1

91. Searches for Quark and Lepton Compositeness91. Searches for Quark and Lepton Compositeness
Revised October 2023 by K. Hikasa (Tohoku U.), M. Tanabashi (Nagoya U.; KMI, Nagoya U.), K.
Terashi (ICEPP, Tokyo U.) and N. Varelas (U. of Illinois at Chicago).

91.1 Limits on contact interactions
If quarks and leptons are made of constituents, then at the scale of constituent binding energies(compositeness scale) there should appear new interactions among them. At energies much below
the compositeness scale (Λ), these interactions are suppressed by inverse powers of Λ. The dominant
effect of the compositeness of fermion ψ should come from the lowest dimensional interactions withfour fermions (contact terms), whose most general flavor-diagonal color-singlet chirally invariant
form reads [1, 2]
L = LLL + LRR + LLR + LRL ,
with
LLL =

2
X ij
gcontactηLL (ψ̄Li γµ ψLi )(ψ̄Lj γ µ ψLj ),
2
2Λ
i,j

LRR =

2
X ij
gcontactj µ jiiγ ψR ),γµ ψR)(ψ̄R
ηRR (ψ̄R
2
2Λ
i,j

LLR =

2
X ij
gcontactj µ jγ ψR ),
ηLR (ψ̄Li γµ ψLi )(ψ̄R
2
2Λ
i,j

LRL =

2
X ij
gcontactiiγµ ψR)(ψ̄Lj γ µ ψLj ),ηRL (ψ̄R2
2Λ
i,j(91.1)

where i, j are the indices of fermion species. Color and other indices are suppressed in Eq. (91.1).
Chiral invariance provides a natural explanation why quark and lepton masses are much smallerijjithan their inverse size (inverse radius) Λ. Note ηαβ= ηβα, thus LLR and LRL are identical.
Therefore, in order to specify the contact interaction among the same fermion species i = j, it isenough to use ηLL , ηRR and ηLR . We will suppress the indices of fermion species hereafter. We
may determine the scale Λ unambiguously by using the above form of the effective interactions;22(Λ)/4π = 1 for the/4π = gcontact
the conventional method [1] is to fix its scale by setting gcontact
new strong interaction coupling and by setting the largest magnitude of the coefficients ηαβ to beunity. In the following, we denote±±±±Λ = Λ±
LL , ΛRR , ΛV V , ΛAA , ΛV −A ,(91.2)for (ηLL , ηRR , ηLR ) = (±1, 0, 0) , (0, ±1, 0) , (±1, ±1, ±1) , (±1, ±1, ∓1) , (0, 0, ±1). Such interactions can arise by interchanging constituents (when the fermions have common constituents),
and/or by exchanging the binding quanta (whenever binding quanta couple to constituents of bothparticles).
Fermion scattering amplitude induced from the contact interaction in Eq. (91.1) interferes with
the Standard Model (SM) amplitude destructively or constructively [2]. The sign of interference
depends on the sign of ηαβ (α, β = L, R). For instance, in the parton level qq → qq scattering crosssection in the Λ±
LL model, the contact interaction amplitude and the SM gluon exchange amplitudeinterfere destructively for ηLL = +1, while they interfere constructively for ηLL = −1. In modelsof quark compositeness, the quark scattering cross sections induced from the contact interactions
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
31st May, 2024 10:19am

