Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields



Leptoquarks is the name given to hypothetical fundamental particles which combine the properties of both quarks and leptons from the standard model of particle physics.

They naturally arise in grand unified theories (e.g. Murayama-Yanagida 92, also AFG 17, III.A)


Experimental hints

The existence of leptoquarks could potentially explain both

  1. the apparently observed flavour anomalies

    (Bauer-Neubert 16, CCDM 16, CCL 17, Crivellin 17 Falkowski17, Müeller 18, Matsuzaki-Nishiwaki 18, Monteux-Rajaraman 18, AMST 18, BDFKFS 18, Crivellin 18, MMR 18, Blanke-Crivellin 18, Kumar-London 19, section 2.2.1, MVT 19, MVK 19, Cata-Mannel 19)

  2. the apparently observed anomaly in the anomalous magnetic moments of the muon and also of the electron (CCDM 16, Müller 18)

From Crivellin 18, p. 2:

the global fit [[ to flavour anomalies ]] even shows compelling evidence for New Physics [[]] The vector leptoquark (LQ) SU(2) LSU(2)_L singlet with hypercharge 4/3-4/3 arising in the famous Pati-Salam model is capable of explaining all the [[flavour ]] anomalies and therefore several attempts to construct a UV completion for this LQ to address the anomalies have been made. It can give a sizeable effect in bc(u)τνb \to c(u)\tau \nu data without violating bounds from bs(d)νν¯b \to s(d)\nu \bar \nu and/or direct searches, provides (at tree level) a C 9=C 10C_9 = - C_{10} solution to bs + b \to s \ell^+ \ell^- data and does not lead to proton decay at any order in perturbation theory.

Experimental constraints

Constraints on the possible parameter space for leptoquarks from LHC data (BGGSS 18, BSS 18, ATLAS 19)

Theoretical conceptualization

Leptoquarks naturally arise in grand unified theories (…, Murayama-Yanagida 92, BDFKFS 18)



  • Nima Assad, Bartosz Fornal, Benjamin Grinstein, Baryon Number and Lepton Universality Violation in Leptoquark and Diquark Models, Phys. Lett. B777 (2018) 324-331 (arXiv:1708.06350)

  • Achintya Rao, The hunt for leptoquarks is on, 2018

Leptoquark effective field theory:

  • Valerio Gherardi, David Marzocca, Elena Venturini, Matching scalar leptoquarks to the SMEFT at one loop (arXiv:2003.12525)

  • Andreas Crivellin, Christoph Greub, Dario Müller, Francesco Saturnino, Scalar Leptoquarks in Leptonic Processes (arXiv:2010.06593)

See also


Constraints from experiment (LHC):

  • I. Doršner, S. Fajfer, A. Greljo, J. F. Kamenik, N. Košnik, Physics of leptoquarks in precision experiments and at particle colliders, Physics Reports Volume 641, 17 June 2016, Pages 1-68 (arXiv:1603.04993)

  • M. Tanabashi et al. (Particle Data Group), 115. Leptoquarks Phys. Rev. D 98, 030001 (2018) (pdf)

  • CMS Collaboration, Search for third-generation scalar leptoquarks decaying to a top quark and a τ\tau lepton at s=13\sqrt{s} = 13 TeV, Eur. Phys. J. C 78 (2018) 707 (arXiv:1803.02864)

  • Andrei Angelescu, Damir Bečirević, Darius A. Faroughy, Olcyr Sumensari, Closing the window on single leptoquark solutions to the BB-physics anomalies, JHEP10(2018)183 (arXiv:1808.08179)

  • Aritra Biswas, Dilip Kumar Ghosh, Nivedita Ghosh, Avirup Shaw, Abhaya Kumar Swain, Novel collider signature of U 1U_1 Leptoquark and BπB \to \pi observables (arXiv:1808.04169)

  • Aritra Biswas, Avirup Shaw, Abhaya Kumar Swain, Collider signature of V 2V_2 Leptoquark with bsb \to s flavour observables (arXiv:1811.08887)

  • Salvatore Rappoccio, section 6 of The experimental status of direct searches for exotic physics beyond the standard model at the Large Hadron Collider, Reviews in Physics 4 (2019) 100027 (arXiv:1810.10579)

  • ATLAS collaboration, Searches for scalar leptoquarks and differential cross-section measurements in dilepton-dijet events in proton-proton collisions at a centre-of-mass energy of s√ = 13 TeV with the ATLAS experiment (arXiv:1902.00377)

  • ZEUS Collaboration, Limits on contact interactions and leptoquarks at HERA (arXiv:1902.03048)

Alternative detection channel:

  • Priyotosh Bandyopadhyay, Saunak Dutta, Anirban Karan, Investigating the Production of Leptoquarks by Means of Zeros of Amplitude at Photon Electron Collider (arXiv:2003.11751)

