94. Leptoquarks

1

94. Leptoquarks
Revised October 2023 by S. Rolli (DOE) and M. Tanabashi (Nagoya U.; KMI, Nagoya U.).
Leptoquarks are hypothetical particles carrying both baryon number (B) and lepton number(L). The possible quantum numbers of leptoquark states can be restricted by assuming that theirdirect interactions with the ordinary Standard Model (SM) fermions are dimensionless and invariant
under the SM gauge group. Table 94.1 shows the list of all possible quantum numbers with thisassumption [1]. The columns of SU (3)C , SU (2)W , and U (1)Y in Table 94.1 indicate the QCD
representation, the weak isospin representation, and the weak hypercharge, respectively. The spinof a leptoquark state is taken to be 1 (vector leptoquark) or 0 (scalar leptoquark).
Table 94.1: Possible leptoquarks and their quantum numbers.
Spin
0
0
0
1
1
0
0
1
1
1

3B + L
−2
−2
−2
−2
−2
0
0
0
0
0

SU (3)c
3̄
3̄
3̄
3̄
3̄
3
3
3
3
3

SU (2)W
1
1
3
2
2
2
2
1
1
3

U (1)Y
1/3
4/3
1/3
5/6
−1/6
7/6
1/6
2/3
5/3
2/3

Allowed couplingq̄Lc `L or ūcR eR
d¯cR eRq̄Lc `Lcµq̄L γ eR or d¯cR γ µ `LūcR γ µ `Lq̄L eR or ūR `Ld¯R `Lµq̄L γ `L or d¯R γ µ eRūR γ µ eRq̄L γ µ `L

If we do not require leptoquark states to couple directly with SM fermions, different assignmentsof quantum numbers become possible [2, 3].
Leptoquark states are expected to exist in various extensions of the SM. The Pati-Salam model[4] is an example predicting the existence of a leptoquark state. Leptoquark states also exist in grandunification theories based on SU (5) [5], SO(10) [6] which includes Pati-Salam color SU (4), andlarger gauge groups. The existence of leptoquarks at TeV-scale also affect the renormalization groupof the standard model gauge coupling strengths and may allow for the gauge coupling unification
required by the grand unification theories [7]. Scalar quarks in supersymmetric models with Rparity violation may also have leptoquark-type Yukawa couplings. The bounds on the leptoquark
states can therefore be applied to constrain R-parity-violating supersymmetric models [8,9]. Scalar
leptoquarks are expected to exist at the TeV scale in extended technicolor models [10, 11] whereleptoquark states appear as the bound states of techni-fermions. Compositeness of quarks andleptons also provides examples of models which may have light leptoquark states [12].
Bounds on leptoquark states are obtained both directly and indirectly. Direct limits are fromtheir production cross sections at colliders, while indirect limits are calculated from bounds on
leptoquark-induced two-quark two-lepton interactions, which are obtained from low-energy experiments, or from collider experiments below threshold. The quantum number assignment ofTable 94.1 allows several leptoquark states to couple to both left- and right-handed quarks simultaneously. Such leptoquark states are called non-chiral and may cause low-energy interactions(ūR qLi )(ēR `Lj )ij

(d¯R qLi )(`¯iL eR ) .

S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
31st May, 2024 10:16am(94.1)

94. Leptoquarks

2

Here i, j are indices for the weak isospin. These two-quark two-lepton interactions affect the(π → eν)/(π → µν) ratio [13]. Non-chiral scalar leptoquarks also contribute to the anomalous
magnetic moments of charged leptons [14, 15]. On the other hand, the exchanges of the chiral
leptoquarks produce effective two-quark two-lepton interactions(q̄Li γ µ qLi )(`¯jL γµ `Lj ) ,(ūR γ µ uR )(`¯j γµ `Lj ) ,