2

91. Searches for Quark and Lepton Compositenessreceive sizable QCD radiative corrections. The exact next-to-leading order (NLO) QCD corrections
to the quark scatterings cross sections induced by the contact interactions are given in [3].
Over the last three decades experiments at the CERN Spp̄S [4, 5], the Fermilab Tevatron [6, 7],
and the CERN LHC [8–12] have searched for quark contact interactions, characterized by thefour-fermion effective Lagrangian in Eq. (91.1), using jet final states. These searches have been
performed primarily by studying the angular distribution of the two highest transverse momentum,
pT , jets (dijets), and the inclusive jet pT spectrum. The variable χ = exp(|(y1 − y2 )|) is used tomeasure the dijet angular distribution, where y1 and y2 are the rapidities of the two jets with thehighest transverse momenta. For collinear massless parton scattering, χ is related to the polar
scattering angle θ∗ in the partonic center-of-mass frame by χ = (1 + | cos θ∗ |)/(1 − | cos θ∗ |). The
choice of χ is motivated by the fact that the angular distribution for Rutherford scattering, which
is proportional to 1/(1 − cos θ∗ )2 , is independent of χ. In perturbative QCD the χ distributions
are relatively uniform and only mildly modified by higher-order QCD or electroweak corrections.
Signatures of quark contact interactions exhibit more isotropic angular distribution than QCD and
can be identified as an excess at low values of χ. In the inclusive jet cross section measurement,
quark contact interaction effects are searched for as deviations from the predictions of perturbative
QCD in the tails of the high-pT jet spectrum [11].
Recent results from the LHC, using data collected at proton-proton center-of-mass energy of√s = 13 TeV, extend previous limits on quark contact interactions. Figure 91.1 shows the normal√
ized dijet angular distributions for several dijet mass ranges measured in ATLAS [9] at s = 13 TeV.
The data distributions are compared with SM predictions, estimated using PYTHIA8 [13] with
GEANT4-based [14] ATLAS detector simulation and corrected to NLO QCD calculation provided
by NLO Jet++ [15] including electroweak corrections [16]. Predictions including a contact interaction term in which only left-handed quarks participate at compositeness scale Λ+
LL = 15 TeV
(Λ−
=
22
TeV)
with
destructive(constructive)
interference
arealso
shown.
Overa wide range
LLof χ and dijet mass the data are well described by the SM predictions. Using the dijet angular√
distributions measured at high dijet masses and s = 13 TeV, the ATLAS [9] and CMS [12] Collaborations have set 95% confidence level (C.L.) lower limits on the contact interaction scale Λ,
ranging from 9.2 to 29.5 TeV for different quark contact interaction models that correspond tovarious combinations of (ηLL , ηRR , ηLR ), as summarized in Figure 91.2. The contact interaction
scale limits extracted using the dijet angular distributions include the exact NLO QCD corrections
to dijet production induced by contact interactions [3]. In proton-proton collisions, the Λ±
LL andcontact
interaction
modelsresultinidentical
tree-levelcross
sections
and
NLO
QCD
correcΛ±RR±±
tions and yield the same exclusion limits. For ΛV V and ΛAA , the contact interaction predictions
are identical at tree level, but exhibit different NLO QCD corrections and yield different exclusion
limits.
If leptons (l) and quarks (q) are composite with common constituents, the interaction of these
constituents will manifest itself in the form of a llqq-type four-fermion contact interaction Lagrangian at energies below the compositeness scale Λ. The llqq terms in the contact interaction
Lagrangian can be expressed as

LLL =

2
X ij
gcontactj µ j
ηLL (q̄Li γµ qLi )(¯lL
γ lL ),
Λ2
i,j

LRR =

2
X ij
gcontactj µ jiiηRR (q̄Rγ µ qR)(¯lR
γ lR ),2Λ
i,j31st May, 2024

(91.3)

91. Searches for Quark and Lepton Compositeness

3

LLR =

2
X ij
gcontactj µ j
ηLR (q̄Li γµ qLi )(¯lR
γ lR ),
2
Λ
i,j

LRL =

2
X ij
gcontactj µ jiiηRL (q̄Rγ µ qR)(¯lL
γ lL ).
Λ2i,j

1/N dN/dχs=13 TeV, 37.0 fb-1
mjj > 5.4 TeV

0.06(91.4)

ATLAS
Data
SM
CI η =−1, Λ=22 TeV
LLCI η =+1, Λ=15 TeV
LL

0.04

Theoretical uncert.
Total uncertainty

0.06

4.9 < mjj < 5.4 TeV

4.6 < mjj < 4.9 TeV

4.3 < mjj < 4.6 TeV

4.0 < mjj < 4.3 TeV

3.7 < mjj < 4.0 TeV

3.4 < mjj < 3.7 TeV

0.04

0.05
0.04
0.03
0.05
0.04
0.03

1

2

3 4 5 6 7 10

20 301χ

2

3 4 5 6 7 10

20 30
χ

Figure 91.1: Normalized dijet angular distributions in several dijet mass (mjj ) ranges. The data
distributions are compared to PYTHIA8 predictions with NLO and electroweak corrections applied(solid line) and with the predictions including a contact interaction (CI) term in which only left−
handed quarks participate of compositeness scale Λ+
LL = 15 TeV (dashed line) and ΛLL = 22 TeV(dotted line). The theoretical uncertainties and the total theoretical and experimental uncertainties
in the predictions are displayed as shaded bands around the SM prediction. Figure adopted from [9].
Searches on quark-lepton compositeness have been reported from experiments at LEP [18–21],
HERA [22, 23], the Tevatron [24, 25], and recently from the ATLAS [26, 27] and CMS [28, 29]
experiments at the LHC. The most stringent searches for llqq contact interactions are performed
31st May, 2024

