Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Data-driven analyses and model-independent fits for present b→sℓℓ results

Tobias Hurth*

Farvah Mahmoudi†

Yann Monceaux‡ and Siavash Neshatpour§

  • Université Claude Bernard Lyon 1, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, UMR 5822, F-69622, Villeurbanne, France; Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland, and Institut Universitaire de France (IUF), 75005 Paris, France

  • *Contact author: tobias.hurth@cern.ch
  • †Contact author: nazila@cern.ch
  • ‡Contact author: y.monceaux@ip2i.in2p3.fr
  • §Contact author: s.neshatpour@ip2i.in2p3.fr

Phys. Rev. D 112, 113003 – Published 15 December, 2025

DOI: https://doi.org/10.1103/bc5h-8jm3

Abstract

We present a critical assessment of the present B anomalies in the exclusive b→sℓℓ mode based on the QCD factorization (QCDf) approach. In particular, we analyze the impact of different local form factor calculations and of the largest bin in the low-q2 region. We also present a model-independent analysis of the new results of the LHCb and CMS experiments on the B→K*μ+μ− angular observables. In addition, we update the global fit by including all b→s observables incorporating the new data from CMS and the LHCb. In these analyses, we use 10% or higher guesstimates of the nonfactorizable power corrections as additional uncertainties, serving as a placeholder for robust estimates of these contributions. Updating earlier results, we also analyze the combined LHCb and CMS data on the B→K*μ+μ− angular observables using data-driven approaches to find indications of whether these tensions between the QCDf predictions and the present data are due to underestimated subleading hadronic contributions or due to new physics effects.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (101)

  1. R. Aaij et al. (LHCb Collaboration), Measurement of lepton universality parameters in B+→K+ℓ+ℓ− and B0→K*0ℓ+ℓ− decays, Phys. Rev. D 108, 032002 (2023).
  2. R. Aaij et al. (LHCb Collaboration), Measurement of form-factor-independent observables in the decay B0→K*0μ+μ−, Phys. Rev. Lett. 111, 191801 (2013).
  3. R. Aaij et al. (LHCb Collaboration), Differential branching fractions and isospin asymmetries of B→K(*)μ+μ− decays, J. High Energy Phys. 06 (2014) 133.
  4. R. Aaij et al. (LHCb Collaboration), Differential branching fraction and angular analysis of Λb0→Λμ+μ− decays, J. High Energy Phys. 06 (2015) 115; 09 (2018) 145(E).
  5. R. Aaij et al. (LHCb Collaboration), Angular analysis and differential branching fraction of the decay Bs0→ϕμ+μ−, J. High Energy Phys. 09 (2015) 179.
  6. R. Aaij et al. (LHCb Collaboration), Angular analysis of the B0→K*0μ+μ− decay using 3  fb−1 of integrated luminosity, J. High Energy Phys. 02 (2015) 104.
  7. R. Aaij et al. (LHCb Collaboration), Measurement of CP-averaged observables in the B0→K*0μ+μ− decay, Phys. Rev. Lett. 125, 011802 (2020).
  8. R. Aaij et al. (LHCb Collaboration), Angular analysis of the B+→K*+μ+μ− decay, Phys. Rev. Lett. 126, 161802 (2021).
  9. R. Aaij et al. (LHCb Collaboration), Angular analysis of the rare decay Bs0→ϕμ+μ−, J. High Energy Phys. 11 (2021) 043.
  10. R. Aaij et al. (LHCb Collaboration), Branching fraction measurements of the rare Bs0→ϕμ+μ− and Bs0→f2′(1525)μ+μ−- decays, Phys. Rev. Lett. 127, 151801 (2021).
  11. A. Hayrapetyan et al. (CMS Collaboration), Angular analysis of the B0→K*(892)0μ+μ− decay in proton-proton collisions at s=13  TeV, Phys. Lett. B 864, 139406 (2025).
  12. LHCb collaboration, LHCb-PAPER-2025-041 (to be published).
  13. M. Beneke, T. Feldmann, and D. Seidel, Systematic approach to exclusive B→Vl+l−, Vγ decays, Nucl. Phys. B612, 25 (2001).
  14. M. Beneke, T. Feldmann, and D. Seidel, Exclusive radiative and electroweak b→d and b→s penguin decays at NLO, Eur. Phys. J. C 41, 173 (2005).
  15. R. Aaij et al. (LHCb Collaboration), Test of lepton universality with B0→K*0ℓ+ℓ− decays, J. High Energy Phys. 08 (2017) 055.
  16. R. Aaij et al. (LHCb Collaboration), Test of lepton universality in beauty-quark decays, Nat. Phys. 18, 277 (2022); 19 1517 (2023).
  17. C. Bobeth, M. Chrzaszcz, D. van Dyk, and J. Virto, Long-distance effects in B→K*ℓℓ from analyticity, Eur. Phys. J. C 78, 451 (2018).
  18. N. Gubernari, D. van Dyk, and J. Virto, Non-local matrix elements in B(s)→{K(*).ϕ}ℓ+ℓ−, J. High Energy Phys. 02 (2020) 088.
  19. N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, Improved theory predictions and global analysis of exclusive b→sμ+μ− processes, J. High Energy Phys. 09 (2022) 133.
  20. A. Gopal and N. Gubernari, Unitarity bounds with subthreshold and anomalous cuts for b-hadron decays, Phys. Rev. D 111, L031501 (2025).
  21. M. Ciuchini, M. Fedele, E. Franco, A. Paul, L. Silvestrini, and M. Valli, Constraints on lepton universality violation from rare B decays, Phys. Rev. D 107, 055036 (2023).
  22. S. Mutke, M. Hoferichter, and B. Kubis, Anomalous thresholds in B→(P,V)γ* form factors, J. High Energy Phys. 07 (2024) 276.
  23. M. L. Piscopo and A. V. Rusov, Non-factorisable effects in the decays B¯s0→Ds+π− and B¯0→D+K− from LCSR, J. High Energy Phys. 10 (2023) 180.
  24. Within the SCET context soft functions which live on both light cones have been recently discussed for exclusive and also for inclusive mode in Refs. [25, 26].

