. Only weak limits on W 0 → µν
exist for MW 0 < 150 GeV [23]. Note that masses of the order of the electroweak scale are interestingfrom a theoretical point of view, while lepton universality does not necessarily apply to a W 0 boson.
10
ATLAS
Expected limits = 13 TeV, 139 fb-1
W’ → eν95% CL1
10−1

Expected ± 1σ
Expected ± 2σ
Observed limit

−2

SSM

10

10−3
10−4
1

2

3

4

5

6

7

m(W’) [TeV]

Figure 86.1: Upper limit on σ(pp → W 0 X)×B(W 0 → `ν) in the eν channel from ATLAS [18] (left)
and the µν channel from CMS [21] (right). The red (black) line shows the theoretical prediction in
the Sequential SM in the eν (µν) channel.
Searches for W 0 → τ ν have been performed at 13 TeV by CMS with 138 fb−1 [24], and by
ATLAS with 139 fb−1 [25]. Limits are set on σ × B for MW 0 between 0.5 and 6 TeV. A mass
lower limit of 5.0 TeV is set in the Sequential SM, and the upper limit on the cross section times
branching fraction to τ ν at 13 TeV varies between 0.4 and 9 fb for MW 0 values between 1 and5 TeV [25].
The W 0 decay into a charged lepton and a right-handed neutrino, νR , may also be followed bythe νR decay through a virtual W 0 boson into a charged lepton and two quark jets. The CMS [26]√and ATLAS [27] searches in the eejj and µµjj channels have set limits at s = 13 TeV on the
cross section times branching fractions as a function of the νR mass and of MW 0 . No requirementis placed on the charge of the lepton pair. A related W 0 search in the τ τ jj channel with hadronicτ decays was also performed by CMS [28].
The tb̄ channel is particularly important because a W 0 boson that couples only to right-handed
fermions cannot decay to leptons when the right-handed neutrinos are heavier than MW 0 . Additional motivations are provided by a W 0 boson with enhanced couplings to the third generation [12],and by a leptophobic W 0 boson. The usual signature for W 0 → tb̄ consists of a leptonically-decaying
W boson and two b-jets. Recent studies have also incorporated the fully hadronic decay channel
for MW 0  mt with the use of jet substructure techniques to tag highly boosted top-jets. For adetailed discussion of this channel, see Ref. [29].
Searches for dijet resonances may be used to set limits on W 0 → q q̄ 0 . ATLAS [30] and CMS [31]provide similar coverage in the ∼ 1.5−8 TeV mass range with 139 and 137 fb−1 of data, respectively,√
collected at s = 13 TeV. Interpretation in terms of W 0 decays with 139 fb−1 of 13 TeV data yields
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086. W -Boson Searches

4

10

102
ATLAS
10
1
10−1

s = 13 TeV, 139 fb-1
W' combined (0L+1L) limit

95% CL limit
Observed limit
Expected limit
Expected ±1 s.d.
Expected ±2 s.d.
HVT Model A, g =1
V
HVT Model B, g =3
V
Expected limit (0L)
Expected limit (1L)

