Reconciling B-meson decay anomalies with neutrino masses, dark matter and constraints from flavour violation


Motivated by an explanation of the \( {R}_{K^{\left(*\right)}} \) anomalies, we propose a Standard Model extension via two scalar SU(2)L triplet leptoquarks and three generations of triplet Majorana fermions. The gauge group is reinforced by a Z2 symmetry, ensuring the stability of the lightest Z2-odd particle, which is a potentially viable dark matter candidate. Neutrino mass generation occurs radiatively (at the three-loop level), and leads to important constraints on the leptoquark couplings to leptons. We consider very generic textures for the flavour structure of the h1 leptoquark Yukawa couplings, identifying classes which succeed in saturating the \( {R}_{K^{\left(*\right)}} \) anomalies. We subsequently carry a comprehensive analysis of the model’s contributions to numerous high-intensity observables such as meson oscillations and decays, as well as charged lepton flavour violating processes, which put severe constraints on the flavour structure of these leptoquark extensions. Our findings suggest that the most constraining observables are \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) decays, and charged lepton flavour violating μe conversion in nuclei (among others). Nevertheless, for several classes of flavour textures and for wide mass regimes of the new mediators (within collider reach), this Standard Model extension successfully addresses neutrino mass generation, explains the current \( {R}_{K^{\left(*\right)}} \) tensions, and offers a viable dark matter candidate.

A preprint version of the article is available at ArXiv.


  1. [1]

    Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].

  2. [2]

    G. Hiller and F. Krüger, More model-independent analysis of bs processes, Phys. Rev. D 69 (2004) 074020 [hep-ph/0310219] [INSPIRE].

  3. [3]

    LHCb collaboration, Test of lepton universality using B +K + + decays, Phys. Rev. Lett. 113 (2014) 151601 [arXiv:1406.6482] [INSPIRE].

  4. [4]

    M. Bordone, G. Isidori and A. Pattori, On the standard model predictions for R K and \( {R}_{K^{*}} \), Eur. Phys. J. C 76 (2016) 440 [arXiv:1605.07633] [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    B. Capdevila et al., Patterns of new physics in bsℓ + transitions in the light of recent data, JHEP 01 (2018) 093 [arXiv:1704.05340] [INSPIRE].

    ADS  Article  Google Scholar 

  6. [6]

    LHCb collaboration, Test of lepton universality with B 0K *0 + decays, JHEP 08 (2017) 055 [arXiv:1705.05802] [INSPIRE].

  7. [7]

  8. [8]

    BaBar collaboration, J.P. Lees et al., Evidence for an excess of \( \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } \) decays, Phys. Rev. Lett. 109 (2012) 101802 [arXiv:1205.5442] [INSPIRE].

  9. [9]

    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].

  10. [10]

    Belle collaboration, M. Huschle et al., Measurement of the branching ratio of \( \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } \) relative to \( \overline{B}\to {D}^{\left(\ast \right)}{\ell}^{-}{\overline{\nu}}_{\ell } \) decays with hadronic tagging at Belle, Phys. Rev. D 92 (2015) 072014 [arXiv:1507.03233] [INSPIRE].

  11. [11]

    Belle collaboration, I. Adachi et al., Measurement of BD (*) τν using full reconstruction tags, arXiv:0910.4301 [INSPIRE].

  12. [12]

    Belle collaboration, A. Bozek et al., Observation of \( {B}^{+}\to {\overline{D}}^0{\tau}^{+}{\nu}_{\tau } \) and evidence for \( {B}^{+}\to {\overline{D}}^0{\tau}^{+}{\nu}_{\tau } \) at Belle, Phys. Rev. D 82 (2010) 072005 [arXiv:1005.2302] [INSPIRE].

  13. [13]

    LHCb collaboration, Measurement of the ratio of branching fractions \( \mathrm{\mathcal{B}}\left({\overline{B}}^0\to {D}^{\ast +}{\tau}^{-}{\overline{\nu}}_{\tau}\right)/\mathrm{\mathcal{B}}\left({\overline{B}}^0\to {D}^{\ast +}{\mu}^{-}{\overline{\nu}}_{\mu}\right) \), Phys. Rev. Lett. 115 (2015) 111803 [Erratum ibid. 115 (2015) 159901] [arXiv:1506.08614] [INSPIRE].

  14. [14]

    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].

  15. [15]

    D. Bigi and P. Gambino, Revisiting BDℓν, Phys. Rev. D 94 (2016) 094008 [arXiv:1606.08030] [INSPIRE].

    ADS  Google Scholar 

  16. [16]

    HFLAV collaboration, Y. Amhis et al., Averages of b-hadron, c-hadron and τ-lepton properties as of summer 2016, Eur. Phys. J. C 77 (2017) 895 [arXiv:1612.07233] [INSPIRE].

  17. [17]

    D. Bigi, P. Gambino and S. Schacht, R(D *), |V cb| and the Heavy Quark Symmetry relations between form factors, JHEP 11 (2017) 061 [arXiv:1707.09509] [INSPIRE].

    ADS  Article  Google Scholar 

  18. [18]

    Z. Ligeti, M. Papucci and D.J. Robinson, New physics in the visible final states of BD (*) τν, JHEP 01 (2017) 083 [arXiv:1610.02045] [INSPIRE].

