flavour anomaly



Fields and quanta


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



In the current standard model of particle physics the fundamental particles in the three generations of fermions have identical properties from one generation to the next, except for their mass, a state of affairs referred to as lepton universality. A possible violation of lepton universality is called a flavor anomaly, which would be a sign of “New Physics” (NP) beyond the standard model.

graphics grabbed from Cartelle 18

Statistical significance

Indications of flavour anomalies have been observed consistently and with increasing statistical significance around 33 σ in B meson processes in various experiments such as at the LHC, specifically at the LHCb, the Belle experiment and the BaBar experiment (see references below).

The global tension with the standard model by end of 2018 has statistical significance around 4.14.1 σ (Strumia et al. 17, Cartelle 18, slide 22/25, Dey 18, slide 16/23, HAMN 18, p. 4). Various authors see the global tension (i.e. of all decay channels jointly) at over 5σ5 \sigma already (CCDGMV 17, CFMVV 17 CGMS 18, Dordei 18, slide 12), which traditionally qualifies as detection (see here), some authors already quote 5.3σ5.8σ5.3 \sigma - 5.8 \sigma (ACDGMM 19) or 6σ6 \sigma (Kumar-London 19).

graphics grabbed from Dey 18

If the ongoing evaluation of the data of LHC‘s Run 2 confirms the measurements of Run 1, then the statistical significance of the effect in each decay channel separately should have reached 5 σ (Crivellin et. al 18, p. 12) and hence conventionally count as detection of flavour anomaly (see here), which would make it the first established “new physics” seen at the LHC.

Moreover, it had been argued (Lyons 13b, Dorigo 15) that due to the specific nature of the experiment, the statistical significance-threshold for detection of anomalies in B meson-decays should not be taken to be 5σ5 \sigma, but just 3σ3 \sigma, hence well exceeded already by the experimental significance:

table taken from Lyons 13b, p. 4

table taken from Dorigo 15, p. 16

In conclusion, with currently available data, the observed flavour anomalies are possible signs of New Physics beyond the current standard model of particle physics.

graphics taken from Dordei 18, slide 22

In any case, further and more sensitive experiments are needed to confirm and explore the effect, such as possibly the “HL-LHC” or “HE-LHC” experiment. General outlook, prospects and suggestions for future collider design in this respect are discussed in detail in Allanach-Gripaios-You 17, Crivellin et al. 18.

Possible models

Candidate models of “New Physics” beyond the standard model of particle physics that could possibly explain the flavour anomalies (if indeed they are real) includes the following:


One apparently promising model that could potentially explain the apparently observed flavour anomalies are leptoquarks, which naturally arise in, and hence potentially point to, models of SU(5)SU(5)-grand unified theory.

(see Bauer-Neubert 15, CCDM 16, Crivellin 17, Falkowski17, Mueller 18, Matsuzaki-Nishiwaki 18, Monteux-Rajaraman 18, AMST 18, BDFKFS 18, Crivellin 18, MMR 18, Kumar-London 19, section 2.2.1, MVT 19)

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.

Incidentally, leptoquarks are also a candidate explanation of the anomaly seen at over 4σ\sigma statistical significance in the anomalous magnetic moment of the muon, see there.

(Blanke Crivellin 18, Crivellin 18)


Other possible models besides leptoquarks (above) which have been proposed as possible explanations of the apparently observed flavour anomalies include the following:



Measurements include

  • LHCb collaboration, Differential branching fractions and isospin asymmetries of BK (*)μ +μ B \to K^{(\ast)}\mu^+ \mu^- decays, JHEP 06 (2014) 133 (arXiv:1403.8044)

  • LHCb collaboration, Test of lepton universality using B +K + + B^+\to K^+ \ell^+ \ell^- decays, Phys. Rev. Lett. 113, 151601 (2014) (arXiv:1406.6482)

  • LHCb collaboration, Angular analysis and differential branching fraction of the decay B s 0ϕμ +μ B^0_s \to \phi \mu^+ \mu^-, JHEP09(2015)179 (arXivL1506.08777)

  • LHCb collaboration, Differential branching fraction and angular analysis of Λ b 0Λμ +μ \Lambda^0_b \to \Lambda \mu^+ \mu^- decays, JHEP 06 (2015) 115; JHEP 09 (2018) 145 (arXiv:1503.07138)

  • LHCb collaboration, Test of lepton universality using B 0K *0 + B^0\to K^{\ast 0} \ell^+ \ell^- decays, JHEP 08 (2017) 055 (arXiv:1705.05802)

Review includes


Emphasis of non-perturbative effects:

  • Ulrich Nierste, Flavour Anomalies: Phenomenology and BSM Interpretations, talk at Planck 2018, Bonn 2018 (pdf)

  • Saeed Kamali, New physics in inclusive semileptonic BB decays including nonperturbative corrections (arXiv:1811.07393)