10−2
10−3
10−4

σ x Β (DY W' → WH) [pb]σ(pp → W' → Wh) [pb]a W 0 mass lower limit of 4.0 TeV in the Sequential SM [30]. For masses in the range ∼ 0.5−1.5 TeV,
analyses based on jets reconstructed online provide the best sensitivity because they circumvent
trigger bandwidth limitations [32, 33]. For W 0 masses below ∼ 0.5 TeV, the best limits are set
in novel analyses exploiting boosted technologies and initial state radiation [34–37]. Cross-section
limits for W 0 masses below ∼ 1.5 TeV can be derived from the dijet limits on Z 0 bosons summarized
in Ref. [3].
In some theories [5] the W 0 couplings to SM fermions are suppressed by discrete symmetries.
0
W production then occurs in pairs, through a photon or Z boson. The decay modes are modeldependent and often involve other new particles. The ensuing collider signals arise from cascadedecays and often include missing transverse momentum or boosted multi-jet topologies. Even whensingle production of W 0 is large enough, it is possible that its main decay mode is into a new particle
and a SM one. An example is a search performed by CMS [38] for W 0 decays into a vector-likequark and a top or a bottom quark. The final state studied in this analysis involves a boosted SM
Higgs or Z boson, as well as a tt̄ or bb̄ pair, with all heavy particles decaying into jets. Anotherexample is a search performed by ATLAS [39] for W 0 decays into a W boson and a Z 0 boson, thelatter decaying into a jet pair.
Searches for W Z resonances at the LHC have focused on the process pp → W 0 → W Z with the
production mainly from ud¯ → W 0 , assuming SM-like couplings to quarks. ATLAS and CMS have
set upper limits on the W 0 W Z coupling for MW 0 in the 0.2 − 5.0 TeV range with a combinationof fully leptonic, semi-leptonic and fully hadronic channels with ∼ 36 − 139 fb−1 at 13 TeV [40–42](see also Ref. [29]). Recent constraints with 138–139 fb−1 at 13 TeV were also set in individual
channels by ATLAS [43–45] and CMS [46–49]. The strongest lower limit on the W 0 mass is set by
ATLAS [44] in the semi-leptonic channel with a lower limit on MW 0 of 3.9 TeV [44] in the context
of the Heavy Vector Triplet (HVT) weakly-coupled scenario A [50]. A similar result is obtainedby CMS in the fully-hadronic channel [46]. A fermiophobic W 0 boson that couples to W Z may be
produced at hadron colliders in association with a Z boson, or via W Z fusion. This would giverise to (W Z)Z and (W Z)jj final states [51]. Results of the search for the latter are reported inRefs. [40, 44, 46, 47, 49].
138 fb-1 (13 TeV)CMS Supplementary

Observed
Expected ± 1 std. deviation

1

Expected ± 2 std. deviation
σTH x Β (W' → WH) HVTB

−1

10

10−2
10−3
10−4

500 1000 1500 2000 2500 3000 3500 4000 4500 5000
mW' [GeV]

10−5

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

MW' [TeV]

Figure 86.2: Upper limits on W 0 production cross section times branching fraction into a W anda SM Higgs boson decaying into heavy-flavor quarks, from ATLAS [52] (left) and CMS [46] (right).
W 0 bosons have also been searched for in final states with a W boson and a SM Higgs boson in
the channels W → `ν or W → q q̄ 0 and h0 → bb̄ by ATLAS [52, 53] and CMS [46, 49] with 138–139√
fb−1 at s = 13 TeV. CMS also searched for W 0 bosons in the q q̄ 0 τ τ final state [54]. Cross-section
limits are set for W 0 masses between 0.4 and 6.0 TeV. The most stringent upper limit on the cross
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5086. W -Boson Searches

section is set by the ATLAS analysis with W → `ν at low MW 0 and the CMS analysis with W → q q̄ 0
at high MW 0 , as shown in Fig. 86.2.
At lepton colliders, W 0 bosons may be produced in pairs via their photon coupling, which ismodel independent. At LEP-II, although dedicated searches for W 0 bosons have not been performed, the large cross section for e+ e− → γ ∗ → W 0+ W 0− and small backgrounds suggest that√
any W 0 is ruled out up to the kinematic limit, MW 0 < s/2 ≈ 105 GeV, for most decay modes.
√
Sensitivity to MW 0 above s could be achieved [55] using the e+ e− → γν ν̄ process via a t-channel
W 0 exchange, if the W 0 coupling to eν is large enough.

