# Leptoquark

A leptoquark (LQ) is a hypothetical particle that would couple directly to a quark and a lepton, allowing the two kinds of matter particles to transform into each other and giving a unified picture of the fundamental constituents of matter.<sup>[1](https://atlas.cern/Glossary/leptoquarks)</sup> No leptoquark has been observed; experiments at colliders have instead set lower limits on the masses such a particle could have.

| Key fact | Detail |
|---|---|
| Definition | Hypothetical boson coupling simultaneously to a quark and a lepton, carrying both baryon number (B ≠ 0) and lepton number (L ≠ 0)<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> |
| Spin and color | Spin 0 (scalar) or spin 1 (vector); color-triplet under QCD, so it interacts via the strong force<sup>[1](https://atlas.cern/Glossary/leptoquarks)</sup><sup> • </sup><sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> |
| Decays | Generically decays to a charged lepton and a quark, or to a neutrino and a quark<sup>[3](https://cds.cern.ch/record/2888841/files/2402.08668.pdf)</sup> |
| Production at the LHC | Pair production via gluon-gluon fusion and quark-antiquark annihilation; single production via gluon-quark fusion, with rates depending on the Yukawa coupling λ<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> |
| Strongest mass limits | Vector LQs excluded below 1530 GeV (Yang-Mills, κ = 1) by CMS pair production; ATLAS excludes vector LQs decaying to bτ below 1.75 TeV and scalar LQs decaying exclusively to tμ below 1.64 TeV<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup><sup> • </sup><sup>[4](https://www.atlas.cern/Updates/Briefing/leptoquarks-thirdgeneration)</sup> |
| Physics motivation | Candidate explanation for anomalies in B-meson decays, hints of lepton flavor universality violation, and the muon anomalous magnetic moment; TeV-scale LQs may also aid gauge coupling unification<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> |

## Properties and quantum numbers

Leptoquarks are bosons that carry both baryon number and lepton number, quantum numbers that in the standard model are separately assigned to quarks and leptons.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> Assuming their direct interactions with standard model fermions are dimensionless and invariant under the standard model gauge group, the possible quantum-number assignments are finite and tabulated: each state is a color triplet or anti-triplet under SU(3)c, with a definite [weak isospin](https://www.edgepedia.org/weak-isospin) representation and weak hypercharge, and spin 0 or 1.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> Because they carry color charge, leptoquarks interact through the strong force as well as through their lepton-quark coupling.<sup>[1](https://atlas.cern/Glossary/leptoquarks)</sup>

A leptoquark would generically decay either to a charged lepton and a quark, or to a neutrino and a quark.<sup>[3](https://cds.cern.ch/record/2888841/files/2402.08668.pdf)</sup> Searches organize the possibilities by generation: a first-generation leptoquark couples to electrons and first-generation quarks, and so on, while cross-generational couplings (for example to muons and bottom quarks) have drawn renewed attention because they evade the tightest indirect constraints.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> A useful organizing scheme is the leptoquark matrix of Bastian Diaz, Martin Schmaltz, and Yi-Ming Zhong, whose nine entries are the experimentally distinguishable decays of any of {light-jet, b-jet, top} with any of {neutrino, e/μ, τ}; the authors noted that three of the nine had not been adequately covered by searches.<sup>[5](https://link.springer.com/article/10.1007/JHEP10%282017%29097)</sup>

## Where leptoquarks come from theoretically

Leptoquark states are expected in various extensions of the standard model. The Pati-Salam model, formulated by [Jogesh Pati](https://www.edgepedia.org/jogesh-pati) and [Abdus Salam](https://www.edgepedia.org/abdus-salam), predicts a leptoquark state, and leptoquarks also appear in grand unification theories based on SU(5) and SO(10), the latter including Pati-Salam color SU(4).<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> The 2000 Dirac Medal of ICTP was awarded to [Howard Georgi](https://www.edgepedia.org/howard-georgi), Jogesh Pati, and Helen Quinn for contributions to the quest for a unified theory of quarks and leptons, with the award to Pati recognizing his formulation, with Salam, of the original gauge theory with quark-lepton unification.<sup>[6](https://www.ictp.it/home/dirac-medallists-2000)</sup> TeV-scale leptoquarks also modify the renormalization-group running of the standard model gauge couplings and may allow the gauge coupling unification required by grand unification.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> Scalar quarks in supersymmetric models with R-parity violation can carry leptoquark-type couplings, so leptoquark bounds also constrain those models.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup>