  25. Q. Qin, Y. L. Shen, C. Wang, and Y. M. Wang, Deciphering the long-distance penguin contribution to B¯d,s→γγ decays, Phys. Rev. Lett. 131, 091902 (2023).
  26. R. Bartocci, P. Böer, and T. Hurth, Renormalisation group evolution of the shape function g17 in B¯→Xsγ and B¯→Xsℓ+ℓ− at subleading power, J. High Energy Phys. 04 (2025) 066.
  27. D. Melikhov, Nonfactorizable charming loops in FCNC B decays versus B-decay semileptonic form factors, Phys. Rev. D 106, 054022 (2022).
  28. D. Melikhov, Three-particle distribution in the B meson and charm-quark loops in FCNC B decays, Phys. Rev. D 108, 034007 (2023).
  29. T. Huber, T. Hurth, J. Jenkins, E. Lunghi, Q. Qin, and K. K. Vos, Inclusive B¯→Xsℓ+ℓ− at the LHC: Theory predictions and new-physics reach, J. High Energy Phys. 11 (2024) 130; 05 (2025) 99.
  30. T. Huber, T. Hurth, J. Jenkins, E. Lunghi, Q. Qin, and K. K. Vos, Phenomenology of inclusive B¯→Xsℓ+ℓ− for the Belle II era, J. High Energy Phys. 10 (2020) 088.
  31. W. Altmannshofer et al. (Belle-II Collaboration), The Belle II physics book, Prog. Theor. Exp. Phys. 2019, 123C01 (2019); 2020, 029201(E) (2020).
  32. Y. Amhis and P. Owen, Isospin extrapolation as a method to study inclusive B¯→Xsℓ+ℓ− decays, Eur. Phys. J. C 82, 371 (2022).
  33. Z. L. Liu, B. Mecaj, M. Neubert, and X. Wang, Factorization at subleading power and endpoint divergences in h→γγ decay. Part II. Renormalization and scale evolution, J. High Energy Phys. 01 (2020) 077.
  34. M. Beneke, M. Garny, S. Jaskiewicz, J. Strohm, R. Szafron, L. Vernazza, and J. Wang, Next-to-leading power endpoint factorization and resummation for off-diagonal “gluon” thrust, J. High Energy Phys. 07 (2022) 144.
  35. T. Hurth and R. Szafron, Refactorisation in subleading B¯→Xsγ, Nucl. Phys. B991, 116200 (2023).
  36. T. Hurth, F. Mahmoudi, and S. Neshatpour, Global fits to b→sℓℓ data and signs for lepton non-universality, J. High Energy Phys. 12 (2014) 053.
  37. T. Hurth, F. Mahmoudi, and S. Neshatpour, On the anomalies in the latest LHCb data, Nucl. Phys. B909, 737 (2016).
  38. T. Hurth, C. Langenbruch, and F. Mahmoudi, Direct determination of Wilson coefficients using B0→K*0μ+μ− decays, J. High Energy Phys. 11 (2017) 176.
  39. A. Arbey, T. Hurth, F. Mahmoudi, D. Martínez Santos, and S. Neshatpour, Update on the b→  s anomalies, Phys. Rev. D 100, 015045 (2019).
  40. T. Hurth, F. Mahmoudi, and S. Neshatpour, Model independent analysis of the angular observables in B0→K*0μ+μ− and B+→K*+μ+μ−, Phys. Rev. D 103, 095020 (2021).
  41. T. Hurth, F. Mahmoudi, D. M. Santos, and S. Neshatpour, More indications for lepton nonuniversality in b→sℓ+ℓ−, Phys. Lett. B 824, 136838 (2022).
  42. T. Hurth, F. Mahmoudi, and S. Neshatpour, B anomalies in the post RK(*) era, Phys. Rev. D 108, 115037 (2023).
  43. F. Mahmoudi and Y. Monceaux, Overview of B→K(*)ℓℓ theoretical calculations and uncertainties, Symmetry 16, 1006 (2024).
  44. F. Mahmoudi, T. Hurth, and S. Neshatpour, Present status of b→sℓ+ℓ− anomalies, Nucl. Part. Phys. Proc. 285–286, 39 (2017).
  45. B. Grinstein and D. Pirjol, Exclusive rare B→K*ℓ+ℓ− decays at low recoil: Controlling the long-distance effects, Phys. Rev. D 70, 114005 (2004).
  46. C. Bobeth, G. Hiller, D. van Dyk, and C. Wacker, The decay B→Kℓ+ℓ− at low hadronic recoil and model-independent ΔB=1 constraints, J. High Energy Phys. 01 (2011) 107.
  47. C. Bobeth, G. Hiller, and D. van Dyk, More benefits of semileptonic rare B decays at low recoil: CP violation, J. High Energy Phys. 07 (2011) 067.
  48. A. Greljo, J. Salko, A. Smolkovič, and P. Stangl, Rare b decays meet high-mass Drell-Yan, J. High Energy Phys. 05 (2022) 087.