    ADS  Article  Google Scholar 

  19. [19]

    A. Crivellin, J. Fuentes-Martin, A. Greljo and G. Isidori, Lepton flavor non-universality in B decays from dynamical Yukawas, Phys. Lett. B 766 (2017) 77 [arXiv:1611.02703] [INSPIRE].

    ADS  Article  Google Scholar 

  20. [20]

    B. Capdevila, S. Descotes-Genon, L. Hofer and J. Matias, Hadronic uncertainties in BK * μ + μ : a state-of-the-art analysis, JHEP 04 (2017) 016 [arXiv:1701.08672] [INSPIRE].

    ADS  Article  Google Scholar 

  21. [21]

    Belle collaboration, S. Wehle et al., Lepton-flavor-dependent angular analysis of BK * + , Phys. Rev. Lett. 118 (2017) 111801 [arXiv:1612.05014] [INSPIRE].

  22. [22]

    A. Datta, M. Duraisamy and D. Ghosh, Explaining the BK * μ + μ data with scalar interactions, Phys. Rev. D 89 (2014) 071501 [arXiv:1310.1937] [INSPIRE].

    ADS  Google Scholar 

  23. [23]

    D. Ghosh, M. Nardecchia and S.A. Renner, Hint of lepton flavour non-universality in B meson decays, JHEP 12 (2014) 131 [arXiv:1408.4097] [INSPIRE].

    ADS  Article  Google Scholar 

  24. [24]

    S.L. Glashow, D. Guadagnoli and K. Lane, Lepton flavor violation in B decays?, Phys. Rev. Lett. 114 (2015) 091801 [arXiv:1411.0565] [INSPIRE].

    ADS  Article  Google Scholar 

  25. [25]

    B. Bhattacharya, A. Datta, D. London and S. Shivashankara, Simultaneous explanation of the R K and R(D (*)) puzzles, Phys. Lett. B 742 (2015) 370 [arXiv:1412.7164] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  26. [26]

    M. Freytsis, Z. Ligeti and J.T. Ruderman, Flavor models for \( \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} \), Phys. Rev. D 92 (2015) 054018 [arXiv:1506.08896] [INSPIRE].

    ADS  Google Scholar 

  27. [27]

    D. Bardhan, P. Byakti and D. Ghosh, A closer look at the R D and \( {R}_{D^{*}} \) anomalies, JHEP 01 (2017) 125 [arXiv:1610.03038] [INSPIRE].

    ADS  Article  Google Scholar 

  28. [28]

    D. Ghosh, Explaining the R K and \( {R}_{K^{*}} \) anomalies, Eur. Phys. J. C 77 (2017) 694 [arXiv:1704.06240] [INSPIRE].

    ADS  Article  Google Scholar 

  29. [29]

    M. Ciuchini et al., On flavourful easter eggs for new physics hunger and lepton flavour universality violation, Eur. Phys. J. C 77 (2017) 688 [arXiv:1704.05447] [INSPIRE].

    Article  Google Scholar 

  30. [30]

    D. Choudhury, A. Kundu, R. Mandal and R. Sinha, Minimal unified resolution to \( {R}_{K^{\left(*\right)}} \) and R(D (*)) anomalies with lepton mixing, Phys. Rev. Lett. 119 (2017) 151801 [arXiv:1706.08437] [INSPIRE].

    ADS  Article  Google Scholar 

  31. [31]

    D. Choudhury, A. Kundu, R. Mandal and R. Sinha, \( {R}_{K^{\left(*\right)}} \) and R(D (*)) anomalies resolved with lepton mixing, Nucl. Phys. B 933 (2018) 433 [arXiv:1712.01593] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  32. [32]

    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].

    ADS  Google Scholar 

  33. [33]

    A. Crivellin, G. D’Ambrosio and J. Heeck, Explaining hμ ± τ , BK * μ + μ and B + μ /BKe + e in a two-Higgs-doublet model with gauged L μL τ, Phys. Rev. Lett. 114 (2015) 151801 [arXiv:1501.00993] [INSPIRE].

    ADS  Article  Google Scholar 

  34. [34]

    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].

    ADS  Google Scholar 

  35. [35]

    D. Aristizabal Sierra, F. Staub and A. Vicente, Shedding light on the bs anomalies with a dark sector, Phys. Rev. D 92 (2015) 015001 [arXiv:1503.06077] [INSPIRE].

    ADS  Google Scholar 

  36. [36]

    A. Crivellin et al., Lepton-flavour violating B decays in generic Zmodels, Phys. Rev. D 92 (2015) 054013 [arXiv:1504.07928] [INSPIRE].

    ADS  Google Scholar 

  37. [37]

    A. Celis, J. Fuentes-Martin, M. Jung and H. Serodio, Family nonuniversal Zmodels with protected flavor-changing interactions, Phys. Rev. D 92 (2015) 015007 [arXiv:1505.03079] [INSPIRE].

    ADS  Google Scholar 

  38. [38]

    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].

    ADS  Article  Google Scholar 

  39. [39]

    J.F. Kamenik, Y. Soreq and J. Zupan, Lepton flavor universality violation without new sources of quark flavor violation, Phys. Rev. D 97 (2018) 035002 [arXiv:1704.06005] [INSPIRE].