Emphasis of higher loop order-effects:

  • Andreas Crivellin, Christoph Greub, Dario Müller, Francesco Saturnino, Importance of Loop Effects in Explaining the Accumulated Evidence for New Physics in B Decays with a Vector Leptoquark, Phys. Rev. Lett. 122, 011805 (2019) (arXiv:1807.02068)

See also

Original articles include:

  • Guido D’Amico, Marco Nardecchia, Paolo Panci, Francesco Sannino, Alessandro Strumia, Riccardo Torre, Alfredo Urbano,

    Flavour anomalies after the R K *R_{K^\ast} measurement,

    J. High Energ. Phys. (2017) 2017 (arXiv:1704.05438)

  • Andrea Mauri, Nicola Serra, Rafael Silva Coutinho, Towards establishing Lepton Flavour Universality violation in B¯K¯ * + \bar B \to \bar K^\ast \ell^+ \ell^- decays (arXiv:1805.06401)

  • Bernat Capdevila, Andreas Crivellin, Sébastien Descotes-Genon, Joaquim Matias, Javier Virto, Patterns of New Physics in bs + b \to s \ell^+ \ell^- transitions in the light of recent data, JHEP 1801 (2018) 093 (arXiv:1704.05340)

  • Alejandro Celis, Javier Fuentes-Martin, Avelino Vicente, Javier Virto, Gauge-invariant implications of the LHCb measurements on Lepton-Flavour Non-Universality, Phys. Rev. D 96, 035026 (2017) (arXiv:1704.05672)

  • Monika Blanke, Andreas Crivellin, Stefan de Boer, Teppei Kitahara, Marta Moscati, Ulrich Nierste, Ivan Nišandžić, Impact of polarization observables and B cτνB_c \to \tau \nu on new physics explanations of the bcτνb \to c \tau \nu anomaly (arXiv:1811.09603)

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

  • Domagoj Leljak, Blazenka Melic, Monalisa Patra, On lepton flavour universality in semileptonic B cη c,J/ψB_c \to \eta_c, J/\psi decays (arXiv:1901.08368)

Cautionary remarks include

In contrast, an argument that the threshold statistical significance for flavour anomalies should be taken to be 3σ3\sigma instead of 5σ5 \sigma is made in

Possible explanations/models

General EFT [parameterization]

  • T. Hurth, A. Arbey, F. Mahmoudi, S. Neshatpour, New global fits to bsb \to s data with all relevant parameters, Proceedings of the Seventh Workshop on Theory, Phenomenology and Experiments in Flavour Physics, Capri, 8-10 June 2018 (arXiv:1812.07602)

  • Srimoy Bhattacharya, Aritra Biswas, Zaineb Calcuttawala, Sunando Kumar Patra, An in-depth analysis of bc(s)b \to c(s) semileptonic observables with possible μτ\mu \to \tau mixing (arXiv:1902.02796)

  • Marcel Algueró, Bernat Capdevila, Sébastien Descotes-Genon, Pere Masjuan, Joaquim Matias, What R KR_K and Q 5Q_5 can tell us about New Physics in bsb \to s \ell \ell transitions? (arXiv:1902.04900)


Attempts to explain the anomaly include


  • 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)

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

  • 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)

  • 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)

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

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

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

leptoquarks within a Randall-Sundrum model:

and as possible explanation also of the anomalies seen in the ANITA experiment

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


composite Higgs boson:

  • David Marzocca, Addressing the B-physics anomalies in a fundamental Composite Higgs Model, JHEP07(2018)121 (arXiv:1803.10972)

dark matter:

  • Seungwon Baek, Scalar dark matter behind bsμμb \to s \mu \mu anomaly (arXiv:1901.04761)

  • D.G. Cerdeno, A. Cheek, P. Martin-Ramiro, J.M. Moreno, B anomalies and dark matter: a complex connection (arXiv:1902.01789)

right-handed neutrino:

  • Carlo Marzo, Luca Marzola, Martti Raidal, Common explanation to the R K (*)R_{K^{(\ast)}}, R K (*)R_{K^{(\ast)}} and ϵ/ϵ\epsilon'/\epsilon anomalies in a 3HDM+ν R\nu_R and connections to neutrino physics (arXiv:1901.08290)


  • Rhorry Gauld, Florian Goertz, Ulrich Haisch, An explicit Z’-boson explanation of the BK *μ +μ B \to K^\ast \mu^+ \mu^- anomaly, JHEP01(2014)069 (arXiv:1310.1082)

  • G. D’Ambrosio, A. M. Iyer, F. Piccinini, A.D. Polosa, Confronting BB anomalies with atomic physics (arXiv:1902.00893)

Last revised on February 14, 2019 at 02:01:52. See the history of this page for a list of all contributions to it.