91. Searches for Quark and Lepton Compositeness

4

ATLAS
CMS

Λ+LL/RR
Λ−LL/RR
Λ+VV
Λ−VV
Λ+AA
Λ−AA
Λ+(V-A)Λ−(V-A)
5

Observed
Expected
10

15

20

25

30

Contact Interaction Scale Limit [TeV]
Figure 91.2: Observed (solid lines) and expected (dashed lines) 95% C.L. lower limits on thecontact interaction scale Λ for different contact interaction models from ATLAS [9] and CMS [12]using the dijet angular distributions. The contact interaction models used for the dijet angular
distributions include the exact NLO QCD corrections to dijet production. The shaded band for theΛ+
LL/RR model indicates the range of contact interaction scale that was not excluded in ATLAS [9],due to an observed excess in the data that produced a weaker limit. The observed 95% C.L. lower
limit on the Λ−
LL from CMS [17] is shown as the second solid line in brown.

by the LHC experiments using high-mass oppositely-charged lepton pairs produced through the
qq → l+ l− Drell-Yan process. The contact interaction amplitude of the uū → l+ l− process (l = e
ul = −1or µ) interferes with the corresponding SM amplitude constructively (destructively) for ηαβ√ul = +1). The ATLAS Collaboration, using a 139 fb−1 dataset at(ηαβs = 13 TeV, has extracted
limits on the llqq contact interaction for the right-right (ηRR = ±1, ηLL = ηLR = ηRL = 0),
left-left (ηLL = ±1, ηRR = ηLR = ηRL = 0), and left-right (ηLR = ηRL = ±1, ηRR = ηLL = 0)
models. In Ref. [27], ATLAS used a background estimate directly obtained from data. Combining
the dielectron and dimuon channels, the 95% C.L. lower limits on the llqq contact interaction scaleΛ are 36 TeV (27 TeV) for the right-right model, 36 TeV (26 TeV) for the left-left model, and 33
TeV (29 TeV) for the left-right model, each with constructive (destructive) interference [27]. The
CMS Collaboration, using a 140 fb−1 dataset at 13 TeV, has set 95% C.L. exclusion limits on
the llqq contact interaction scale that range from ΛLL > 23.9 TeV for the destructive interferenceto ΛRR > 36.4 TeV for the constructive interference, for the left-left and the right-right models,
respectively [29].
Note that the contact interactions arising from the compositeness of quarks and leptons in
31st May, 2024

91. Searches for Quark and Lepton Compositeness5

Eq. (91.1) can also be regarded as a part of more general dimension-six operators in the context
of low-energy standard-model effective field theory (SMEFT). For a complete list of SM gaugeinvariant dimension-six operators, see [30,31]. A computation of the one-loop anomalous dimension
matrix for SMEFT operators are found in Refs. [32–34]. See also Refs. [35–37] for recent reviews.
Ref. [17] sets limits on the Wilson coefficients of the contact interaction operators in the SMEFT
framework, using the CMS data of the inclusive jet production cross sections together with the
deep inelastic scattering data from HERA and the CMS tt̄ cross section data. The results aretranslated into a 95% C.L. exclusion limit on the quark compositeness Λ−
LL > 24 TeV, which isshown as the second solid line in brown in Figure 91.2. In models where the SM fermions get theirmasses though the mixing with the composite states, the top-quark is expected to show compositeness properties [38] resulting in the tt̄tt̄ contact interaction operators in the SMEFT context.
An enhancement of the four-top-quark production cross section is expected at hadron colliders inthese models [39]. The ATLAS Collaboration has extracted 95% C.L. observed (expected) limits
on the tt̄tt̄ contact interaction operator |C4t |/Λ2 < 1.9 TeV−2 (1.6 TeV−2 ) using their 36.1 fb−1√
data at s = 13 TeV [40]. Consistent SMEFT reinterpretations of top-quark data, and high energy
non-resonant dijet and dilepton data are provided, e.g., in Refs. [41, 42].
Interactions of hypothetical dark matter candidate particles with SM particles through mediators can also be described as contact interactions at low energy. See “Searches for WIMPs
and Other Particles” in this volume for limits on the interactions involving dark matter candidate
particles.