    ADS  Google Scholar 

  40. [40]

    J.E. Camargo-Molina, A. Celis and D.A. Faroughy, Anomalies in bottom from new physics in top, Phys. Lett. B 784 (2018) 284 [arXiv:1805.04917] [INSPIRE].

    ADS  Article  Google Scholar 

  41. [41]

    G. Hiller and M. Schmaltz, R K and future bsℓℓ physics beyond the standard model opportunities, Phys. Rev. D 90 (2014) 054014 [arXiv:1408.1627] [INSPIRE].

    ADS  Google Scholar 

  42. [42]

    B. Gripaios, M. Nardecchia and S.A. Renner, Composite leptoquarks and anomalies in B-meson decays, JHEP 05 (2015) 006 [arXiv:1412.1791] [INSPIRE].

    ADS  Article  Google Scholar 

  43. [43]

    S. Sahoo and R. Mohanta, Scalar leptoquarks and the rare B meson decays, Phys. Rev. D 91 (2015) 094019 [arXiv:1501.05193] [INSPIRE].

    ADS  Google Scholar 

  44. [44]

    I. de Medeiros Varzielas and G. Hiller, Clues for flavor from rare lepton and quark decays, JHEP 06 (2015) 072 [arXiv:1503.01084] [INSPIRE].

    Article  Google Scholar 

  45. [45]

    R. Alonso, B. Grinstein and J. Martin Camalich, Lepton universality violation and lepton flavor conservation in B-meson decays, JHEP 10 (2015) 184 [arXiv:1505.05164] [INSPIRE].

    ADS  Article  Google Scholar 

  46. [46]

    M. Bauer and M. Neubert, Minimal leptoquark explanation for the \( {R}_{D^{\left(*\right)}} \) , R K and (g − 2)g anomalies, Phys. Rev. Lett. 116 (2016) 141802 [arXiv:1511.01900] [INSPIRE].

  47. [47]

    C. Hati, G. Kumar and N. Mahajan, \( \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} \) excesses in ALRSM constrained from B, D decays and \( {D}^0\hbox{-} {\overline{D}}^0 \) mixing, JHEP 01 (2016) 117 [arXiv:1511.03290] [INSPIRE].

  48. [48]

    S. Fajfer and N. Košnik, Vector leptoquark resolution of R K and \( {R}_{D^{\left(*\right)}} \) puzzles, Phys. Lett. B 755 (2016) 270 [arXiv:1511.06024] [INSPIRE].

    ADS  Article  Google Scholar 

  49. [49]

    D. Das, C. Hati, G. Kumar and N. Mahajan, Towards a unified explanation of \( {R}_{D^{\left(*\right)}} \) , R K and (g − 2)μ anomalies in a left-right model with leptoquarks, Phys. Rev. D 94 (2016) 055034 [arXiv:1605.06313] [INSPIRE].

    ADS  Google Scholar 

  50. [50]

    D. Bečirević, S. Fajfer, N. Košnik and O. Sumensari, Leptoquark model to explain the B-physics anomalies, R K and R D, Phys. Rev. D 94 (2016) 115021 [arXiv:1608.08501] [INSPIRE].

    ADS  Google Scholar 

  51. [51]

    S. Sahoo, R. Mohanta and A.K. Giri, Explaining the R K and \( {R}_{D^{\left(*\right)}} \) anomalies with vector leptoquarks, Phys. Rev. D 95 (2017) 035027 [arXiv:1609.04367] [INSPIRE].

    ADS  Google Scholar 

  52. [52]

    P. Cox, A. Kusenko, O. Sumensari and T.T. Yanagida, SU(5) unification with TeV-scale leptoquarks, JHEP 03 (2017) 035 [arXiv:1612.03923] [INSPIRE].

    ADS  Article  Google Scholar 

  53. [53]

    A. Crivellin, D. Müller and T. Ota, Simultaneous explanation of R(D (*)) and b + μ : the last scalar leptoquarks standing, JHEP 09 (2017) 040 [arXiv:1703.09226] [INSPIRE].

    ADS  Article  Google Scholar 

  54. [54]

    D. Bečirević and O. Sumensari, A leptoquark model to accommodate R exp K  < R SM K and \( {R}_{K^{*}}^{\exp }<{R}_{K^{*}}^{\mathrm{SM}} \), JHEP 08 (2017) 104 [arXiv:1704.05835] [INSPIRE].

    ADS  Google Scholar 

  55. [55]

    Y. Cai, J. Gargalionis, M.A. Schmidt and R.R. Volkas, Reconsidering the one leptoquark solution: flavor anomalies and neutrino mass, JHEP 10 (2017) 047 [arXiv:1704.05849] [INSPIRE].

    ADS  Article  Google Scholar 

  56. [56]

    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].

    ADS  Article  Google Scholar 

  57. [57]

    I. Doršner, S. Fajfer, D.A. Faroughy and N. Košnik, The role of the S 3 GUT leptoquark in flavor universality and collider searches, arXiv:1706.07779 [INSPIRE].

  58. [58]

    M. Blanke and A. Crivellin, B meson anomalies in a Pati-Salam model within the Randall-Sundrum background, Phys. Rev. Lett. 121 (2018) 011801 [arXiv:1801.07256] [INSPIRE].

