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 flavour 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 2.532.5-3 σ in B meson processes in various channels by a number of independent experiments: the LHCb experiment, the Belle experiment and the BaBar experiment:

table grabbed from BGV 19

The global (all channels and experiments combined) tension with the standard model by end of 2018 had 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, Bouchard-Cao-Owen 19). Various authors see the global tension (i.e. of all decay channels jointly) at over 5σ5 \sigma (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

This situation was confirmed with the completed measurements presented at Moriond 2019, which showed (Straub 19, Allanach 19) smaller discrepancy but also with smaller uncertainty, thus keeping the statistical significance essentially unaffected. On the other hand, Caria 19, slide 9 reported an as yet unpublished measurement by the Belle collaboration by which the previous statistical significance of 3.8σ3.8 \sigma in the R DR_D sector would decrease to 3.1σ3.1 \sigma or 2.8σ2.8 \sigma (Gambino-Jung-Schacht 19 (6)). Comprehensive assessments of the situation after Moriond 2019 are given in AHMSN 19, Descotes-Genon 19, Bardhan-Ghosh 19 and agree that the flavour anomalies have been confirmed:

It appears the reason is that, given the amount of independent measurements (~180!) a smaller deviation because of new physics is easier to accommodate than a large one. Thus the new measurements actually fit better with new physics.

(Axel Maas, reporting from ALPS2019, tweet, 23 Apr 2019)

graphics grabbed from Zupan 19

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, Zupan 19, 4.6) and hence conventionally count as detection of flavour anomaly (see here), which would make it the first established “new physics” seen at the LHC.

In fact, it had been argued prior to the detection of the anomalies (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 experimentally seen statistical significance:

table taken from Lyons 13b, p. 4

table taken from Dorigo 15, p. 16

This attitude is reflected in SGGJC 19, p. 2:

For some time now, the ratios of semileptonicB-decay rates have appeared to be enhanced with respect to the Standard Model (SM) predictions with a global significance above the evidence threshold.

Status and Outlook

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.

From Isodori 19, slide 6:

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:

Leptoquarks and Grand unified theory

One promising model that could potentially explain the apparently observed flavour anomalies are leptoquarks, which naturally arise in, and hence potentially point to, grand unified theory models, such as notably the Pati-Salam model (Heek-Teresi 18, Heek-Teresi 19)

(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, AMM 19, MVK 19, Cata-Mannel 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.

(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:

Relation to other anomalies

There is possibly a relation between the flavour anomalies an the anomaliesagnetic moment#Anomalies) observed in the anomalous magnetic moment of the electron and/or the muon (e.g. Chiang-Okada 17)

Indeed, leptoquark models preferred by the flavour anomalies 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.



Early suggestion to look for relevant channels are due to

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)

  • LHCb collaboration, Measurement of the ratio of the B 0D *τ +vu τB^0 \to D^{\ast -} \tau^+ \vu_\tau and B 0D *μ +ν μB^0 \to D^{\ast - \mu^+ \nu_\mu} branching fractions using three-prong τ-lepton decays (arXiv:1708.08856)

  • Belle collaboration, Measurement of the τ\tau lepton polarization and R(D *)R(D^\ast) in the decay B¯D *τ ν¯ τ\bar B \to D^\ast \tau^- \bar \nu_\tau with one-prong hadronic τ decays at Belle (arXiv:1709.00129)

  • Belle collaboration, Measurement of the D *D^{\ast -} polarization in the decay B 0D *τ +ν τB^0 \to D^{\ast -} \tau^+ \nu_\tau (arXiv:1903.03102)

  • LHCb collaboration, Search for lepton-universality violation in B +K + + B^+ \to K^+ \ell^+ \ell^- decays (cern:2668514)

  • Belle Collaboration, Test of lepton flavor universality in BK * + B \to K^\ast \ell^+ \ell^- decays at Belle (arXiv:1904.02440)

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)

  • Monika Blanke, Andreas Crivellin, Stefan de Boer, Teppei Kitahara, Marta Moscati, Ulrich Nierste, Ivan Nišandžić, Addendum: “Impact of polarization observables and B cτνB_c \to \tau \nu on new physics explanations of the bcτνb \to c \tau \nu anomaly” (arXiv:1905.08253)

  • 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)

  • Rui-Xiang Shi, Li-Sheng Geng, Benjamín Grinstein, Sebastian Jäger, Jorge Martin Camalich, Revisiting the new-physics interpretation of the bcτνb \to c \tau \nu data (arXiv:1905.08498)

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)

  • Marcel Algueró, Bernat Capdevila, Andreas Crivellin, Sébastien Descotes-Genon, Pere Masjuan, Joaquim Matias, Javier Virto, Addendum: “Patterns of New Physics in bs + b \to s \ell^+ \ell^- transitions in the light of recent data” (arXiv:1903.09578)

  • Ashutosh Kumar Alok, Amol Dighe, Shireen Gangal, Dinesh Kumar, Continuing search for new physics in bμssb \to \mu s s decays: two operators at a time (arXiv:1903.09617)

