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


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].

    ADS  Article  MATH  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    Article  Google Scholar 

  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].

    Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  30. [30]

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

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    Article  ADS  MathSciNet  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  Google Scholar 

  57. [57]

    UTfit collaboration, http://www.utfit.org/UTfit/WebHome.

  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].

    Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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 https://hflav.web.cern.ch/.

  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].

    ADS  Article  Google Scholar 

  73. [73]

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

    ADS  Article  Google Scholar 

  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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  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].

    ADS  Article  Google Scholar 

  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].

    ADS  Article  Google Scholar 

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Correspondence to Marzia Bordone.

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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). https://doi.org/10.1007/JHEP01(2020)067

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  • Beyond Standard Model
  • Effective Field Theories