Relation to flavour anomalies

As a potential solution of the apparent B meson flavour anomaly:

  • Martin Bauer, Matthias Neubert, One Leptoquark to Rule Them All: A Minimal Explanation for R D (*)R_{D^{(\ast)}}, R KR_K and (g2) μ(g-2)_\mu, Phys. Rev. Lett. 116, 141802 (2016) (arXiv:1511.01900)

  • Estefania Coluccio Leskow, Andreas Crivellin, Giancarlo D’Ambrosio, Dario Müller, (g2) μ(g-2)_\mu, Lepton Flavour Violation and Z Decays with Leptoquarks: Correlations and Future Prospects, Phys. Rev. D 95, 055018 (2017) (arXiv:1612.06858)

  • Yi Cai, John Gargalionis, Michael A. Schmidt, Raymond R. Volkas, Reconsidering the One Leptoquark solution: flavor anomalies and neutrino mass (arXiv:1704.05849)

  • Lorenzo Calibbi, Andreas Crivellin, Tianjun Li, A model of vector leptoquarks in view of the BB-physics anomalies, Phys. Rev. D 98, 115002 (2018) (arXiv:1709.00692)

  • Andreas Crivellin, New Physics in Flavour Observables (arXiv:1706.00929)

  • Adam Falkowski, Leptoquarks strike back, November 2017

  • Dario Müller, Leptoquarks in Flavour Physics, EPJ Web of Conferences 179, 01015 (2018) (arXiv:1801.03380)

  • Shinya Matsuzaki, Kenji Nishiwaki, Kei Yamamoto, Simultaneous interpretation of K and B anomalies in terms of chiral-flavorful vectors (arXiv:1806.02312)

  • Angelo Monteux, Arvind Rajaraman, B Anomalies and Leptoquarks at the LHC: Beyond the Lepton-Quark Final State, Phys. Rev. D 98, 115032 (2018) (arXiv:1803.05962)

  • Ufuk Aydemir, Djordje Minic, Chen Sun, Tatsu Takeuchi, BB-decay anomalies and scalar leptoquarks in unified Pati-Salam models from noncommutative geometry, JHEP 09 (2018) 117 (arXiv:1804.05844)

  • Damir Bečirević, Ilja Doršner, Svjetlana Fajfer, Nejc Košnik, Darius A. Faroughy, Olcyr Sumensari, Scalar leptoquarks from GUT to accommodate the BB-physics anomalies, Phys. Rev. D 98, 055003 (2018) (arXiv:1806.05689)

  • Tanumoy Mandal, Subhadip Mitra, Swapnil Raz, R D (*)R_{D^{(\ast)}} in minimal leptoquark scenarios: impact of interference on the exclusion limits from LHC data (arXiv:1811.03561)

  • Jason Aebischer, Andreas Crivellin, Christoph Greub, QCD Improved Matching for Semi-Leptonic B Decays with Leptoquarks (arXiv:1811.08907)

  • Jacky Kumar, David London, New physics in bse +e b \to s e^+ e^-? (arXiv:1901.04516)

  • Ivo de Medeiros Varzielas, Jim Talbert, Simplified Models of Flavourful Leptoquarks (arXiv:1901.10484)

  • Michael J. Baker, Javier Fuentes-Martin, Gino Isidori, Matthias König, High-pT Signatures in Vector-Leptoquark Models (arXiv:1901.10480)

  • Natascia Vignaroli, Seeking leptoquarks in the tt¯t \bar t plus missing energy channel at the high-luminosity LHC (arXiv:1808.10309)

  • Ufuk Aydemir, Tanumoy Mandal, Subhadip Mitra, A single TeV-scale scalar leptoquark in SO(10) grand unification and B-decay anomalies (arXiv:1902.08108)

  • Ivo de Medeiros Varzielas, Stephen F. King, Origin of Yukawa couplings for Higgs and leptoquarks (arXiv:1902.09266)

  • Oscar Cata, Thomas Mannel, Linking lepton number violation with BB anomalies (arXiv:1903.01799)

  • Bhubanjyoti Bhattacharya, Alakabha Datta, Saeed Kamali, David London, CP Violation in B¯ 0D *+μ ν¯ μ\bar B^0 \to D^{\ast +} \mu^- \bar \nu_\mu, (arXiv:1903.02567)

  • Han Yan, Ya-Dong Yang, Xing-Bo Yuan, Phenomenology of bcτν¯b \to c \tau \bar \nu decays in a scalar leptoquark model (arXiv:1905.01795)

  • Alakabha Datta, Divya Sachdeva, John Waite, A unified explanation of bsμ =μ b \to s\mu^= \mu^- anomalies, neutrino masses and BπKB \to \pi K puzzle (arXiv:1905.04046)

