Abstract
We present a model to explain LHCb’s recent measurements of RK and \( {R}_{K^{\left(\ast \right)}} \) based on an anomaly-free, spontaneously-broken U(1)F gauge symmetry, without any fermionic fields beyond those of the Standard Model (SM). The model explains the hierarchical heaviness of the third family and the smallness of quark mixing. The U(1)F charges of the third family of SM fields and the Higgs doublet are set equal to their respective hypercharges. A heavy Z′ particle with flavour-dependent couplings can modify the \( \left[\overline{b_L}{\gamma}^{\rho }{s}_L\right]\left[\overline{\mu_L}{\gamma}_{\rho }{\mu}_L\right] \) effective vertex in the desired way. The Z′ contribution to \( {B}_s-\overline{B_s} \) mixing is suppressed by a small mixing angle connected to Vts, making the constraint coming from its measurement easier to satisfy. The model can explain RK and \( {R}_{K^{*}} \) whilst simultaneously passing other constraints, including measurements of the lepton flavour universality of Z couplings.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
LHCb collaboration, Test of lepton universality using B + → K + ℓ + ℓ − decays, Phys. Rev. Lett. 113 (2014) 151601 [arXiv:1406.6482] [INSPIRE].
LHCb collaboration, Test of lepton universality with B 0 → K *0 ℓ + ℓ − decays, JHEP 08 (2017) 055 [arXiv:1705.05802] [INSPIRE].
G. Hiller and F. Krüger, More model-independent analysis of b → s processes, Phys. Rev. D 69 (2004) 074020 [hep-ph/0310219] [INSPIRE].
G. D’Amico, M. Nardecchia, P. Panci, F. Sannino, A. Strumia, R. Torre et al., Flavour anomalies after the \( {R}_{K^{*}} \) measurement, JHEP 09 (2017) 010 [arXiv:1704.05438] [INSPIRE].
B. Gripaios, M. Nardecchia and S.A. Renner, Linear flavour violation and anomalies in B physics, JHEP 06 (2016) 083 [arXiv:1509.05020] [INSPIRE].
A. Carmona and F. Goertz, Lepton Flavor and Nonuniversality from Minimal Composite Higgs Setups, Phys. Rev. Lett. 116 (2016) 251801 [arXiv:1510.07658] [INSPIRE].
A. Carmona and F. Goertz, Recent B physics anomalies: a first hint for compositeness?, Eur. Phys. J. C 78 (2018) 979 [arXiv:1712.02536] [INSPIRE].
B. Gripaios, M. Nardecchia and S.A. Renner, Composite leptoquarks and anomalies in B-meson decays, JHEP 05 (2015) 006 [arXiv:1412.1791] [INSPIRE].
I. Garcia Garcia, LHCb anomalies from a natural perspective, JHEP 03 (2017) 040 [arXiv:1611.03507] [INSPIRE].
M. Carena, E. Megías, M. Quíros and C. Wagner, \( {R}_{D^{\left(\ast \right)}} \) in custodial warped space, arXiv:1809.01107 [INSPIRE].
R. Gauld, F. Goertz and U. Haisch, On minimal Z′ explanations of the B → K * μ + μ − anomaly, Phys. Rev. D 89 (2014) 015005 [arXiv:1308.1959] [INSPIRE].
A.J. Buras, F. De Fazio and J. Girrbach, 331 models facing new b → sμ + μ − data, JHEP 02 (2014) 112 [arXiv:1311.6729] [INSPIRE].
A.J. Buras and J. Girrbach, Left-handed Z′ and Z FCNC quark couplings facing new b → sμ + μ − data, JHEP 12 (2013) 009 [arXiv:1309.2466] [INSPIRE].
W. Altmannshofer, S. Gori, M. Pospelov and I. Yavin, Quark flavor transitions in L μ − L τ models, Phys. Rev. D 89 (2014) 095033 [arXiv:1403.1269] [INSPIRE].
A.J. Buras, F. De Fazio and J. Girrbach-Noe, Z-Z′ mixing and Z-mediated FCNCs in SU(3)C × SU(3)L × U(1)X models, JHEP 08 (2014) 039 [arXiv:1405.3850] [INSPIRE].