    ADS  Article  Google Scholar 

  59. [59]

    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].

    ADS  Article  Google Scholar 

  60. [60]

    M. Bordone, C. Cornella, J. Fuentes-Martín and G. Isidori, Low-energy signatures of the PS 3 model: from B-physics anomalies to LFV, arXiv:1805.09328 [INSPIRE].

  61. [61]

    S. Sahoo and R. Mohanta, Impact of vector leptoquark on \( \overline{B}\to {\overline{K}}^{*}{l}^{+}{l}^{-} \) anomalies, J. Phys. G 45 (2018) 085003 [arXiv:1806.01048] [INSPIRE].

    ADS  Article  Google Scholar 

  62. [62]

    D. Bečirević et al., Scalar leptoquarks from grand unified theories to accommodate the B-physics anomalies, Phys. Rev. D 98 (2018) 055003 [arXiv:1806.05689] [INSPIRE].

    ADS  Google Scholar 

  63. [63]

    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].

    ADS  Article  Google Scholar 

  64. [64]

    P. Arnan, D. Bečirević, F. Mescia and O. Sumensari, Two Higgs doublet models and bs exclusive decays, Eur. Phys. J. C 77 (2017) 796 [arXiv:1703.03426] [INSPIRE].

    ADS  Article  Google Scholar 

  65. [65]

    L.-S. Geng et al., Towards the discovery of new physics with lepton-universality ratios of bsℓℓ decays, Phys. Rev. D 96 (2017) 093006 [arXiv:1704.05446] [INSPIRE].

    ADS  Google Scholar 

  66. [66]

    W. Altmannshofer, P. Bhupal Dev and A. Soni, \( {R}_{D^{\left(*\right)}} \) anomaly: a possible hint for natural supersymmetry with R-parity violation, Phys. Rev. D 96 (2017) 095010 [arXiv:1704.06659] [INSPIRE].

    Google Scholar 

  67. [67]

    D. Das, C. Hati, G. Kumar and N. Mahajan, Scrutinizing R-parity violating interactions in light of \( {R}_{K^{\left(*\right)}} \) data, Phys. Rev. D 96 (2017) 095033 [arXiv:1705.09188] [INSPIRE].

    ADS  Google Scholar 

  68. [68]

    K. Earl and T. Grégoire, Contributions to bsℓℓ anomalies from R-parity violating interactions, JHEP 08 (2018) 201 [arXiv:1806.01343] [INSPIRE].

    ADS  Article  Google Scholar 

  69. [69]

    Y. Cai et al., From the trees to the forest: a review of radiative neutrino mass models, Front. in Phys. 5 (2017) 63 [arXiv:1706.08524] [INSPIRE].

    ADS  Article  Google Scholar 

  70. [70]

    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].

    ADS  Google Scholar 

  71. [71]

    A. Zee, Quantum numbers of Majorana neutrino masses, Nucl. Phys. B 264 (1986) 99 [INSPIRE].

    ADS  Article  Google Scholar 

  72. [72]

    K.S. Babu, Model ofcalculableMajorana neutrino masses, Phys. Lett. B 203 (1988) 132 [INSPIRE].

    ADS  Article  Google Scholar 

  73. [73]

    S.-Y. Guo et al., Interpreting the \( {R}_{K^{\left(*\right)}} \) anomaly in the colored Zee-Babu model, Nucl. Phys. B 928 (2018) 435 [arXiv:1707.00522] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  74. [74]

    T. Nomura, H. Okada and N. Okada, A colored KNT neutrino model, Phys. Lett. B 762 (2016) 409 [arXiv:1608.02694] [INSPIRE].

    ADS  Article  Google Scholar 

  75. [75]

    K. Cheung, T. Nomura and H. Okada, Three-loop neutrino mass model with a colored triplet scalar, Phys. Rev. D 95 (2017) 015026 [arXiv:1610.04986] [INSPIRE].

    ADS  Google Scholar 

  76. [76]

    L.M. Krauss, S. Nasri and M. Trodden, A model for neutrino masses and dark matter, Phys. Rev. D 67 (2003) 085002 [hep-ph/0210389] [INSPIRE].

  77. [77]

    R. Foot, H. Lew, X.G. He and G.C. Joshi, Seesaw neutrino masses induced by a triplet of leptons, Z. Phys. C 44 (1989) 441 [INSPIRE].

    Google Scholar 

  78. [78]

    I. Dorsner, S. Fajfer, J.F. Kamenik and N. Kosnik, Can scalar leptoquarks explain the f(D s) puzzle?, Phys. Lett. B 682 (2009) 67 [arXiv:0906.5585] [INSPIRE].

    ADS  Article  Google Scholar 

  79. [79]

    C. Hati and U. Sarkar, BL violating nucleon decays as a probe of leptoquarks, arXiv:1805.06081 [INSPIRE].

  80. [80]

    A. Ahriche and S. Nasri, Dark matter and strong electroweak phase transition in a radiative neutrino mass model, JCAP 07 (2013) 035 [arXiv:1304.2055] [INSPIRE].