  • Andrei Angelescu, Single Leptoquark Solutions to the BB-physics Anomalies, contribution to the 2019 EW session of the 54th Rencontres de Moriond (arXiv:1905.06044)

  • Andreas Crivellin, Francesco Saturnino, Explaining the Flavor Anomalies with a Vector Leptoquark (Moriond 2019 update) (arXiv:1906.01222)

  • Innes Bigaran, John Gargalionis, Raymond R. Volkas, A near-minimal leptoquark model for reconciling flavour anomalies and generating radiative neutrino masses (arXiv:1906.01870)

  • Javier Fuentes-Martin, Gino Isidori, Matthias König, Nudzeim Selimovic, Vector Leptoquarks Beyond Tree Level (arxiv:1910.13474)

within GUT-models and specifically within Pati-Salam models:

  • Julian Heeck, Daniele Teresi, Pati-Salam explanations of the B-meson anomalies, JHEP 12 (2018) 103 (arXiv:1808.07492)

  • Julian Heeck, Daniele Teresi, Pati-Salam and lepton universality in B decays (arXiv:1905.05211)

  • Oleg Popov, Michael A. Schmidt, Graham White, R 2R_2 as a single leptoquark solution to R D (*)R_{D^{(\ast)}} and R K (*)R_{K^{(\ast)}} (arXiv:1905.06339)

  • Andreas Crivellin, Francesco Saturnino, Correlating Tauonic B Decays to the Neutron EDM via a Scalar Leptoquark (arXiv:1905.08257)

  • Michal Malinský, Lepton non-universality in BB-decays in the minimal leptoquark gauge model (arXiv:1906.09174)

  • Jordan Bernigaud, Ivo de Medeiros Varzielas, Jim Talbert, Finite Family Groups for Fermionic and Leptoquark Mixing Patterns (arXiv:1906.11270)

  • Junichiro Kawamura, Stuart Raby, Andreas Trautner, Complete Vector-like Fourth Family and new U(1)U(1)' for Muon Anomalies (arXiv:1906.11297)

  • Leandro Da Rold, Federico Lamagna, A vector leptoquark for the B-physics anomalies from a composite GUT (arXiv:1906.11666)

  • C. Hati, J. Kriewald, J. Orloff, A.M. Teixeira, A nonunitary interpretation for a single vector leptoquark combined explanation to the B-decay anomalies (arXiv:1907.05511)

  • Shyam Balaji, Michael A. Schmidt, A unified SU(4)SU(4) theory for the R D (*)R_D^{(\ast)} and R K (*)R_K^{(\ast)} anomalies (arXiv:1911.08873)

  • Shaikh Saad, Anil Thapa, A Common Origin of Neutrino Masses and R D *R_{D^\ast}, R K *R_{K^\ast} Anomalies (arXiv:2004.07880)

  • P. S. Bhupal Dev, Rukmani Mohanta, Sudhanwa Patra, Suchismita Sahoo, Unified explanation of flavor anomalies, radiative neutrino mass and ANITA anomalous events in a vector leptoquark model (arXiv:2004.09464)

  • Suman Kumbhakar, Rukmani Mohanta, Investigating the effect of U 1U_1 vector leptoquark on buτν¯b \to u \tau \bar\nu mediated B decays (arXiv:2008.04016)

  • Valerio Gherardi, David Marzocca, Elena Venturini, Low-energy phenomenology of scalar leptoquarks at one-loop accuracy (arXiv:2008.09548)

  • Andreas Crivellin, Dario Mueller, Francesco Saturnino, Leptoquarks in Oblique Corrections and Higgs Signal Strength: Status and Prospects (arXiv:2006.10758)

  • Marco Ciuchini, Marco Fedele, Enrico Franco, Ayan Paul, Luca Silvestrini, Mauro Valli, Lessons from the B 0,+B *,0,+μ +μ B^{0,+} \to B^{\ast, 0,+} \mu^+ \mu^- angular analysis (arXiv:2011.01212)

In the Standard Model Effective Theory (SMEFT) [41, 42], the significance of NewPhysics from the global bs + b \to s \ell^+ \ell^- analysis increases with the inclusion of new data, reaching a maximum of almost 6σ for the simple hypothesis of a non-vanishing [[leptoquark contribution]].

and within Randall-Sundrum models

and as a possible explanation also of the anomalies seen at the ANITA experiment:

  • Bhavesh Chauhan, Subhendra Mohanty, A common leptoquark solution of flavor and ANITA anomalies (arXiv:1812.00919)

Appearance in GUTs

Appearance in GUT-theories:

Last revised on November 3, 2020 at 04:25:55. See the history of this page for a list of all contributions to it.