Effective theory approach to new physics with flavour: general framework and a leptoquark example

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Extending the Standard Model with higher-dimensional operators in an effective field theory (EFT) approach provides a systematic framework to study new physics (NP) effects from a bottom-up perspective, as long as the NP scale is sufficiently large compared to the energies probed in the experimental observables. However, when taking into account the different quark and lepton flavours, the number of free parameters in- creases dramatically, which makes generic studies of the NP flavour structure infeasible. In this paper, we address this issue in view of the recently observed “flavour anomalies” in B-meson decays, which we take as a motivation to develop a general framework that allows us to systematically reduce the number of flavour parameters in the EFT. This framework can be easily used in global fits to flavour observables at Belle II and LHCb as well as in analyses of flavour-dependent collider signatures at the LHC. Our formalism represents an extension of the well-known minimal-flavour-violation approach, and uses Froggatt-Nielsen charges to define the flavour power-counting. As a relevant illustration of the formalism, we apply it to the flavour structures which could be induced by a U1 vector leptoquark, which represents one of the possible explanations for the recent hints of flavour non-universality in semileptonic B-decays. We study the phenomenological viability of this specific framework performing a fit to low-energy flavour observables.

A preprint version of the article is available at ArXiv.


  1. [1]

    W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys.B 268 (1986) 621 [INSPIRE].

  2. [2]

    B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the Standard Model lagrangian, JHEP10 (2010) 085 [arXiv:1008.4884] [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]

    LHCb collaboration, Test of lepton universality with B 0→ K *0+decays, JHEP08 (2017) 055 [arXiv:1705.05802] [INSPIRE].

  5. [5]

    LHCb collaboration, Search for lepton-universality violation in B +→ K ++decays, Phys. Rev. Lett.122 (2019) 191801 [arXiv:1903.09252] [INSPIRE].

  6. [6]

    LHCb collaboration, Angular analysis of the B 0→ K *0μ +μ decay using 3 fb 1of integrated luminosity, JHEP02 (2016) 104 [arXiv:1512.04442] [INSPIRE].

  7. [7]

    BaBar collaboration, 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].

  8. [8]

    BaBar collaboration, 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].

  9. [9]

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

  10. [10]

    Belle collaboration, 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].

  11. [11]

    Belle collaboration, Measurement of the τ lepton polarization and R(D *) in the decay \( \overline{B}\to {D}^{\ast }{\tau}^{-}{\overline{\nu}}_{\tau } \)with one-prong hadronic τ decays at Belle, Phys. Rev.D 97 (2018) 012004 [arXiv:1709.00129] [INSPIRE].

  12. [12]

    LHCb collaboration, Measurement of the ratio of the B 0→ D *−τ +ν τand B 0→ D *μ +ν μbranching fractions using three-prong τ-lepton decays, Phys. Rev. Lett.120 (2018) 171802 [arXiv:1708.08856] [INSPIRE].

  13. [13]

    LHCb collaboration, Test of lepton flavor universality by the measurement of the B 0→ D *τ +ν τbranching fraction using three-prong τ decays, Phys. Rev.D 97 (2018) 072013 [arXiv:1711.02505] [INSPIRE].

  14. [14]

    Belle collaboration, Measurement of \( \mathcal{R} \)(D) and \( \mathcal{R} \)(D *) with a semileptonic tagging method, arXiv:1904.08794 [INSPIRE].

  15. [15]

    G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: an effective field theory approach, Nucl. Phys.B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].

  16. [16]

    A.J. Buras, Minimal flavor violation, Acta Phys. Polon.B 34 (2003) 5615 [hep-ph/0310208] [INSPIRE].

  17. [17]

    R. Barbier et al., U(2) and minimal flavour violation in supersymmetry, Eur. Phys. J.C 71 (2011) 1725 [arXiv:1105.2296] [INSPIRE].

  18. [18]

    I. de Medeiros Varzielas and G. Hiller, Clues for flavor from rare lepton and quark decays, JHEP06 (2015) 072 [arXiv:1503.01084] [INSPIRE].