L
j
µ
¯
¯
(dR γ dR )(`L γµ `Lj ) ,(q̄Li γ µ qLi )(ēR γµ eR ) ,(ūR γ µ uR )(ēR γµ eR ) ,(d¯R γ µ dR )(ēR γµ eR )(q̄Li γ µ (~σ )i j qLj ) · (`¯kL γµ (~σ )k l `Ll ) ,(94.2)

below the leptoquark mass scale. Note that labels for the generations of quarks and leptons aresuppressed in (94.1) and (94.2). If a leptoquark couples to quarks (leptons) belonging to morethan a single generation in the mass eigenbasis, it can induce two-quark two-lepton interactions
causing flavor-changing neutral currents (lepton-family-number violations). Since indirect limits
provide more stringent constraints on non-chiral or flavor-violating leptoquarks, in the searchesof leptoquark states at collider experiments, it is often assumed that a leptoquark state couples
only to a single generation of quarks and a single generation of leptons in a chiral interaction, forwhich indirect limits become much weaker. Additionally, this assumption gives strong constraints
on models of leptoquarks.
Refs. [16–18] give extensive lists of the bounds on the leptoquark-induced two-quark two-lepton
interactions. For the isoscalar scalar and vector leptoquarks S0 and V0 , for example, which couple
with the first- (second-) generation left-handed quark, and the first-generation left-handed lepton,
the bounds λ2 < 0.07 × (MLQ /1 TeV)2 for S0 , and λ2 < 0.4 × (MLQ /1 TeV)2 for V0 (λ2 <0.7 × (MLQ /1 TeV)2 for S0 , and λ2 < 0.5 × (MLQ /1 TeV)2 for V0 ) with λ being the leptoquark
coupling strength, can be derived from the limits listed in Ref. [18]. See also Refs. [19, 20] forearlier studies. The e+ e− collider experiments are sensitive to the indirect effects coming from tand u-channel exchanges of leptoquarks in the e+ e− → q q̄ process. The HERA experiments givebounds on the leptoquark-induced two-quark two-lepton interaction. It should also be stressedthat the measurements of the high-mass Drell-Yan cross sections, pp → `ν and pp → `+ `− , are also
sensitive to these leptoquark-induced interactions. For detailed bounds obtained in this way, seee.g., Ref. [17], and the Heavy Boson Particle Listings for “Indirect Limits for Leptoquarks” andtheir references.
Note that the two-quark two-lepton interactions arising from the leptoquark exchanges inEq.(94.1) and Eq.(94.2) can also be regarded as a part of more general dimension-six operatorsin the context of low-energy standard-model effective field theory (SMEFT). For a complete list of
SM gauge-invariant dimension-six operators, see [21,22]. A computation of the one-loop anomalous
dimension matrix for SMEFT operators are found in Refs. [23–25]. The leptoquark induced twoquark two-lepton interactions often cause lepton-flavor non-universalities in heavy quark decays.
The R(D), R(D∗ ) anomaly observed in the semi-leptonic B decays [26] may be explained in models
with TeV scale leptoquarks.
Collider experiments provide direct limits on the leptoquark states through limits on the pairand single-production cross sections. The leading-order cross sections of the parton processes
q + q̄ → LQ + LQg + g → LQ + LQ
e + q → LQ
(94.3)
may be written as [27]31st May, 2024