  49. M. Algueró, A. Biswas, B. Capdevila, S. Descotes-Genon, J. Matias, and M. Novoa-Brunet, To (b)e or not to (b)e: No electrons at LHCb, Eur. Phys. J. C 83, 648 (2023).
  50. M. I. Ali, U. Chattopadhyay, D. K. Ghosh, and N. Rajeev, Constraints on lepton flavor universal and non-universal New Physics in b→sℓ+ℓ− decays: A global SMEFT survey, arXiv:2502.20145.
  51. V. G. Chobanova, T. Hurth, F. Mahmoudi, D. Martinez Santos, and S. Neshatpour, Large hadronic power corrections or new physics in the rare decay B→K*μ+μ−?, J. High Energy Phys. 07 (2017) 025.
  52. S. Neshatpour, V. G. Chobanova, T. Hurth, F. Mahmoudi, and D. Martinez Santos, Direct comparison of global fits to the B→K*μ+μ− data assuming hadronic corrections or new physics, in 52nd Rencontres de Moriond on QCD and High Energy Interactions (2017), pp. 87–90, arXiv:1705.10730.
  53. A. Arbey, T. Hurth, F. Mahmoudi, and S. Neshatpour, Hadronic and new physics contributions to b→s transitions, Phys. Rev. D 98, 095027 (2018).
  54. T. Hurth, F. Mahmoudi, and S. Neshatpour, Implications of the new LHCb angular analysis of B→K*μ+μ−: Hadronic effects or new physics?, Phys. Rev. D 102, 055001 (2020).
  55. M. Algueró, B. Capdevila, A. Crivellin, S. Descotes-Genon, P. Masjuan, J. Matias, M. Novoa Brunet, and J. Virto, Emerging patterns of new physics with and without lepton flavour universal contributions, Eur. Phys. J. C 79, 714 (2019); 80, 511(A) (2020).
  56. M. Bordone, G. isidori, S. Mächler, and A. Tinari, Short- vs. long-distance physics in B→K(*)ℓ+ℓ−: A data-driven analysis, Eur. Phys. J. C 84, 547 (2024).
  57. J. Matias, F. Mescia, M. Ramon, and J. Virto, Complete anatomy of B¯d→K¯*0(→Kπ)l+l− and its angular distribution, J. High Energy Phys. 04 (2012) 104.
  58. S. Descotes-Genon, T. Hurth, J. Matias, and J. Virto, Optimizing the basis of B→K*ll observables in the full kinematic range, J. High Energy Phys. 05 (2013) 137.
  59. S. Neshatpour, T. Hurth, F. Mahmoudi, and D. Martinez Santos, Neutral current B-decay anomalies, Springer Proc. Phys. 292, 11 (2023).
  60. W. Altmannshofer, P. Ball, A. Bharucha, A. J. Buras, D. M. Straub, and M. Wick, Symmetries and asymmetries of B→K*μ+μ− decays in the standard model and beyond, J. High Energy Phys. 01 (2009) 019.
  61. N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, Dispersive analysis of B→K(*) and Bs→ϕ form factors, J. High Energy Phys. 12 (2023) 153; 01 (2025) 125(E).
  62. R. R. Horgan, Z. Liu, S. Meinel, and M. Wingate, Lattice QCD calculation of form factors describing the rare decays B→K*ℓ+ℓ− and Bs→ϕℓ+ℓ−, Phys. Rev. D 89, 094501 (2014).
  63. R. R. Horgan, Z. Liu, S. Meinel, and M. Wingate, Rare B decays using lattice QCD form factors, Proc. Sci., LATTICE2014 (2015) 372 [arXiv:1501.00367].
  64. N. Gubernari, A. Kokulu, and D. van Dyk, B→P and B→V form factors from B-meson light-cone sum rules beyond leading twist, J. High Energy Phys. 01 (2018) 150.
  65. A. Bharucha, D. M. Straub, and R. Zwicky, B→Vℓ+ℓ− in the standard model from light-cone sum rules, J. High Energy Phys. 08 (2015) 098.
  66. A. Khodjamirian, T. Mannel, A. A. Pivovarov, and Y. M. Wang, Charm-loop effect in B→K(*)ℓ+ℓ− and B→K*γ, J. High Energy Phys. 09 (2010) 089.
  67. A. Khodjamirian, T. Mannel, and Y. M. Wang, B→Kℓ+ℓ− decay at large hadronic recoil, J. High Energy Phys. 02 (2012) 010.
  68. H. M. Asatrian, C. Greub, and J. Virto, Exact NLO matching and analyticity in b→sℓℓ, J. High Energy Phys. 04 (2019) 012.
  69. The LHCb Collaboration provides the data in six different configurations; in this work, unless otherwise stated, we consider configuration 2, which includes the Pi(′) observables.