  19. [19]

    G. Hiller, D. Loose and K. Schönwald, Leptoquark flavor patterns & B decay anomalies, JHEP12 (2016) 027 [arXiv:1609.08895] [INSPIRE].

  20. [20]

    I. de Medeiros Varzielas and J. Talbert, Simplified models of flavourful leptoquarks, Eur. Phys. J.C 79 (2019) 536 [arXiv:1901.10484] [INSPIRE].

  21. [21]

    T. Feldmann and T. Mannel, Minimal flavour violation and beyond, JHEP02 (2007) 067 [hep-ph/0611095] [INSPIRE].

  22. [22]

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

  23. [23]

    A. Smolkovič, M. Tammaro and J. Zupan, Anomaly free Froggatt-Nielsen models of flavor, JHEP10 (2019) 188 [arXiv:1907.10063] [INSPIRE].

  24. [24]

    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].

  25. [25]

    L. Calibbi, A. Crivellin and T. Li, Model of vector leptoquarks in view of the B-physics anomalies, Phys. Rev.D 98 (2018) 115002 [arXiv:1709.00692] [INSPIRE].

  26. [26]

    R. Barbieri and A. Tesi, B-decay anomalies in Pati-Salam SU(4), Eur. Phys. J.C 78 (2018) 193 [arXiv:1712.06844] [INSPIRE].

  27. [27]

    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].

  28. [28]

    L. Di Luzio et al., Maximal flavour violation: a Cabibbo mechanism for leptoquarks, JHEP11 (2018) 081 [arXiv:1808.00942] [INSPIRE].

  29. [29]

    T. Faber et al., A unified leptoquark model confronted with lepton non-universality in B-meson decays, Phys. Lett.B 787 (2018) 159 [arXiv:1808.05511] [INSPIRE].

  30. [30]

    J. Heeck and D. Teresi, Pati-Salam explanations of the B-meson anomalies, JHEP12 (2018) 103 [arXiv:1808.07492] [INSPIRE].

  31. [31]

    A. Angelescu, D. Bečirević, D.A. Faroughy and O. Sumensari, Closing the window on single leptoquark solutions to the B-physics anomalies, JHEP10 (2018) 183 [arXiv:1808.08179] [INSPIRE].

  32. [32]

    M. Schmaltz and Y.-M. Zhong, The leptoquark Hunter’s guide: large coupling, JHEP01 (2019) 132 [arXiv:1810.10017] [INSPIRE].

  33. [33]

    A. Greljo, J. Martin Camalich and J.D. Ruiz-Álvarez, Mono-τ signatures at the LHC constrain explanations of b-decay anomalies, Phys. Rev. Lett.122 (2019) 131803 [arXiv:1811.07920] [INSPIRE].

  34. [34]

    B. Fornal, S.A. Gadam and B. Grinstein, Left-right SU(4) vector leptoquark model for flavor anomalies, Phys. Rev.D 99 (2019) 055025 [arXiv:1812.01603] [INSPIRE].

  35. [35]

    M.J. Baker, J. Fuentes-Martín, G. Isidori and M. König, High-p Tsignatures in vector–leptoquark models, Eur. Phys. J.C 79 (2019) 334 [arXiv:1901.10480] [INSPIRE].

  36. [36]

    C. Cornella, J. Fuentes-Martin and G. Isidori, Revisiting the vector leptoquark explanation of the B-physics anomalies, JHEP07 (2019) 168 [arXiv:1903.11517] [INSPIRE].

  37. [37]

    L. Da Rold and F. Lamagna, A vector leptoquark for the B-physics anomalies from a composite GUT, JHEP12 (2019) 112 [arXiv:1906.11666] [INSPIRE].

  38. [38]

    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].

  39. [39]

    M. Bordone, C. Cornella, J. Fuentes-Martín and G. Isidori, Low-energy signatures of the PS3model: from B-physics anomalies to LFV, JHEP10 (2018) 148 [arXiv:1805.09328] [INSPIRE].