94. Leptoquarks

32αs2 π 3
β ,
27ŝ
h
i
α2 π h1 + βiσ̂LO gg → LQ + LQ = s × β(41 − 31β 2 ) + (18β 2 − β 4 − 17) log
,
96ŝ
1−β
h
i
πλ2
2
σ̂LO eq → LQ =δ(ŝ − MLQ)(94.4)
4√forq a scalar leptoquark. Here ŝ is the invariant energy of the parton subprocess, and β ≡2 /ŝ. The leptoquark Yukawa coupling is given by λ. The cross sections of the pair
1 − 4MLQ
productions of scalar leptoquarks in pp collisions at the LHC energies have been computed inRefs. [28, 29] at the next-to-leading order in QCD. Leptoquarks are also produced singly at hadroncolliders through g + q → LQ + ` [30], which allows extending to higher masses the collider reach in
the leptoquark search [31], depending on the leptoquark Yukawa coupling. The next-to-leading order computations for the single production of the leptoquark states at the LHC energies have been
performed in Refs. [32–35]. Since protons contain leptons inside, it is possible to target leptoninduced processes at high energy pp colliders. The single leptoquark production cross sections
induced from the lepton-quark collisions at the LHC have been computed in Refs. [36,37]. Ref. [38]performed searches for the leptoquark states produced in lepton-quark collisions at the LHC.
See Ref. [17] for a comprehensive review on the leptoquark phenomenology in precision experiments and particle colliders.
Leptoquark states which couple only to left- or right-handed quarks are called chiral leptoquarks.
Leptoquark states which couple only to the first (second, third) generation are referred as the first(second-, third-) generation leptoquarks.
The LHC, Tevatron and LEP experiments have been searching for pair production of the leptoquark states, which arises from the leptoquark gauge interaction. Due to the typical decay of the
leptoquark into charged and neutral leptons and quarks, the searches are carried on in signatures
including high pT charged leptons, high ET jets and large missing transverse energy. Additionally,
searches for pair produced LQs are often organized by the decay mode of the pair of LQs, via the decay parameter β, which represents the branching fraction into a charge lepton vs a neutrino: β = 1
for LQs decaying into a charged lepton with 100% branching fraction, β = 0.5 for LQs decaying
into a charged lepton with 50% branching fraction. The gauge couplings of a scalar leptoquark aredetermined uniquely according to its quantum numbers in Table 94.1. Since all of the leptoquark
states belong to color-triplet representation, the scalar leptoquark QCD-induced pair-production
cross section at the Tevatron and LHC can be determined solely as a function of the leptoquark
mass without making further assumptions. This is in contrast to the indirect or single-production
limits, which give constraints in the leptoquark mass-coupling plane.
Older results from the Tevatron run can be found here: [39–42].
Since the previous version of this review, both ATLAS and CMS continue to update theirresults concerning searches for first, second, and third generation LQs and leptoquark states which
couple only with the i-th generation quarks and the j-th generation leptons (i 6= j) without causing
conflicts with severe indirect constraints. The datasets were almost all collected at center of massenergy of 13 TeV and corresponding to the latest integrated luminosity collected before the shutdownof the LHC occurring in 2019 and 2020.
It is worthy to note that organizing LQs by flavor quantum number first before organizing themby gauge quantum number is becoming more common and advantageous because it relates moreclosely to some of the experimental searches being performed. The traditional nomenclature for 1st,hiσ̂LO q q̄ → LQ + LQ =31st May, 2024