  • Marco Ciuchini, António M. Coutinho, Marco Fedele, Enrico Franco, Ayan Paul, Luca Silvestrini, Mauro Valli, New Physics in bs + b \to s \ell^+ \ell^- confronts new data on Lepton Universality (arXiv:1903.09632)

  • Jason Aebischer, Wolfgang Altmannshofer, Diego Guadagnoli, Meril Reboud, Peter Stangl, David M. Straub, B-decay discrepancies after Moriond 2019 (arXiv:1903.10434)

  • Alakabha Datta, Jacky Kumar, David London, The BB Anomalies and New Physics in bse +e b \to s e^+ e^- (arXiv:1903.10086)

  • Ashutosh Kumar Alok, Dinesh Kumar, Suman Kumbhakar, S Uma Sankar, Impact of D *D^\ast polarization measurement on solutions to R DR_D-R D *R_{D^\ast} anomalies (arXiv:1903.10486)

  • Pere Arnan, Andreas Crivellin, Marco Fedele, Federico Mescia, Generic Loop Effects of New Scalars and Fermions in bs + b \to s \ell^+ \ell^- and a Vector-like 4th Generation (arXiv:1904.05890)

  • A. Arbey, T. Hurth, F. Mahmoudi, D. Martinez Santos, S. Neshatpour, Update on the bsb \to s anomalies (arXiv:1904.08399)

  • Pouya Asadi, David Shih, Maximizing the Impact of New Physics in bcτνb \to c \tau \nu Anomalies, (arXiv:1905.03311)

  • J. E. Chavez-Saab, Marxil Sánchez, Genaro Toledo, R D *R_{D^\ast} or R D πR_{D_\pi}: closing the theoretical gap? (arXiv:1905.03394)

  • Suman Kumbhakar, Ashutosh Kumar Alok, Dinesh Kumar, S Uma Sankar, Resolving R DR_D and R D *R_{D^\ast} anomalies (arXiv:1905.03513)

  • Jyoti Saini, Dinesh Kumar, Shireen Gangal, S. B. Dasm, Probing signatures of beyond standard model physics through B s *μ +μ B_s^\ast \to \mu^+ \mu^- decay (arXiv:1905.03933)

  • David London, CP Violation in B¯ 0D *+ ν¯ \bar B^0 \to D^{\ast +} \ell^- \bar \nu_\ell (arXiv:1906.07752)

  • Marta Moscati, New Physics in bcτνb \to c \tau \nu: Impact of Polarisation Observables and B cτνB_c \to \tau \nu (arXiv:1906.08035)


explanation via assumption of leptoquarks:

  • 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)

  • 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)

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

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

leptoquarks within a Randall-Sundrum model:

leptoquarks particularly as fields in a grand unified theory:

  • 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)

leptoquarks 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)


explanations via ssumption of Z'-bosons:

  • 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)

  • P. Ko, Takaaki Nomura, Chaehyun Yu, bsμ +μ b \to s \mu^+ \mu^- anomalies and related phenomenology in U(1) B 3x μL μx τL τU(1)_{B_{3-x_\mu L_\mu - x_\tau L_\tau}} flavor gauge models (arXiv:1902.06107)

  • Joe Davighi, Connecting neutral current BB anomalies with the heaviness of the third family, Contribution to the 2019 QCD session of the 54th Rencontres de Moriond (arXiv:1905.06073)


composite Higgs boson:

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

  • Andreas Crivellin, Dario Müller, Christoph Wiegand, bs + b \to s \ell^+ \ell^- Transitions in Two-Higgs-Doublet Models (arXiv:1903.10440)

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)

  • Anirban Biswas, Avirup Shaw, Reconciling dark matter, R K (*)R_{K^{(\ast)}} anomalies and (g2) μ(g-2)_\mu in an L μL τL_\mu-L_\tau scenario (arXiv:1903.08745)

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)

  • Luigi Delle Rose, Shaaban Khalil, Simon J.D. King, Stefano Moretti, R KR_K and R K *R_{K^\ast} in an Aligned 2HDM with Right-Handed Neutrinos (arXiv:1903.11146)

MSSM with R-parity-violation

  • Dong-Yang Wang, Ya-Dong Yang, Xing-Bo Yuan, bcτν¯b \to c \tau \bar \nu decays in supersymmetry with R-parity violation (arXiv:1905.08784)

Horava-Witten theory-type KK-compactification:

  • Jong-Phil Lee, BB anomalies in the nonminimal universal extra dimension model (arXiv:1906.07345)

Joint explanation with the anomaliesagnetic moment#Anomalies) observed in the muon anomalous magnetic moment:

  • Cheng-Wei Chiang, Hiroshi Okada, A simple model for explaining muon-related anomalies and dark matter (arXiv:1711.07365)

Last revised on June 24, 2019 at 02:56:12. See the history of this page for a list of all contributions to it.