    ADS  Article  Google Scholar 

  81. [81]

    G. Passarino and M.J.G. Veltman, One loop corrections for e + e annihilation into μ + μ in the Weinberg model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].

    ADS  Article  Google Scholar 

  82. [82]

    J.A. Casas and A. Ibarra, Oscillating neutrinos and μ, Nucl. Phys. B 618 (2001) 171 [hep-ph/0103065] [INSPIRE].

  83. [83]

    M. Cirelli, N. Fornengo and A. Strumia, Minimal dark matter, Nucl. Phys. B 753 (2006) 178 [hep-ph/0512090] [INSPIRE].

  84. [84]

    E. Ma and D. Suematsu, Fermion triplet dark matter and radiative neutrino mass, Mod. Phys. Lett. A 24 (2009) 583 [arXiv:0809.0942] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  85. [85]

    K. Griest and D. Seckel, Three exceptions in the calculation of relic abundances, Phys. Rev. D 43 (1991) 3191 [INSPIRE].

    ADS  Google Scholar 

  86. [86]

    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].

  87. [87]

    M. Cirelli, A. Strumia and M. Tamburini, Cosmology and astrophysics of minimal dark matter, Nucl. Phys. B 787 (2007) 152 [arXiv:0706.4071] [INSPIRE].

    ADS  Article  Google Scholar 

  88. [88]

    S. Choubey, S. Khan, M. Mitra and S. Mondal, Singlet-triplet fermionic dark matter and LHC phenomenology, Eur. Phys. J. C 78 (2018) 302 [arXiv:1711.08888] [INSPIRE].

    ADS  Article  Google Scholar 

  89. [89]

    W. Altmannshofer et al., Symmetries and asymmetries of BK * μ + μ decays in the standard model and beyond, JHEP 01 (2009) 019 [arXiv:0811.1214] [INSPIRE].

    ADS  Article  Google Scholar 

  90. [90]

    D. Bečirević, N. Košnik, O. Sumensari and R. Zukanovich Funchal, Palatable leptoquark scenarios for lepton flavor violation in exclusive bsℓ 1 2 modes, JHEP 11 (2016) 035 [arXiv:1608.07583] [INSPIRE].

    Google Scholar 

  91. [91]

    G. Hiller and I. Nisandzic, R K and \( {R}_{K^{*}} \) beyond the standard model, Phys. Rev. D 96 (2017) 035003 [arXiv:1704.05444] [INSPIRE].

    ADS  Google Scholar 

  92. [92]

    S. Descotes-Genon, L. Hofer, J. Matias and J. Virto, Global analysis of bsℓℓ anomalies, JHEP 06 (2016) 092 [arXiv:1510.04239] [INSPIRE].

    ADS  Article  Google Scholar 

  93. [93]

    T. Hurth, F. Mahmoudi and S. Neshatpour, Global fits to bsℓℓ data and signs for lepton non-universality, JHEP 12 (2014) 053 [arXiv:1410.4545] [INSPIRE].

    ADS  Article  Google Scholar 

  94. [94]

    W. Altmannshofer and D.M. Straub, New physics in bs transitions after LHC run 1, Eur. Phys. J. C 75 (2015) 382 [arXiv:1411.3161] [INSPIRE].

    ADS  Article  Google Scholar 

  95. [95]

    F. Beaujean, C. Bobeth and D. van Dyk, Comprehensive Bayesian analysis of rare (semi)leptonic and radiative B decays, Eur. Phys. J. C 74 (2014) 2897 [Erratum ibid. C 74 (2014) 3179] [arXiv:1310.2478] [INSPIRE].

  96. [96]

    Belle collaboration, R. Glattauer et al., Measurement of the decay BDℓν in fully reconstructed events and determination of the Cabibbo-Kobayashi-Maskawa matrix element |V cb|, Phys. Rev. D 93 (2016) 032006 [arXiv:1510.03657] [INSPIRE].

  97. [97]

    Belle collaboration, A. Abdesselam et al., Precise determination of the CKM matrix element |V cb| with \( {\overline{B}}^0\to {D}^{\ast +}{\ell}^{-}{\overline{\nu}}_{\ell } \) decays with hadronic tagging at Belle, arXiv:1702.01521 [INSPIRE].

  98. [98]

    A.J. Buras, D. Buttazzo, J. Girrbach-Noe and R. Knegjens, \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and \( {K}_L\to {\pi}^0\nu \overline{\nu} \) in the Standard Model: status and perspectives, JHEP 11 (2015) 033 [arXiv:1503.02693] [INSPIRE].

  99. [99]

    E949 collaboration, A.V. Artamonov et al., New measurement of the \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) branching ratio, Phys. Rev. Lett. 101 (2008) 191802 [arXiv:0808.2459] [INSPIRE].

  100. [100]

    NA62 collaboration, \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) : first NA62 results, contribution to the 3rd Rencontres de Moriond on Electroweak Interactions and Unified Theories (Moriond EW 2018), March 10–17, La Thuile, Italy (2018).

  101. [101]

    E391a collaboration, J.K. Ahn et al., Experimental study of the decay \( {K}_L^0\to {\pi}^0\nu \overline{\nu} \), Phys. Rev. D 81 (2010) 072004 [arXiv:0911.4789] [INSPIRE].