91.2 Limits on excited fermions
Another typical consequence of compositeness is the appearance of excited leptons and quarks(l∗ and q ∗ ). Phenomenologically, an excited lepton is defined to be a heavy lepton which shares a
leptonic quantum number with one of the existing leptons (an excited quark is defined similarly).
For example, an excited electron e∗ is characterized by a nonzero transition-magnetic coupling withelectrons. The smallness of the lepton mass and the success of QED prediction for g − 2 suggest
chirality conservation, i.e., an excited lepton should not couple to both left- and right-handed
components of the corresponding lepton [43–45].
Excited leptons may be classified by SU (2) × U (1) quantum numbers. Typical examples are:1. Sequential type
ν∗
l∗

!

,

∗
[νR
],

∗
lR
.

L

∗ is necessary if we assume ν ∗ has a Dirac mass.
νR

2. Mirror type[νL∗ ],

∗
lL
,

ν∗
l∗

!

.
R

3. Homodoublet type
ν∗
l∗

!

,
L

ν∗
l∗

!

.
R

Similar classification can be made for excited quarks.
Excited fermions can be pair produced via their minimal gauge couplings. The couplings ofexcited leptons with Z are given bye
2 sin θW cos θWh(−1 + 2 sin2 θW )l¯∗ γ µ l∗ Zµ + ν¯∗ γ µ ν ∗ Zµ31st May, 2024i

91. Searches for Quark and Lepton Compositeness6

in the homodoublet model. The corresponding couplings of excited quarks can be easily obtained.
Although form factor effects can be present for the gauge couplings at q 2 6= 0, they are usuallyneglected.
Excited fermions may also be produced via the contact interactions with ordinary quarks andleptons [46]
L=

2
h
i
gcontact
0
∗ µ ∗
00
∗ µ
η
(
ψ̄
γ
ψ
)(
ψ̄
γ
ψ
)
+(η
(
ψ̄
γ
ψ
)(
ψ̄
γ
ψ
)
+
h.c.)
+
·
·
·
.
µ
µ
L
L
L
L
L
LL
L
L
LL
L
Λ2

(91.5)

2
000 = 1,
Again, the coefficient is conventionally taken gcontact= 4π. It is widely assumed ηLL= ηLL
000 = η 0
00
0
00
ηLR
= ηLR
RL = ηRL = ηRR = ηRR = 0 in experimental analyses for simplicity.
In addition, transition-magnetic type couplings with a gauge boson are expected. These couplings can be generally parameterized as follows:(ψ ∗ )

1 + γ51 − γ5λγ e ∗ µν
+ ηR
)ψFµν
ψ̄ σ (ηL
L=
2mψ∗
2
2
(ψ ∗ )λe ∗ µν
1 − γ5
1 + γ5+ Z
ψ̄ σ (ηL
+ ηR
)ψZµν
2mψ∗
2
2
(l∗ )

λ g
1 − γ5+ W ¯l∗ σ µν
νWµν
2ml∗
2
(ν ∗ )λ g
1 − γ5
1 + γ5†+ W ν̄ ∗ σ µν (ηL
+ ηR
)lWµν
2mν ∗
2
2
+ h.c.,(91.6)

where g = e/ sin θW , ψ = ν or l, Fµν = ∂µ Aν −∂ν Aµ is the photon field strength, Zµν = ∂µ Zν −∂ν Zµ ,etc.. The normalization of the coupling is chosen such thatmax(|ηL |, |ηR |) = 1.
Chirality conservation requires
ηL ηR = 0.