494. Leptoquarks

2nd, and 3rd generation LQ encourages only looking for the diagonal elements in a flavor matrixof possibilities, which has been the traditional experimental search strategy.
Current results extend previous mass limits for scalar leptoquarks to > 1435 GeV (first genera√√tion, CMS, β =1, s = 13 TeV) and > 1270 GeV(first generation, CMS, β =0.5, s = 13 TeV) [43];√> 1800 GeV (first generation, ATLAS, β =1, s = 13 TeV) [44] and > 1290 GeV (first generation,√√
ATLAS, β =0.5, s = 13 TeV ) [45]; > 1530 GeV (second generation, CMS, β =1, s = 13 TeV)√
and > 1285 GeV (second generation, CMS, β =0.5, s = 13 TeV) [46]; and > 1700 GeV (second√
generation, ATLAS, β =1, s = 13 TeV) [44] and > 1230 GeV (second generation, ATLAS, β√=0.5, s = 13 TeV) [45]. All limits are presented at 95% C.L.
As for third generation leptoquarks, CMS results are the following: 1) assuming that all leptoquarks decay to a top quark and a τ lepton, the existence of pair produced, third-generation
leptoquark up to a mass of 1120 GeV (β =1, 13 TeV) is excluded at 95% confidence level [47];2) assuming that all leptoquarks decay to a bottom quark and a τ lepton, the existence of pair
produced, third-generation leptoquark up to a mass of 1020 GeV (β =1, 13 TeV) is excluded at 95%
confidence level [48]; 3) assuming that all leptoquarks decay to a bottom quark and a τ neutrino,
the existence of pair produced, third-generation leptoquark up to a mass of 1185 GeV (β =0, 13
TeV) is excluded at 95% confidence level [49]. In a recent paper [50] signatures of top quark τ
lepton ν bottom and top τ ν - not previously explored in dedicated searches, were analyzed in thecontext of searches for scalar leptoquark of charge -1/3e coupling to a top quark plus a τ lepton(tτ ) or a bottom quark plus a neutrino (bν), or a vector particle of charge +2/3e, coupling to tν orbτ . These choices are motivated by models that can explain a series of anomalies observed in themeasurement of B meson decays. The data are found to be in agreement with the standard model
prediction. Lower limits at 95% confidence level are set on the LQ mass in the range 0.98–1.73
TeV, depending on the LQ spin and its coupling λ to a lepton and a quark, and assuming equal
couplings for the two LQ decay modes considered. These are the most stringent constraints to dateon the existence of leptoquarks in this scenario.
In [51] ATLAS present the result of searches for pair production of third-generation scalar
leptoquarks decaying into a top quark and a τ -lepton, using 139 fb−1 of data collected at 13 TeV.
Scalar leptoquarks decaying exclusively into tτ are excluded up to masses of 1.43 TeV while, fora branching fraction of 50% into tτ , the lower mass limit is 1.22 TeV. In two recent papers[52] and [53] ATLAS searched for pair-produced scalar or vector leptoquarks decaying into a bquark and a τ -lepton and single production of vector leptoquarks with electric charge of 2/3eand scalar leptoquarks with an electric charge of 4/3e. For pair production of scalar leptoquarks,
masses below 1490 GeV are excluded assuming a 100% branching ratio, while for vector leptoquarks
the corresponding limit is 1690 GeV (1960 GeV) in the minimal-coupling (Yang–Mills) scenario.
For single vector leptoquark production two models are considered: the Yang–Mills and Minimal
coupling models. In the Yang–Mills (Minimal coupling) scenario, vector leptoquarks with a mass
below 1.58 (1.35) TeV are excluded for a gauge coupling of 1.0 and below 2.05 (1.99) TeV for a gauge
coupling of 2.5. In the case of single scalar leptoquark production, masses below 1.28 TeV (1.53 TeV)
are excluded for a Yukawa coupling of 1.0 (2.5). Additionally, a search for pair production of
leptoquarks with decays into third-generation leptons and quarks. in final states with hadronicallydecaying τ leptons, b-jets, and missing transverse momentum was performed in [54]: depending on
the branching fraction into charged leptons, leptoquarks with masses up to around 1.25 TeV can be
excluded at the 95% confidence level for the case of scalar leptoquarks and up to 1.8 TeV (1.5 TeV)
for vector leptoquarks in a Yang–Mills (minimal-coupling) scenario.
It is also possible to consider leptoquark states which couple only with the i-th generation
quarks and the j-th generation leptons (i 6= j) without causing conflicts with severe indirect constraints. Such couplings have received renewed attention because they may provide an explanation
31st May, 2024