86.3 Low-energy constraints
The properties of W 0 bosons are also constrained by measurements of processes at energies
much below MW 0 . The bounds on W − W 0 mixing [4] are mostly due to the change in W properties
compared to the SM. Limits on deviations in the ZW W couplings provide a leading constraint for
fermiophobic W 0 bosons [14].
Constraints arising from low-energy effects of W 0 exchange are strongly model-dependent. If
the W 0 couplings to quarks are not suppressed, then box diagrams involving a W and a W 0 boson
contribute to neutral meson-mixing. In the case of W 0 couplings to right-handed quarks as in
the left-right symmetric model, the limit from KL − KS mixing is severe: MW 0 > 2.9 TeV for
CqR = gVCKM [56]. However, if no correlation between the W 0 and W couplings is assumed, thenthe limit on MW 0 may be significantly relaxed [57].
W 0 exchange also contributes at tree level to various low-energy processes. In particular, it
would impact the measurement of the Fermi constant GF in muon decay, which in turn wouldchange the predictions of many other electroweak processes. A recent test of parity violation inpolarized muon decay [58] has set limits of about 600 GeV on MW 0 , assuming W 0 couplings to righthanded leptons as in left-right symmetric models and a light νR . There are also W 0 contributions
to the neutron electric dipole moment, β decays, and other processes [4].
If right-handed neutrinos have Majorana masses, then there are tree-level contributions toneutrinoless double-beta decay, and a limit on MW 0 versus the νR mass may be derived [59]. ForνR masses below a few GeV, the W 0 boson contributes to leptonic and semileptonic B meson
decays, so that limits may be placed on various combinations of W 0 parameters [57]. For νR masses
below ∼ 30 MeV, the most stringent constraints on MW 0 are due to the limits on νR emission fromsupernovae [60].
References[1] M. Bando, T. Kugo and K. Yamawaki, Phys. Rept. 164, 217 (1988).
[2] H.-C. Cheng et al., Phys. Rev. D 64, 065007 (2001), [hep-th/0104179].
[3] See the Section on “Z 0 -boson searches” in this Review.
[4] See the particle listings for W 0 in this Review.
[5] H.-C. Cheng and I. Low, JHEP 09, 051 (2003), [hep-ph/0308199].
[6] B. A. Dobrescu and Z. Liu, JHEP 10, 118 (2015), [arXiv:1507.01923].
[7] G. Altarelli, B. Mele and M. Ruiz-Altaba, Z. Phys. C 45, 109 (1989), [Erratum: Z. Phys. C
47, 676 (1990)].
[8] R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11, 566 (1975).
[9] K. S. Babu, X.-G. He and E. Ma, Phys. Rev. D 36, 878 (1987).
[10] H. Georgi, E. E. Jenkins and E. H. Simmons, Nucl. Phys. B 331, 541 (1990).
[11] X.-y. Li and E. Ma, J. Phys. G 19, 1265 (1993), [hep-ph/9208210].
[12] D. J. Muller and S. Nandi, Phys. Lett. B 383, 345 (1996), [hep-ph/9602390].
31st May, 2024