A. Crivellin, G. D’Ambrosio and J. Heeck, Explaining h → μ ± τ ∓ , B → K * μ + μ − and B → Kμ + μ − /B → Ke + e − in a two-Higgs-doublet model with gauged L μ − L τ, Phys. Rev. Lett. 114 (2015) 151801 [arXiv:1501.00993] [INSPIRE].
A. Crivellin, G. D’Ambrosio and J. Heeck, Addressing the LHC flavor anomalies with horizontal gauge symmetries, Phys. Rev. D 91 (2015) 075006 [arXiv:1503.03477] [INSPIRE].
D. Aristizabal Sierra, F. Staub and A. Vicente, Shedding light on the b → s anomalies with a dark sector, Phys. Rev. D 92 (2015) 015001 [arXiv:1503.06077] [INSPIRE].
A. Crivellin, L. Hofer, J. Matias, U. Nierste, S. Pokorski and J. Rosiek, Lepton-flavour violating B decays in generic Z′ models, Phys. Rev. D 92 (2015) 054013 [arXiv:1504.07928] [INSPIRE].
A. Celis, J. Fuentes-Martin, M. Jung and H. Serodio, Family nonuniversal Z′ models with protected flavor-changing interactions, Phys. Rev. D 92 (2015) 015007 [arXiv:1505.03079] [INSPIRE].
A. Greljo, G. Isidori and D. Marzocca, On the breaking of Lepton Flavor Universality in B decays, JHEP 07 (2015) 142 [arXiv:1506.01705] [INSPIRE].
W. Altmannshofer and I. Yavin, Predictions for lepton flavor universality violation in rare B decays in models with gauged L μ − L τ, Phys. Rev. D 92 (2015) 075022 [arXiv:1508.07009] [INSPIRE].
B. Allanach, F.S. Queiroz, A. Strumia and S. Sun, Z′ models for the LHCb and g − 2 muon anomalies, Phys. Rev. D 93 (2016) 055045 [Erratum ibid. D 95 (2017) 119902] [arXiv:1511.07447] [INSPIRE].
A. Falkowski, M. Nardecchia and R. Ziegler, Lepton Flavor Non-Universality in B-meson Decays from a U(2) Flavor Model, JHEP 11 (2015) 173 [arXiv:1509.01249] [INSPIRE].
C.-W. Chiang, X.-G. He and G. Valencia, Z′ model for \( b\to s\ell \overline{\ell} \) flavor anomalies, Phys. Rev. D 93 (2016) 074003 [arXiv:1601.07328] [INSPIRE].
D. Bečirević, O. Sumensari and R. Zukanovich Funchal, Lepton flavor violation in exclusive b → s decays, Eur. Phys. J. C 76 (2016) 134 [arXiv:1602.00881] [INSPIRE].
S.M. Boucenna, A. Celis, J. Fuentes-Martin, A. Vicente and J. Virto, Non-abelian gauge extensions for B-decay anomalies, Phys. Lett. B 760 (2016) 214 [arXiv:1604.03088] [INSPIRE].
S.M. Boucenna, A. Celis, J. Fuentes-Martin, A. Vicente and J. Virto, Phenomenology of an SU(2) × SU(2) × U(1) model with lepton-flavour non-universality, JHEP 12 (2016) 059 [arXiv:1608.01349] [INSPIRE].
P. Ko, Y. Omura, Y. Shigekami and C. Yu, LHCb anomaly and B physics in flavored Z′ models with flavored Higgs doublets, Phys. Rev. D 95 (2017) 115040 [arXiv:1702.08666] [INSPIRE].
R. Alonso, P. Cox, C. Han and T.T. Yanagida, Anomaly-free local horizontal symmetry and anomaly-full rare B-decays, Phys. Rev. D 96 (2017) 071701 [arXiv:1704.08158] [INSPIRE].
R. Alonso, P. Cox, C. Han and T.T. Yanagida, Flavoured B − L local symmetry and anomalous rare B decays, Phys. Lett. B 774 (2017) 643 [arXiv:1705.03858] [INSPIRE].
Y. Tang and Y.-L. Wu, Flavor non-universal gauge interactions and anomalies in B-meson decays, Chin. Phys. C 42 (2018) 033104 [arXiv:1705.05643] [INSPIRE].
C.-H. Chen and T. Nomura, Penguin b → sℓ′+ ℓ′− and B-meson anomalies in a gauged L μ − L τ, Phys. Lett. B 777 (2018) 420 [arXiv:1707.03249] [INSPIRE].