  40. [40]

    D. Buttazzo, A. Greljo, G. Isidori and D. Marzocca, B-physics anomalies: a guide to combined explanations, JHEP11 (2017) 044 [arXiv:1706.07808] [INSPIRE].

  41. [41]

    R. Alonso, B. Grinstein and J. Martin Camalich, Lepton universality violation and lepton flavor conservation in B-meson decays, JHEP10 (2015) 184 [arXiv:1505.05164] [INSPIRE].

  42. [42]

    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].

  43. [43]

    A. Crivellin, C. Greub, D. Müller and F. Saturnino, Importance of loop effects in explaining the accumulated evidence for new physics in B decays with a vector leptoquark, Phys. Rev. Lett.122 (2019) 011805 [arXiv:1807.02068] [INSPIRE].

  44. [44]

    R. Alonso, B. Grinstein and J. Martin Camalich, SU(2) × U(1) gauge invariance and the shape of new physics in rare B decays, Phys. Rev. Lett.113 (2014) 241802 [arXiv:1407.7044] [INSPIRE].

  45. [45]

    O. Catà and M. Jung, Signatures of a nonstandard Higgs boson from flavor physics, Phys. Rev.D 92 (2015) 055018 [arXiv:1505.05804] [INSPIRE].

  46. [46]

    M. Algueró et al., Emerging patterns of new physics with and without Lepton Flavour Universal contributions, Eur. Phys. J.C 79 (2019) 714 [arXiv:1903.09578] [INSPIRE].

  47. [47]

    J. Aebischer et al., B-decay discrepancies after Moriond 2019, arXiv:1903.10434 [INSPIRE].

  48. [48]

    M. Ciuchini et al., New physics in b → sℓ + confronts new data on lepton universality, Eur. Phys. J.C 79 (2019) 719 [arXiv:1903.09632] [INSPIRE].

  49. [49]

    A.K. Alok et al., Continuing search for new physics in b → sμμ decays: two operators at a time, JHEP06 (2019) 089 [arXiv:1903.09617].

  50. [50]

    S. Fajfer, J.F. Kamenik and I. Nisandzic, On the \( B\to {D}^{\ast}\tau {\overline{\nu}}_{\tau } \)sensitivity to new physics, Phys. Rev.D 85 (2012) 094025 [arXiv:1203.2654] [INSPIRE].

  51. [51]

    MILC collaboration, B → Dℓν form factors at nonzero recoil and |V cb| from 2 + 1-flavor lattice QCD, Phys. Rev.D 92 (2015) 034506 [arXiv:1503.07237] [INSPIRE].

  52. [52]

    HPQCD collaboration, B → Dlν form factors at nonzero recoil and extraction of |V cb|, Phys. Rev.D 92 (2015) 054510 [Erratum ibid.D 93 (2016) 119906] [arXiv:1505.03925] [INSPIRE].

  53. [53]

    J. Fuentes-Martín, G. Isidori, J. Pagès and K. Yamamoto, With or without U(2)? Probing non-standard flavor and helicity structures in semileptonic B decays, Phys. Lett.B 800 (2020) 135080 [arXiv:1909.02519] [INSPIRE].

  54. [54]

    C. Murgui, A. Peñuelas, M. Jung and A. Pich, Global fit to b → cτν transitions, JHEP09 (2019) 103 [arXiv:1904.09311] [INSPIRE].

  55. [55]

    R.-X. Shi et al., Revisiting the new-physics interpretation of the b → cτν data, JHEP12 (2019) 065 [arXiv:1905.08498] [INSPIRE].

  56. [56]

    J. Buchner et al., X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue, Astron. Astrophys.564 (2014) A125 [arXiv:1402.0004] [INSPIRE].

  57. [57]

    UTfit collaboration,

  58. [58]

    Particle Data Group collaboration, Review of particle physics, Phys. Rev.D 98 (2018) 030001.