(91.7)

These couplings in Eq. (91.6) can arise from SU (2) × U (1)-invariant higher-dimensional interactions. A well-studied model is the interaction of homodoublet type l∗ with the Lagrangian(see [47, 48])
1 ∗ µν
τa a
1 − γ5
L=L̄ σ (gf Wµν+ g 0 f 0 Y Bµν )L + h.c.,(91.8)2Λ
22
where L denotes the lepton doublet (ν, l), Λ is the compositeness scale, g, g 0 are SU (2) and U (1)Ya and Bgauge couplings, and Wµνµν are the field strengths for SU (2) and U (1)Y gauge fields. These
couplings satisfy the relation√
λW = − 2 sin2 θW (λZ cot θW + λγ ) ,(91.9)(`∗ )(ν ∗ )

with λW,Z,γ being defined in Eq. (91.6) with λW,Z,γ = λW,Z,γ or λW,Z,γ = λW,Z,γ . Here (ηL , ηR ) =(1, 0) is assumed. It should be noted that the electromagnetic radiative decay of l∗ (ν ∗ ) is forbidden
if f = −f 0 (f = f 0 ).
Additional coupling with gluons is possible for excited quarks:
1 ∗ µν
λa
τa a
1 − γ5+ g 0 f 0 Y Bµν ×L=Q̄ σ
gs fs Gaµν + gf Wµν
Q + h.c. ,
2Λ
2
2
2




31st May, 2024

(91.10)7

91. Searches for Quark and Lepton Compositenesswhere Q denotes a quark doublet, gs is the QCD gauge coupling, and Gaµν the gluon field strength.
If leptons are made of color triplet and antitriplet constituents, we may expect their color-octet
partners. Transitions between the octet leptons (l8 ) and the ordinary lepton (l) may take place via
the dimension-five interactionsL=o
1 X n¯αα µν
l8 gS Fµνσ (ηL lL + ηR lR ) + h.c.
2Λ l(91.11)

where the summation is over charged leptons and neutrinos. The leptonic chiral invariance implies
ηL ηR = 0 as before.
Searches for the excited quarks and leptons have been performed over the last decades inexperiments at the LEP [49–52], HERA [53,54], Tevatron [55,56], and LHC [57–89]. Most stringent
constraints, which are described below at 95% confidence level, come from the LHC experiments.
The signature of excited quarks q ∗ at hadron colliders is characterized by a narrow resonantpeak in the reconstructed invariant mass distribution of the q ∗ decay products. The decays via
the transition-magnetic type operator in Eq. (91.10) are considered for excited quarks in LHC
searches, and the final states to search for are dijet (qg) [57, 58, 70–73] or a jet in association witha photon (qγ) [59, 60, 74, 75, 89] or a weak gauge boson (qW , qZ) [76, 77]. All analyses consider
only spin-1/2 excited states of first generation quarks (u∗ , d∗ ) with degenerate masses, expected
to be predominantly produced in proton-proton collisions except for the excited b quark searches
described below. Only the minimal gauge interactions and the transition-magnetic couplings withthe form given in Eq. (91.10) are considered in the production process, and hence the contact
interactions in Eq. (91.5) are not considered. The compositeness scale Λ is taken to be the same as
the excited quark mass mq∗ . The transition-magnetic coupling coefficients fs , f and f 0 are assumed
to be equal to 1 (denoted by f ).
√With proton-proton collision data recorded at s = 13 TeV at the LHC, the excited quark
masses are excluded in dijet resonance searches up to 6.7 TeV in ATLAS using 139 fb−1 [58] and6.3 TeV in CMS using 137 fb−1 [73]. Figure 91.3 shows the dijet mass (mjj ) distribution measured
in CMS [73] by using the two highest pT jets reconstructed with the anti-k
T algorithm [90] of ap2
distance parameter of 0.4, and by combining nearby jets within ∆R = ∆η + ∆φ2 < 1.1 aroundthe leading two jets. The measured dijet mass spectrum is compared to a fit with smoothly fallingbackground shape (solid curve) at mjj > 1.5 TeV and the background prediction obtained from ∆ηjj
control regions (open squares), denoted as Ratio method, at mjj > 2.4 TeV to look for a narrow
resonance. Here ∆ηjj is the pseudorapidity separation between the two jets. An excited quark
signal with mass of 4.0 TeV is shown in the figure (denoted by qg) as one of the benchmark signals
considered in the analysis.
The photon + jet resonance searches, targeting excited quarks decaying into a quark and aphoton (q ∗ → q + γ), have excluded q ∗ masses up to 5.3 TeV in ATLAS [60] and 6.0 TeV in√
CMS [89] using collision data at s = 13 TeV. The W/Z boson + jet final states are examined
to look for the q ∗ → q + W and q + Z signal in CMS [77], exploiting jet substructure techniquedesigned to provide sensitivity for highly-boosted hadronically decaying W and Z bosons. The
lower mass limit of 5.0 (4.8) TeV is obtained from the W + jet (Z + jet) search using dataset√
recorded at s = 13 TeV.
The excited b quarks (b∗ ) are also considered in the present searches at the LHC. Assuming
the similar production processes to the first-generation excited quarks, the b∗ has been searched
for in final states containing at least one jet identified as originating from a b quark (b-tagging).
The searches using two jets including at least one b-tagged jet have been performed at 8 and
13 TeV [58, 61, 62, 71, 85], resulting in b∗ lower mass limits of 3.2 TeV in ATLAS using 139 fb−1 at√√s = 13 TeV [58] and 4.0 TeV in CMS using 138 fb−1 at s = 13 TeV [85]. The CMS Collaboration
31st May, 2024