594. Leptoquarks

to anomalies in rare B − meson decays and the anomalous magnetic moment of the muon. See
Ref. [55, 56] and [57] and references therein for collider search strategies and limits on the pair
production cross sections of this class of leptoquark states. In this framework, in [58] and [47]CMS presents a non-traditional search for pair production of LQs coupled to a top quark and a
leptons. As no deviation from the Standard Model prediction was observed, scalar LQs decaying
exclusively into top quark and lepton are excluded below 1.12 − 1.42 TeV depending on the lepton
flavor. In [59] ATLAS conducted a search for pair production of scalar and vector leptoquarks,
each decaying into first and second generation leptons and a third generation quarks. This is partof leptoquark search using ATLAS data to investigate cross- generational couplings that could provide explanations for recently observed anomalies in B meson decays. All possible decays of thepair-produced leptoquarks into quarks of the third generation and charged or neutral leptons of
the first or second generation with exactly one electron or muon in the final state are investigated.
No significant deviations from the Standard Model expectation are observed. Upper limits on the
production cross-section are provided for different models as a function of the leptoquark mass andthe branching ratio of the leptoquark into the charged or neutral lepton. Some of these models
have the goal of providing an explanation for the recent B-anomalies. In such models, a vector leptoquark decays into charged and neutral leptons of the second generation with a similar branching
fraction. Lower limits of 1.9 TeV and 1.7 TeV are set on the leptoquark mass for these two models.
The magnetic-dipole-type and the electric-quadrupole-type interactions of a vector leptoquark
are not determined even if we fix its gauge quantum numbers as listed in the Table 94.1 [60].
The production of vector leptoquarks depends in general on additional assumptions, where theleptoquark couplings and their pair production cross sections are enhanced relative to the scalar
leptoquark contributions. The most stringent limits on vector LQ production are now from CMS[61] where previous searches for squarks and gluinos have been reinterpreted to constrain models of
leptoquark production. LQ masses below 1530 GeV are excluded assuming the Yang-Mills case withcoupling κ = 1, or 1115 GeV in the minimal coupling case where κ = 0, placing the most stringent
constraint to date from pair production of vector LQs. These results and the ones in [62] were
updated in [49] where searches for phenomena beyond the standard model (BSM) were performed
using events with hadronic jets and significant transverse momentum imbalance to constrain arange of BSM models including the pair production of scalar and vector leptoquarks each decaying
to a neutrino and a top, bottom, or light-flavor quark.
The leptoquark pair-production cross sections in e+ e− collisions depend on the leptoquark
SU (2) × U (1) quantum numbers and Yukawa coupling with electron [63].
Searches for first generation leptoquark singly produced were performed by the HERA experiments. Since the leptoquark single-production cross section depends on its Yukawa coupling, theleptoquark mass limits from HERA are usually displayed in the mass-coupling plane. For leptoquark
Yukawa coupling λ = 0.1, early ZEUS Collaboration bounds on the first-generation leptoquarks
range from 248 to 290 GeV, depending on the leptoquark species [64]. The ZEUS Collaboration has
recently released a new paper [65] where data corresponding to a luminosity of around 1 fb−1 havebeen used in the framework of eeqq contact interactions (CI) to set limits on possible high-energy
contributions beyond the Standard Model to electron-quark scattering. The analysis of the ep
data has been based on simultaneous fits of parton distribution functions including contributions ofContact Interaction (CI) couplings to ep scattering. Several general CI models and scenarios withheavy leptoquarks were considered. As unambiguous deviations from the SM cannot be established,limits for CI compositeness scales and LQ mass scales were set that are in the TeV range. The
H1 Collaboration has a comprehensive summary of searches for first generation leptoquarks using
the full data sample collected in ep collisions at HERA (446 pb−1 ). No evidence of production of
leptoquarks was observed in final states with a large transverse momentum electron or large missing
31st May, 2024

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94. Leptoquarks

transverse momentum. For a coupling strength λ = 0.3, first generation leptoquarks with masses
up to 800 GeV are excluded at 95% C.L. [66].
At the LHC, the CMS collaboration performed searches for single production of first and second
generation leptoquarks [67], which is complementary to the HERA searches in the high λ region (forcoupling strength λ = 1.0, first generation leptoquarks are excluded for masses up to 1.73 TeV andsecond generation leptoquark are excluded up to masses of 530 GeV). CMS also recently searched
for third generation LQ decaying into τ and bottom in [68]. Assuming unit Yukawa coupling (λ), athird generation scalar leptoquark is excluded for masses below 740 GeV. Limits are also set on λof the hypothesized leptoquark as a function of its mass. Above λ = 1.4, the results provide thebest upper limit on the mass of a third-generation scalar leptoquark decaying to a τ lepton and abottom quark.
Searches for LQ will continue with more LHC data, particularly in light of the renewed interestin this type of particle to explain violation of lepton flavor universality and other anomalies, which
point to explanations laying outside the Standard Model.
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31st May, 2024