  59. [59]

    LHCb collaboration, Implications of LHCb measurements and future prospects, Eur. Phys. J.C 73 (2013) 2373 [arXiv:1208.3355] [INSPIRE].

  60. [60]

    Belle-II collaboration, The Belle II physics book, arXiv:1808.10567 [INSPIRE].

  61. [61]

    A. Cerri et al., Report from working group 4, CERN Yellow Rep. Monogr.7 (2019) 867 [arXiv:1812.07638] [INSPIRE].

  62. [62]

    LHCb collaboration, Search for the lepton-flavour-violating decays \( {B}_s^0 \)→ τ ±μ and B 0→ τ ±μ , Phys. Rev. Lett.123 (2019) 211801 [arXiv:1905.06614] [INSPIRE].

  63. [63]

    BaBar collaboration, Searches for the decays B 0→ ℓ ±τ and B +→ ℓ +ν (l = e, μ) using hadronic tag reconstruction, Phys. Rev.D 77 (2008) 091104 [arXiv:0801.0697] [INSPIRE].

  64. [64]

    LHCb collaboration, Physics case for an LHCb Upgrade II — Opportunities in flavour physics and beyond, in the HL-LHC era, arXiv:1808.08865 [INSPIRE].

  65. [65]

    LHCb collaboration, Search for the lepton-flavor violating decays \( {B}_s^0 \)→ e ±μ and B 0→ e ±μ , Phys. Rev. Lett.111 (2013) 141801 [arXiv:1307.4889] [INSPIRE].

  66. [66]

    BNL collaboration, New limit on muon and electron lepton number violation from K0(L) → μ ±e decay, Phys. Rev. Lett.81 (1998) 5734 [hep-ex/9811038] [INSPIRE].

  67. [67]

    LHCb collaboration, Search for the decays \( {B}_s^0 \)→ τ +τ and B 0→ τ +τ , Phys. Rev. Lett.118 (2017) 251802 [arXiv:1703.02508] [INSPIRE].

  68. [68]

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

  69. [69]

    F.U. Bernlochner, Z. Ligeti, M. Papucci and D.J. Robinson, Combined analysis of semileptonic B decays to D and D *: R(D (*)), |V cb| and new physics, Phys. Rev.D 95 (2017) 115008 [arXiv:1703.05330] [INSPIRE].

  70. [70]

    S. Jaiswal, S. Nandi and S.K. Patra, Extraction of |V cb| from B → D (∗)ℓν and the standard model predictions of R(D (*)), JHEP12 (2017) 060 [arXiv:1707.09977] [INSPIRE].

  71. [71]

    Heavy Flavor Averaging Group collaboration, Averages of b-hadron, c-hadron, and τ-lepton properties as of 2018, arXiv:1909.12524, updated results and plots available at

  72. [72]

    D. Bigi, P. Gambino and S. Schacht, R(D *), |V cb| and the heavy quark symmetry relations between form factors, JHEP11 (2017) 061 [arXiv:1707.09509] [INSPIRE].

  73. [73]

    M. Jung and D.M. Straub, Constraining new physics in b → cℓν transitions, JHEP01 (2019) 009 [arXiv:1801.01112] [INSPIRE].

  74. [74]

    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, JHEP02 (2015) 184 [arXiv:1409.4557] [INSPIRE].

  75. [75]

    F. Feruglio, P. Paradisi and A. Pattori, On the importance of electroweak corrections for B anomalies, JHEP09 (2017) 061 [arXiv:1705.00929] [INSPIRE].

  76. [76]

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

  77. [77]

    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].

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Correspondence to Marzia Bordone.

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ArXiv ePrint: 1910.02641

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Bordone, M., Catà, O. & Feldmann, T. Effective theory approach to new physics with flavour: general framework and a leptoquark example. J. High Energ. Phys. 2020, 67 (2020) doi:10.1007/JHEP01(2020)067

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  • Beyond Standard Model
  • Effective Field Theories