  102. [102]

    Belle collaboration, J. Grygier et al., Search for \( B\to h\nu \overline{\nu} \) decays with semileptonic tagging at Belle, Phys. Rev. D 96 (2017) 091101 [arXiv:1702.03224] [INSPIRE].

  103. [103]

    J. Charles et al., Current status of the standard model CKM fit and constraints on ΔF = 2 new physics, Phys. Rev. D 91 (2015) 073007 [arXiv:1501.05013] [INSPIRE].

    ADS  Google Scholar 

  104. [104]

    J. Brod and M. Gorbahn, Next-to-next-to-leading-order charm-quark contribution to the CP-violation parameter ϵ K and ΔM K, Phys. Rev. Lett. 108 (2012) 121801 [arXiv:1108.2036] [INSPIRE].

    ADS  Article  Google Scholar 

  105. [105]

    A. Crivellin, G. D’Ambrosio, M. Hoferichter and L.C. Tunstall, Violation of lepton flavor and lepton flavor universality in rare kaon decays, Phys. Rev. D 93 (2016) 074038 [arXiv:1601.00970] [INSPIRE].

    ADS  Google Scholar 

  106. [106]

    S. Fajfer, N. Košnik and L. Vale Silva, Footprints of leptoquarks: from \( {R}_{K^{\left(*\right)}} \) to \( K\to \pi \nu \overline{\nu} \), Eur. Phys. J. C 78 (2018) 275 [arXiv:1802.00786] [INSPIRE].

    Article  Google Scholar 

  107. [107]

    A.J. Buras, J. Girrbach-Noe, C. Niehoff and D.M. Straub, \( B\to {K}^{\left(\ast \right)}\nu \overline{\nu} \) decays in the Standard Model and beyond, JHEP 02 (2015) 184 [arXiv:1409.4557] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  108. [108]

    C. Bobeth and A.J. Buras, Leptoquarks meet ε/ε and rare Kaon processes, JHEP 02 (2018) 101 [arXiv:1712.01295] [INSPIRE].

    ADS  Article  Google Scholar 

  109. [109]

    M. Bordone, D. Buttazzo, G. Isidori and J. Monnard, Probing Lepton flavour universality with \( K\to \pi \nu \overline{\nu} \) decays, Eur. Phys. J. C 77 (2017) 618 [arXiv:1705.10729] [INSPIRE].

    ADS  Article  Google Scholar 

  110. [110]

    G. Buchalla and A.J. Buras, QCD corrections to rare K and B decays for arbitrary top quark mass, Nucl. Phys. B 400 (1993) 225 [INSPIRE].

    ADS  Article  Google Scholar 

  111. [111]

    M. Misiak and J. Urban, QCD corrections to FCNC decays mediated by Z penguins and W boxes, Phys. Lett. B 451 (1999) 161 [hep-ph/9901278] [INSPIRE].

  112. [112]

    G. Buchalla and A.J. Buras, The rare decays \( K\to \pi \nu \overline{\nu},\kern0.5em B\to X\nu \overline{\nu} \) and Bl + l : an update, Nucl. Phys. B 548 (1999) 309 [hep-ph/9901288] [INSPIRE].

  113. [113]

    J. Brod, M. Gorbahn and E. Stamou, Two-loop electroweak corrections for the \( K\to \pi \nu \overline{\nu} \) decays, Phys. Rev. D 83 (2011) 034030 [arXiv:1009.0947] [INSPIRE].

    ADS  Google Scholar 

  114. [114]

    G. Buchalla and A.J. Buras, The rare decays \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and K Lμ + μ beyond leading logarithms, Nucl. Phys. B 412 (1994) 106 [hep-ph/9308272] [INSPIRE].

  115. [115]

    A.J. Buras, M. Gorbahn, U. Haisch and U. Nierste, The rare decay \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) at the next-to-next-to-leading order in QCD, Phys. Rev. Lett. 95 (2005) 261805 [hep-ph/0508165] [INSPIRE].

  116. [116]

    A.J. Buras, M. Gorbahn, U. Haisch and U. Nierste, Charm quark contribution to \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) at next-to-next-to-leading order, JHEP 11 (2006) 002 [Erratum ibid. 1211 (2012) 167] [hep-ph/0603079] [INSPIRE].

  117. [117]

    G. Isidori, F. Mescia and C. Smith, Light-quark loops in \( K\to {\pi}^{+}\nu \overline{\nu} \), Nucl. Phys. B 718 (2005) 319 [hep-ph/0503107] [INSPIRE].

  118. [118]

    A. Lenz et al., Anatomy of new physics in \( B\hbox{-} \overline{B} \) mixing, Phys. Rev. D 83 (2011) 036004 [arXiv:1008.1593] [INSPIRE].

    ADS  Google Scholar 

  119. [119]

    UTfit collaboration, M. Bona et al., Model-independent constraints on ΔF = 2 operators and the scale of new physics, JHEP 03 (2008) 049 [arXiv:0707.0636] [INSPIRE].

  120. [120]

    T. Inami and C.S. Lim, Effects of superheavy quarks and leptons in low-energy weak processes \( {k}_L\to \mu \overline{\mu} \) , \( {K}^{+}\to \pi +\nu \overline{\nu} \) and \( {K}^0\leftrightarrow {\overline{K}}^0 \), Prog. Theor. Phys. 65 (1981) 297 [Erratum ibid. 65 (1981) 1772] [INSPIRE].