91. Searches for Quark and Lepton Compositenessdσ/dmjj [pb/TeV]

8

137 fb-1 (13 TeV)

103

Data
Fit method
χ2/NDF = 36.63 / 38
Ratio method
χ2/NDF = 42.04 / 32
gg (2.0 TeV)
qg (4.0 TeV)
qq (6.0 TeV)

CMS

102
10
1

10−1

10−2
10−3
10−4
(Data-Prediction)
Uncertainty

10−5

mjj > 1.5 TeV|η| < 2.5, |∆η| < 1.1

4
2
0
−2
−4

2

3

4

5

6 7 8

Dijet mass [TeV]

Figure 91.3: Dijet mass distribution measured by CMS using wide jets
preconstructed from twohighest transverse momentum jets by adding nearby jets within ∆R = ∆η 2 + ∆φ2 < 1.1. The
data distribution is compared to a fit representing a smooth background spectrum (solid curve) andthe background prediction obtained from the ∆ηjj control regions (open squares), denoted as Ratio
method, at mjj > 2.4 TeV. The excited quark signal with mass of 4.0 TeV (labeled as qg) is shown
together with other benchmark signals. Shown at the bottom panel is the difference between thedata and the fitted parametrization from the fit method or the data and the background prediction
from the Ratio method, divided by the statistical uncertainty of the data. Figure adopted from [73].

also performed a search for b∗ → b + γ in events with a b-tagged jet in association with a photon√using data at s = 13 TeV [89], and excluded b∗ masses up to 2.2 TeV. For the same couplingstrength, the observed lower mass bounds on the excited bottom quarks extends to 3.8 TeV, when
the production mode from contact interactions Eq. (91.5) is also considered. Excited b quarks with
31st May, 2024

91. Searches for Quark and Lepton Compositeness9e* (eγ )e* (eZ)e* (ejj)e* (multi-lepton)µ* (µγ )µ* (µZ)µ* (µjj)µ* (multi-lepton)τ* (τjj)
τ* (multi-lepton)ν* (multi-lepton)q* (jj)q* (jγ )

ATLAS
CMS

q* (jW)
Observed
Expectedq* (jZ)
5

6

7

Mass Limit [TeV]01

Λ = m l*

ATLAS
CMS

Observed
Expected
2

3

4

5

6

Mass Limit [TeV]