6086. W -Boson Searches[13] A. Donini et al., Nucl. Phys. B 507, 51 (1997), [hep-ph/9705450].
[14] R. S. Chivukula et al., Phys. Rev. D 74, 075011 (2006), [hep-ph/0607124].
[15] F. Pisano and V. Pleitez, Phys. Rev. D 46, 410 (1992), [hep-ph/9206242].
[16] V. D. Barger and R. J. N. Phillips, Collider Physics (1996), ISBN 978-0201149456.
[17] Z. Sullivan, Phys. Rev. D 66, 075011 (2002), [hep-ph/0207290].
[18] G. Aad et al. (ATLAS), Phys. Rev. D 100, 052013 (2019), [arXiv:1906.05609].
[19] T. G. Rizzo, JHEP 05, 037 (2007), [arXiv:0704.0235].
[20] E. Accomando et al., Phys. Rev. D 85, 115017 (2012), [arXiv:1110.0713].
[21] A. Tumasyan et al. (CMS), JHEP 07, 067 (2022), [arXiv:2202.06075].
[22] F. Abe et al. (CDF), Phys. Rev. Lett. 74, 2900 (1995).
[23] F. Abe et al. (CDF), Phys. Rev. Lett. 67, 2609 (1991).
[24] A. Tumasyan et al. (CMS), JHEP 09, 051 (2023), [arXiv:2212.12604].
[25] G. Aad et al. (ATLAS) (2024), [arXiv:2402.16576].
[26] A. Tumasyan et al. (CMS), JHEP 04, 047 (2022), [arXiv:2112.03949].
[27] G. Aad et al. (ATLAS), Eur. Phys. J. C 83, 12, 1164 (2023), [arXiv:2304.09553].
[28] A. M. Sirunyan et al. (CMS), JHEP 03, 170 (2019), [arXiv:1811.00806].
[29] K.M. Black et al., “Dynamical electroweak symmetry breaking” in this Review.
[30] G. Aad et al. (ATLAS), JHEP 03, 145 (2020), [arXiv:1910.08447].
[31] A. M. Sirunyan et al. (CMS), JHEP 05, 033 (2020), [arXiv:1911.03947].
[32] M. Aaboud et al. (ATLAS), Phys. Rev. Lett. 121, 081801 (2018), [arXiv:1804.03496].
[33] A. M. Sirunyan et al. (CMS), JHEP 08, 130 (2018), [arXiv:1806.00843].
[34] M. Aaboud et al. (ATLAS), Phys. Lett. B 788, 316 (2019), [arXiv:1801.08769].
[35] M. Aaboud et al. (ATLAS), Phys. Lett. B 795, 56 (2019), [arXiv:1901.10917].
[36] A. M. Sirunyan et al. (CMS), Phys. Rev. D 100, 112007 (2019), [arXiv:1909.04114].
[37] A. M. Sirunyan et al. (CMS), Phys. Rev. Lett. 123, 231803 (2019), [arXiv:1905.10331].
[38] A. Tumasyan et al. (CMS), JHEP 09, 088 (2022), [arXiv:2202.12988].
[39] G. Aad et al. (ATLAS), JHEP 07, 202 (2023), [arXiv:2211.08945].
[40] M. Aaboud et al. (ATLAS), Phys. Rev. D 98, 052008 (2018), [arXiv:1808.02380].
[41] ATLAS Collab., ATLAS-CONF-2022-028, May 2022.
[42] A. M. Sirunyan et al. (CMS), Phys. Lett. B 798, 134952 (2019), [arXiv:1906.00057].
[43] G. Aad et al. (ATLAS), JHEP 09, 091 (2019), [Erratum:[arXiv:1906.08589].

JHEP 06 (2020) 042],[44] G. Aad et al. (ATLAS), Eur. Phys. J. C 80, 1165 (2020), [arXiv:2004.14636].
[45] G. Aad et al. (ATLAS), Eur. Phys. J. C 83, 633 (2023), [arXiv:2207.03925].
[46] A. Tumasyan et al. (CMS), Phys. Lett. B 844, 137813 (2023), [arXiv:2210.00043].
[47] A. Tumasyan et al. (CMS), Phys. Rev. D 106, 012004 (2022), [arXiv:2109.08268].
[48] A. Tumasyan et al. (CMS), JHEP 04, 087 (2022), [arXiv:2111.13669].
[49] A. Tumasyan et al. (CMS), Phys. Rev. D 105, 032008 (2022), [arXiv:2109.06055].
[50] D. Pappadopulo et al., JHEP 09, 060 (2014), [arXiv:1402.4431].
31st May, 2024

7086. W -Boson Searches[51] H.-J. He et al., Phys. Rev. D 78, 031701 (2008), [arXiv:0708.2588].
[52] G. Aad et al. (ATLAS), JHEP 06, 016 (2023), [arXiv:2207.00230].
[53] G. Aad et al. (ATLAS), Phys. Rev. D 102, 112008 (2020), [arXiv:2007.05293].
[54] A. M. Sirunyan et al. (CMS), JHEP 01, 051 (2019), [arXiv:1808.01365].
[55] S. Godfrey et al., Phys. Rev. D 61, 113009 (2000), [hep-ph/0001074].
[56] Y. Zhang et al., Phys. Rev. D 76, 091301 (2007), [arXiv:0704.1662].
[57] P. Langacker and S. U. Sankar, Phys. Rev. D 40, 1569 (1989).
[58] J. F. Bueno et al. (TWIST), Phys. Rev. D 84, 032005 (2011), [arXiv:1104.3632].
[59] G. Prezeau, M. Ramsey-Musolf and P. Vogel, Phys. Rev. D 68, 034016 (2003), [hepph/0303205].
[60] G. G. Raffelt, Ann. Rev. Nucl. Part. Sci. 49, 163 (1999), [hep-ph/9903472].

31st May, 2024