**Proton decay is the main hazard.** A leptoquark that also couples to two quarks (a diquark coupling) can mediate rapid proton decay unless the coupling is forbidden or the particle is very heavy.<sup>[7](https://arxiv.org/abs/hep-ph/0210187)</sup> Of the phenomenologically viable color-triplet and color-sextet scenarios, only two leptoquark models avoid tree-level proton decay while retaining the potential to explain the anomalies observed in B-meson decays.<sup>[8](https://arxiv.org/abs/1708.06350)</sup>

## Production and search strategies

At hadron colliders, leptoquarks can be produced in pairs or singly. [Pair production](https://www.edgepedia.org/pair-production) proceeds through gluon-gluon fusion and quark-antiquark annihilation and, for scalar leptoquarks, depends only on the mass, because the gauge couplings of a scalar leptoquark are fixed by its quantum numbers.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> Single production through gluon-quark fusion, g + q → LQ + ℓ, extends the mass reach to higher values but depends on the unknown [Yukawa coupling](https://www.edgepedia.org/yukawa-coupling) λ, so single-production and indirect limits are quoted in the mass-coupling plane.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup> Pair-production searches are conventionally parameterized by β, the [branching fraction](https://www.edgepedia.org/branching-fraction) into a charged lepton rather than a neutrino.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup>

For vector leptoquarks the situation is less predictive: the magnetic-dipole-type and electric-quadrupole-type interactions are not fixed by the gauge quantum numbers, so pair-production cross sections depend on additional assumptions, commonly a Yang-Mills coupling κ = 1 or a minimal-coupling case κ = 0.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup>

A recent addition is lepton-induced production. Because quantum fluctuations give protons a small charged-lepton content, a muon from one beam proton can scatter off a quark from the other, producing a resonant single leptoquark whose signature is a peak in the muon-jet invariant mass at the leptoquark mass.<sup>[9](https://cms-results.web.cern.ch/cms-results/public-results/superseded/EXO-24-005/index.html)</sup>

## Experimental limits

The HERA electron-proton experiments produced the early direct limits: for a Yukawa coupling λ = 0.3, the H1 Collaboration excluded first-generation leptoquarks with masses up to 800 GeV at 95% confidence level, and early ZEUS bounds for λ = 0.1 ranged from 248 to 290 GeV depending on the species.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup>

At the LHC, ATLAS and CMS have searched the full Run 2 dataset, about 139 fb⁻¹ at a center-of-mass energy of 13 TeV.<sup>[4](https://www.atlas.cern/Updates/Briefing/leptoquarks-thirdgeneration)</sup><sup> • </sup><sup>[9](https://cms-results.web.cern.ch/cms-results/public-results/superseded/EXO-24-005/index.html)</sup> Representative results include:

- CMS reinterpreted squark and gluino searches to constrain vector leptoquark pair production, excluding masses below 1530 GeV in the Yang-Mills case (κ = 1) or 1115 GeV in the minimal-coupling case (κ = 0), the most stringent pair-production constraint on vector leptoquarks at the time.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup>
- A CMS search for pair-produced leptoquarks decaying to a muon and a bottom quark, using boosted decision trees and deep-learning b-tagging, found no excess and excluded masses below 1810 GeV for leptoquarks decaying only to muon-bottom pairs.<sup>[10](https://cms.cern/node/2154)</sup>
- ATLAS third-generation searches set a lower limit of 1.58 TeV on the mass of a vector leptoquark with Yang-Mills couplings up to 1, extending to about 2 TeV when couplings up to 2.5 are allowed and single production contributes; a dedicated search for pair production decaying to bτ set a coupling-independent vector limit of 1.75 TeV; and scalar leptoquarks decaying exclusively to a top quark and a muon were excluded below 1.64 TeV.<sup>[4](https://www.atlas.cern/Updates/Briefing/leptoquarks-thirdgeneration)</sup>
- The first CMS search for scalar leptoquarks produced via muon-quark scattering, using 138 fb⁻¹ of 13 TeV data, excluded masses between 1.5 and 3.6 TeV with couplings between 0.2 and 0.6 for the light-quark scenario, and masses above 1.8 TeV with couplings above 1 for the heavy-quark scenario, extending the range probed by other production modes.<sup>[9](https://cms-results.web.cern.ch/cms-results/public-results/superseded/EXO-24-005/index.html)</sup>