Figure 91.4: 95% C.L. lower mass limits for the excited quarks (left) and excited leptons (right) at
ATLAS [58,60,66–68,88] and CMS [73,75,77,80–82,89] experiments. Shown are the most stringent
limits for each final state (denoted in parentheses) of the excited fermions from both experiments.
Only first generation quarks (u, d) with transition-magnetic type interactions with fs = f = f 0 = 1
are considered for the excited quarks. The excited lepton limits are given for the production via
contact interactions with Λ = ml∗ .
charged-current decay into a W -boson and a top quark (b∗ → t + W ) were looked for in both
ATLAS and CMS using the full 8 TeV data [63, 78] and in CMS using the full 13 TeV data [86, 87].
For the left(right)-handed couplings, CMS excluded the masses below 2.6(2.8) TeV in the fully
hadronic final states [86] and 3.0(3.2) TeV in the lepton+jets final states [87].
The excited top quarks (t∗ ) have also been searched for at the LHC. The CMS Collaboration
performed the search for pair-produced t∗ quarks with the assumption of the t∗ quark decay into a
top quark and a gluon, in events with a charged lepton, missing transverse momentum and multiple√
jets including b-tagged jets at s = 8 TeV [84] and 13 TeV [83]. With 35.9 fb−1 data at 13 TeV,CMS excluded the t∗ masses below 1.2 TeV for spin 3/2 t∗ quarks [83].
Searches for excited leptons l∗ are also performed at the LHC using proton-proton collision√
data recorded at s = 7 and 8 TeV [65–69, 79, 80] as well as at 13 TeV [81]. Considering single l∗
production in contact interactions (Eq. (91.5)) and electromagnetic radiative decay to a SM lepton
and a photon (l∗ → l + γ where l = e, µ), the excited electron and muon masses are excluded for√Λ = ml∗ up to 3.9 and 3.8 TeV, respectively, using 35.9 fb−1 at s = 13 TeV in CMS [81] and√2.2 TeV using 13 fb−1 at s = 8 TeV in ATLAS [66].
√With the full 20.3 fb−1 data at s = 8 TeV, the inclusive search on multi-lepton signatures with
3 or more charged leptons in ATLAS [67] further constrains the excited charged leptons and neutrinos. Considering both the transition-magnetic (Eq. (91.8)) and contact interaction (Eq. (91.5))
processes, the lower mass limits for the e∗ , µ∗ , τ ∗ and ν ∗ (for every excited neutrino flavor) are
obtained to be 3.0, 3.0, 2.5 and 1.6 TeV, respectively, for Λ = me∗ , mµ∗ , mτ ∗ and mν ∗ . The rateof pair-produced excited leptons is independent of Λ for the minimal gauge interaction processes,
and it allows to improve search sensitivity with multi-lepton signatures at high Λ, especially for
excited neutrinos because the predominant νl∗ → l + W decays result in a higher acceptance for≥ 3 charged lepton final states.
Both ATLAS and CMS Collaborations performed searches for singly produced excited leptons.
The single excited leptons, both produced and decaying in contact interaction processes (Eq. (91.5)),
were searched for in CMS with 77.4 fb−1 at 13 TeV [82] and in ATLAS with 20.3 fb−1 at 8 TeV [68]31st May, 2024

10

91. Searches for Quark and Lepton Compositenessand 139 fb−1 at 13 TeV [88] using the final states with two leptons and two jets (q q̄ → ll∗ → llq q̄).
The CMS search [82] considered both excited electrons and excited muons, using the invariant massof the combination of the two leptons and two jets as a discriminating variable to separate signal
from background. The ATLAS search considered excited muons [68] and excited τ leptons [88]. The
single excited electrons, produced in contact interactions and decayed either in contact interaction
or charged-current processes, were considered in ATLAS using 36.1 fb−1 at 13 TeV [69] in the
final states with two electrons and two jets (q q̄ → ee∗ → eeq q̄) or an electron, missing transverse
momentum and a hadronically decaying W -boson candidate (q q̄ → ee∗ → eνW ). The excitedelectron (muon) mass was excluded up to 5.6 (5.7) TeV in CMS [82] at Λ = me∗ (Λ = mµ∗ ), whichis the best limit to date on the excited electrons (muons). The excited τ lepton mass was excluded
up to 4.6 TeV in ATLAS [88] at Λ = mτ ∗ .
The CMS Collaboration also performed an excited lepton search in the final states containing a
Z boson [80], probing the excited leptons produced in contact interactions and decayed in neutralcurrent processes (l∗ → l + Z) with f = f 0 = 1 or f = −f 0 = 1. The leptonic and hadronic decaysof Z bosons have been considered in the search, and the most stringent limits are obtained fromthe hadronic Z decay to be 2.08 (2.34) TeV and 2.11 (2.37) TeV for the e∗ and µ∗ , respectively,
with f = f 0 = 1 (f = −f 0 = 1) at Λ = ml∗ .
Figure 91.4 summarizes the most stringent 95% C.L. lower mass limits for excited quarks andleptons obtained from the LHC experiments.
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