  121. [121]

    A.J. Buras, Weak Hamiltonian, CP-violation and rare decays, hep-ph/9806471 [INSPIRE].

  122. [122]

    A.J. Buras, M. Jamin and P.H. Weisz, Leading and next-to-leading QCD corrections to ϵ parameter and \( {B}^0\hbox{-} {\overline{B}}^0 \) mixing in the presence of a heavy top quark, Nucl. Phys. B 347 (1990) 491 [INSPIRE].

    ADS  Article  Google Scholar 

  123. [123]

    J. Brod and M. Gorbahn, ϵ K at next-to-next-to-leading order: the charm-top-quark contribution, Phys. Rev. D 82 (2010) 094026 [arXiv:1007.0684] [INSPIRE].

    ADS  Google Scholar 

  124. [124]

    A.J. Buras, New physics patterns in ε/ε and ε K with implications for rare kaon decays and ΔM K, JHEP 04 (2016) 071 [arXiv:1601.00005] [INSPIRE].

    ADS  Google Scholar 

  125. [125]

    A.J. Buras, F. De Fazio, J. Girrbach and M.V. Carlucci, The anatomy of quark flavour observables in 331 models in the flavour precision era, JHEP 02 (2013) 023 [arXiv:1211.1237] [INSPIRE].

    ADS  Article  Google Scholar 

  126. [126]

    A.J. Buras, J.-M. Gérard and W.A. Bardeen, Large N approach to kaon decays and mixing 28 years later: ΔI = 1/2 rule, \( {\widehat{B}}_K \) and ΔM K, Eur. Phys. J. C 74 (2014) 2871 [arXiv:1401.1385] [INSPIRE].

    ADS  Article  Google Scholar 

  127. [127]

    LHCb, CMS collaboration, Observation of the rare B 0 s  → μ + μ decay from the combined analysis of CMS and LHCb data, Nature 522 (2015) 68 [arXiv:1411.4413] [INSPIRE].

  128. [128]

    ATLAS collaboration, Study of the rare decays of B 0 s and B 0 into muon pairs from data collected during the LHC Run 1 with the ATLAS detector, Eur. Phys. J. C 76 (2016) 513 [arXiv:1604.04263] [INSPIRE].

  129. [129]

    D. Bečirević, O. Sumensari and R. Zukanovich Funchal, Lepton flavor violation in exclusive bs decays, Eur. Phys. J. C 76 (2016) 134 [arXiv:1602.00881] [INSPIRE].

    ADS  Google Scholar 

  130. [130]

    G. D’Ambrosio, G. Isidori and J. Portoles, Can we extract short distance information from B(K Lμ + μ )?, Phys. Lett. B 423 (1998) 385 [hep-ph/9708326] [INSPIRE].

  131. [131]

    MEG collaboration, A.M. Baldini et al., Search for the lepton flavour violating decay μ +e + γ with the full dataset of the MEG experiment, Eur. Phys. J. C 76 (2016) 434 [arXiv:1605.05081] [INSPIRE].

  132. [132]

    MEG II collaboration, A.M. Baldini et al., The design of the MEG II experiment, Eur. Phys. J. C 78 (2018) 380 [arXiv:1801.04688] [INSPIRE].

  133. [133]

    G. Cavoto, A. Papa, F. Renga, E. Ripiccini and C. Voena, The quest for μeγ and its experimental limiting factors at future high intensity muon beams, Eur. Phys. J. C 78 (2018) 37 [arXiv:1707.01805] [INSPIRE].

    ADS  Article  Google Scholar 

  134. [134]

    BaBar collaboration, B. Aubert et al., Searches for lepton flavor violation in the decays τ ±e ± γ and τ ±μ ± γ, Phys. Rev. Lett. 104 (2010) 021802 [arXiv:0908.2381] [INSPIRE].

  135. [135]

    T. Aushev et al., Physics at super B factory, arXiv:1002.5012 [INSPIRE].

  136. [136]

    SINDRUM collaboration, U. Bellgardt et al., Search for the decay μ +e + e + e , Nucl. Phys. B 299 (1988) 1 [INSPIRE].

  137. [137]

    A. Blondel et al., Research proposal for an experiment to search for the decay μeee, arXiv:1301.6113 [INSPIRE].

  138. [138]

    K. Hayasaka et al., Search for lepton flavor violating τ decays into three leptons with 719 million produced τ + τ pairs, Phys. Lett. B 687 (2010) 139 [arXiv:1001.3221] [INSPIRE].

    ADS  Article  Google Scholar 

  139. [139]

    SINDRUM II collaboration, W.H. Bertl et al., A search for muon to electron conversion in muonic gold, Eur. Phys. J. C 47 (2006) 337 [INSPIRE].

  140. [140]

    DeeMe collaboration, T.M. Nguyen, Search for μ-e conversion with DeeMe experiment at J-PARC MLF, PoS(FPCP2015)060.

  141. [141]

    COMET collaboration, B.E. Krikler, An overview of the COMET experiment and its recent progress, arXiv:1512.08564 [INSPIRE].