No search has found a significant deviation from the standard model prediction.<sup>[4](https://www.atlas.cern/Updates/Briefing/leptoquarks-thirdgeneration)</sup><sup> • </sup><sup>[10](https://cms.cern/node/2154)</sup>

## Why leptoquarks remain of interest

The renewed theoretical interest comes from flavor physics. Measurements of semi-leptonic B-meson decays show the R(D) and R(D*) anomaly (measured B-meson decay rates deviating from [Standard Model](https://www.edgepedia.org/standard-model) predictions), and B-meson decays into tau leptons are measured about three standard deviations larger than into muons relative to standard model predictions; TeV-scale leptoquarks with large couplings to third-generation quarks can explain these patterns, along with hints of lepton universality violation and the muon anomalous magnetic moment.<sup>[2](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)</sup><sup> • </sup><sup>[4](https://www.atlas.cern/Updates/Briefing/leptoquarks-thirdgeneration)</sup> The vector leptoquark contained in the Pati-Salam model has been studied as a particle able to address both the b → cτν and b → sμ⁺μ⁻ data simultaneously.<sup>[11](https://arxiv.org/abs/1906.01222)</sup> Leptoquarks have also been proposed as sources of radiatively induced neutrino masses and as aids to gauge coupling unification and vacuum stability.<sup>[12](https://www.sciencedirect.com/science/article/pii/S0550321317302602)</sup>

The ATLAS results exclude part of the coupling-mass region favored by models that explain the B-anomalies, so the interplay between flavor measurements and collider limits continues to narrow the viable parameter space.<sup>[4](https://www.atlas.cern/Updates/Briefing/leptoquarks-thirdgeneration)</sup>

## References

1. [Leptoquarks, ATLAS Experiment glossary, CERN](https://atlas.cern/Glossary/leptoquarks)
2. [S. Rolli and M. Tanabashi, "Leptoquarks," Review of Particle Physics (Particle Data Group), 2024](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-leptoquark-quantum-numbers.pdf)
3. [CERN Document Server, record 2888841 (2402.08668)](https://cds.cern.ch/record/2888841/files/2402.08668.pdf)
4. [Searching from top to bottom for lepton unity, ATLAS physics briefing](https://www.atlas.cern/Updates/Briefing/leptoquarks-thirdgeneration)
5. [B. Diaz, M. Schmaltz, and Y.-M. Zhong, "The leptoquark hunter's guide: pair production," JHEP 10 (2017) 097](https://link.springer.com/article/10.1007/JHEP10%282017%29097)
6. [Dirac Medallists 2000, ICTP](https://www.ictp.it/home/dirac-medallists-2000)
7. [Proton Stability in Leptoquark Models, arXiv:hep-ph/0210187](https://arxiv.org/abs/hep-ph/0210187)
8. [Baryon Number and Lepton Universality Violation in Leptoquark and Diquark Models, arXiv:1708.06350](https://arxiv.org/abs/1708.06350)
9. [CMS-PAS-EXO-24-005: Search for scalar leptoquarks produced via muon-quark scattering in pp collisions at 13 TeV](https://cms-results.web.cern.ch/cms-results/public-results/superseded/EXO-24-005/index.html)
10. [Leptoquarks as intergenerational messengers, CMS Experiment](https://cms.cern/node/2154)
11. [Explaining the Flavor Anomalies with a Vector Leptoquark, arXiv:1906.01222](https://arxiv.org/abs/1906.01222)
12. [One leptoquark to unify them? Nuclear Physics B](https://www.sciencedirect.com/science/article/pii/S0550321317302602)

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*Topic: Encyclopedia › Physical world and mathematics › Physics › Particles and nuclei › Particle physics › Beyond-Standard-Model particle hypotheses › Heavy and weak-scale BSM particles › Leptoquarks*

*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*

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