G. Faisel and J. Tandean, Connecting \( b\to s\ell \overline{\ell} \) anomalies to enhanced rare nonleptonic \( {\overline{B}}_s^0 \) decays in Z ′ model, JHEP 02 (2018) 074 [arXiv:1710.11102] [INSPIRE].
K. Fuyuto, H.-L. Li and J.-H. Yu, Implications of hidden gauged U(1) model for B anomalies, Phys. Rev. D 97 (2018) 115003 [arXiv:1712.06736] [INSPIRE].
L. Bian, H.M. Lee and C.B. Park, B-meson anomalies and Higgs physics in flavored U(1)′ model, Eur. Phys. J. C 78 (2018) 306 [arXiv:1711.08930] [INSPIRE].
M. Abdullah, M. Dalchenko, B. Dutta, R. Eusebi, P. Huang, T. Kamon et al., Bottom-quark fusion processes at the LHC for probing Z′ models and B -meson decay anomalies, Phys. Rev. D 97 (2018) 075035 [arXiv:1707.07016] [INSPIRE].
G.H. Duan, X. Fan, M. Frank, C. Han and J.M. Yang, A minimal U(1)′ extension of MSSM in light of the B decay anomaly, arXiv:1808.04116 [INSPIRE].
C.-W. Chiang, J. Jiang, T. Li and Y.-R. Wang, Top hypercharge, JHEP 12 (2007) 001 [arXiv:0710.1268] [INSPIRE].
C.D. Froggatt and H.B. Nielsen, Hierarchy of Quark Masses, Cabibbo Angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].
J. Ellis, M. Fairbairn and P. Tunney, Anomaly-Free Models for Flavour Anomalies, Eur. Phys. J. C 78 (2018) 238 [arXiv:1705.03447] [INSPIRE].
C. Bonilla, T. Modak, R. Srivastava and J.W.F. Valle, \( U{(1)}_{B_3-3{L}_{\mu }} \) gauge symmetry as a simple description of b → s anomalies, Phys. Rev. D 98 (2018) 095002 [arXiv:1705.00915] [INSPIRE].
D. Bhatia, S. Chakraborty and A. Dighe, Neutrino mixing and R K anomaly in U(1) X models: a bottom-up approach, JHEP 03 (2017) 117 [arXiv:1701.05825] [INSPIRE].
A. Greljo and D. Marzocca, High-p T dilepton tails and flavor physics, Eur. Phys. J. C 77 (2017) 548 [arXiv:1704.09015] [INSPIRE].
S.F. King, \( {R}_{K^{\left(\ast \right)}} \) and the origin of Yukawa couplings, JHEP 09 (2018) 069 [arXiv:1806.06780] [INSPIRE].
F.F. Deppisch, S. Kulkarni, H. Päs and E. Schumacher, Leptoquark patterns unifying neutrino masses, flavor anomalies and the diphoton excess, Phys. Rev. D 94 (2016) 013003 [arXiv:1603.07672] [INSPIRE].
B.C. Allanach, B. Gripaios and T. You, The case for future hadron colliders from B → K (*) μ + μ − decays, JHEP 03 (2018) 021 [arXiv:1710.06363] [INSPIRE].
T. Bandyopadhyay, G. Bhattacharyya, D. Das and A. Raychaudhuri, Reappraisal of constraints on Z′ models from unitarity and direct searches at the LHC, Phys. Rev. D 98 (2018) 035027 [arXiv:1803.07989] [INSPIRE].
Particle Data Group collaboration, M. Tanabashi et al., Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
X.-G. He and G. Valencia, Ansatz for small FCNC with a non-universal Z-prime, Phys. Lett. B 680 (2009) 72 [arXiv:0907.4034] [INSPIRE].
Fermilab Lattice, MILC collaboration, A. Bazavov et al., B 0(s) -mixing matrix elements from lattice QCD for the Standard Model and beyond, Phys. Rev. D 93 (2016) 113016 [arXiv:1602.03560] [INSPIRE].
L. Di Luzio, M. Kirk and A. Lenz, Updated B s -mixing constraints on new physics models for b → sℓ + ℓ − anomalies, Phys. Rev. D 97 (2018) 095035 [arXiv:1712.06572] [INSPIRE].