  142. [142]

    Mu2e collaboration, L. Bartoszek et al., Mu2e technical design report, arXiv:1501.05241 [INSPIRE].

  143. [143]

    Y. Kuno, Prism/Prime, Nucl. Phys. Proc. Suppl. 149 (2005) 376 [INSPIRE].

    ADS  Article  Google Scholar 

  144. [144]

    I. Doršner et al., Physics of leptoquarks in precision experiments and at particle colliders, Phys. Rept. 641 (2016) 1 [arXiv:1603.04993] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  145. [145]

    Y. Kuno and Y. Okada, Muon decay and physics beyond the standard model, Rev. Mod. Phys. 73 (2001) 151 [hep-ph/9909265] [INSPIRE].

  146. [146]

    Y. Okada, K.I. Okumura and Y. Shimizu, μeγ and μ → 3e processes with polarized muons and supersymmetric grand unified theories, Phys. Rev. D 61 (2000) 094001 [hep-ph/9906446] [INSPIRE].

  147. [147]

    S. Davidson, Y. Kuno and A. Saporta, “Spin-dependentμe conversion on light nuclei, Eur. Phys. J. C 78 (2018) 109 [arXiv:1710.06787] [INSPIRE].

    ADS  Article  Google Scholar 

  148. [148]

    R. Kitano, M. Koike and Y. Okada, Detailed calculation of lepton flavor violating muon electron conversion rate for various nuclei, Phys. Rev. D 66 (2002) 096002 [Erratum ibid. D 76 (2007) 059902] [hep-ph/0203110] [INSPIRE].

  149. [149]

    ATLAS collaboration, Search for scalar leptoquarks in pp collisions at \( \sqrt{s}=13 \) TeV with the ATLAS experiment, New J. Phys. 18 (2016) 093016 [arXiv:1605.06035] [INSPIRE].

  150. [150]

    CMS collaboration, Search for third-generation scalar leptoquarks and heavy right-handed neutrinos in final states with two τ leptons and two jets in proton-proton collisions at \( \sqrt{s}=13 \) TeV, JHEP 07 (2017) 121 [arXiv:1703.03995] [INSPIRE].

  151. [151]

    ATLAS collaboration, Further searches for squarks and gluinos in final states with jets and missing transverse momentum at \( \sqrt{s}=13 \) TeV with the ATLAS detector, ATLAS-CONF-2016-078 (2016).

  152. [152]

    ATLAS collaboration, Search for bottom squark pair production in proton–proton collisions at \( \sqrt{s}=13 \) TeV with the ATLAS detector, Eur. Phys. J. C 76 (2016) 547 [arXiv:1606.08772] [INSPIRE].

  153. [153]

    C.D. Froggatt and H.B. Nielsen, Hierarchy of quark masses, Cabibbo angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].

    ADS  Article  Google Scholar 

  154. [154]

    A.E. Cárcamo Hernández, I. de Medeiros Varzielas and E. Schumacher, The 750 GeV diphoton resonance in the light of a 2HDM with S 3 flavour symmetry, arXiv:1601.00661 [INSPIRE].

  155. [155]

    A.E. Cárcamo Hernández, I. de Medeiros Varzielas and E. Schumacher, Fermion and scalar phenomenology of a two-Higgs-doublet model with S 3, Phys. Rev. D 93 (2016) 016003 [arXiv:1509.02083] [INSPIRE].

    Google Scholar 

  156. [156]

    A.E. Cárcamo Hernández, A novel and economical explanation for SM fermion masses and mixings, Eur. Phys. J. C 76 (2016) 503 [arXiv:1512.09092] [INSPIRE].

    Article  Google Scholar 

  157. [157]

    M.D. Campos, A.E. Cárcamo Hernández, H. Päs and E. Schumacher, Higgsμτ as an indication for S 4 flavor symmetry, Phys. Rev. D 91 (2015) 116011 [arXiv:1408.1652] [INSPIRE].

    ADS  Google Scholar 

  158. [158]

    R. Barbieri, G. Isidori, A. Pattori and F. Senia, Anomalies in B-decays and U(2) flavour symmetry, Eur. Phys. J. C 76 (2016) 67 [arXiv:1512.01560] [INSPIRE].

    ADS  Article  Google Scholar 

  159. [159]

    R. Alonso, M. Dhen, M.B. Gavela and T. Hambye, Muon conversion to electron in nuclei in type-I seesaw models, JHEP 01 (2013) 118 [arXiv:1209.2679] [INSPIRE].

    ADS  Article  Google Scholar 

  160. [160]

    P.F. de Salas et al., Status of neutrino oscillations 2018: 3σ hint for normal mass ordering and improved CP sensitivity, Phys. Lett. B 782 (2018) 633 [arXiv:1708.01186] [INSPIRE].

    ADS  Article  Google Scholar 

Download references

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



Corresponding author

Correspondence to Chandan Hati.

Additional information

ArXiv ePrint: 1806.10146

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hati, C., Kumar, G., Orloff, J. et al. Reconciling B-meson decay anomalies with neutrino masses, dark matter and constraints from flavour violation. J. High Energ. Phys. 2018, 11 (2018).

Download citation


  • Beyond Standard Model
  • Heavy Quark Physics
  • Neutrino Physics