J. Charles, S. Descotes-Genon, Z. Ligeti, S. Monteil, M. Papucci and K. Trabelsi, Future sensitivity to new physics in B d , B s and K mixings, Phys. Rev. D 89 (2014) 033016 [arXiv:1309.2293] [INSPIRE].
CMS collaboration, Search for associated production of a Z boson with a single top quark and for tZ flavour-changing interactions in pp collisions at \( \sqrt{s}=8 \) TeV, JHEP 07 (2017) 003 [arXiv:1702.01404] [INSPIRE].
CMS collaboration, Search for high-mass resonances in dilepton final states in proton-proton collisions at \( \sqrt{s}=13 \) TeV, JHEP 06 (2018) 120 [arXiv:1803.06292] [INSPIRE].
ATLAS collaboration, Search for new high-mass phenomena in the dilepton final state using 36 fb −1 of proton-proton collision data at \( \sqrt{s}=13 \) TeV with the ATLAS detector, JHEP 10 (2017) 182 [arXiv:1707.02424] [INSPIRE].
S.L. Glashow, D. Guadagnoli and K. Lane, Lepton Flavor Violation in B Decays?, Phys. Rev. Lett. 114 (2015) 091801 [arXiv:1411.0565] [INSPIRE].
J. Albrecht, F. Bernlochner, M. Kenzie, S. Reichert, D. Straub and A. Tully, Future prospects for exploring present day anomalies in flavour physics measurements with Belle II and LHCb, arXiv:1709.10308 [INSPIRE].
Belle II collaboration, E. Kou et al., The Belle II Physics Book, arXiv:1808.10567 [INSPIRE].
BaBar collaboration, J.P. Lees et al., Measurement of an Excess of \( \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } \) Decays and Implications for Charged Higgs Bosons, Phys. Rev. D 88 (2013) 072012 [arXiv:1303.0571] [INSPIRE].
LHCb collaboration, Measurement of the ratio of branching fractions \( \mathrm{\mathcal{B}}\left({\overline{B}}^0\to {D}^{\ast +}{\tau}^{-}{\nu}_{\tau}\right)/\mathrm{\mathcal{B}}\left({\overline{B}}^0\to {D}^{\ast +}{\mu}^{-}{\overline{\nu}}_{\mu}\right) \), Phys. Rev. Lett. 115 (2015) 111803 [Erratum ibid. 115 (2015) 159901] [arXiv:1506.08614] [INSPIRE].
Belle collaboration, S. Hirose et al., Measurement of the τ lepton polarization and R(D *) in the decay \( \overline{B}\to {D}^{\ast }{\tau}^{-}{\overline{\nu}}_{\tau } \), Phys. Rev. Lett. 118 (2017) 211801 [arXiv:1612.00529] [INSPIRE].
LHCb collaboration, Test of Lepton Flavor Universality by the measurement of the B 0 → D ∗− τ + ν τ branching fraction using three-prong τ decays, Phys. Rev. D 97 (2018) 072013 [arXiv:1711.02505] [INSPIRE].
M. Bordone, C. Cornella, J. Fuentes-Martin and G. Isidori, A three-site gauge model for flavor hierarchies and flavor anomalies, Phys. Lett. B 779 (2018) 317 [arXiv:1712.01368] [INSPIRE].
A. Greljo and B.A. Stefanek, Third family quark-lepton unification at the TeV scale, Phys. Lett. B 782 (2018) 131 [arXiv:1802.04274] [INSPIRE].
N. Assad, B. Fornal and B. Grinstein, Baryon Number and Lepton Universality Violation in Leptoquark and Diquark Models, Phys. Lett. B 777 (2018) 324 [arXiv:1708.06350] [INSPIRE].
L. Di Luzio, A. Greljo and M. Nardecchia, Gauge leptoquark as the origin of B-physics anomalies, Phys. Rev. D 96 (2017) 115011 [arXiv:1708.08450] [INSPIRE].
D. Buttazzo, A. Greljo, G. Isidori and D. Marzocca, B-physics anomalies: a guide to combined explanations, JHEP 11 (2017) 044 [arXiv:1706.07808] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1809.01158
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Allanach, B.C., Davighi, J. Third family hypercharge model for \( {R}_{K^{\left(\ast \right)}} \) and aspects of the fermion mass problem. J. High Energ. Phys. 2018, 75 (2018). https://doi.org/10.1007/JHEP12(2018)075
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2018)075