  70. F. Mahmoudi, SuperIso: A Program for calculating the isospin asymmetry of B→K*γ in the MSSM, Comput. Phys. Commun. 178, 745 (2008).
  71. F. Mahmoudi, SuperIso v2.3: A Program for calculating flavor physics observables in Supersymmetry, Comput. Phys. Commun. 180, 1579 (2009).
  72. F. Mahmoudi, SuperIso v3.0, flavor physics observables calculations: Extension to NMSSM, Comput. Phys. Commun. 180, 1718 (2009).
  73. S. Neshatpour and F. Mahmoudi, Flavour physics phenomenology with superiso, Proc. Sci., CompTools2021 (2022) 010.
  74. C. Bouchard, G. P. Lepage, C. Monahan, H. Na, and J. Shigemitsu (HPQCD Collaboration), Rare decay B→Kℓ+ℓ− form factors from lattice QCD, Phys. Rev. D 88, 054509 (2013); 88, 079901(E) (2013).
  75. In CXY, X refers to the chirality of the quark current and Y to the chirality of the lepton current. Thus, we have δCLL≡δC9=−δC10, δCRL≡δC9′=−δC10′, δCRR≡δC9′=δC10′, δCLR≡δC9=δC10.

  76. S. S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Stat. 9, 60 (1938).
  77. M. Ciuchini, M. Fedele, E. Franco, S. Mishima, A. Paul, L. Silvestrini, and M. Valli, B→K*ℓ+ℓ− decays at large recoil in the standard model: A theoretical reappraisal, J. High Energy Phys. 06 (2015) 116.
  78. S. Jäger and J. Martin Camalich, On B→Vℓℓ at small dilepton invariant mass, power corrections, and new physics, J. High Energy Phys. 05 (2012) 043.
  79. S. Jäger and J. Martin Camalich, Reassessing the discovery potential of the B→K*ℓ+ℓ− decays in the large-recoil region: SM challenges and BSM opportunities, Phys. Rev. D 93, 014028 (2016).
  80. M. Ciuchini, A. M. Coutinho, M. Fedele, E. Franco, A. Paul, L. Silvestrini, and M. Valli, On flavourful easter eggs for new physics hunger and lepton flavour universality violation, Eur. Phys. J. C 77, 688 (2017).
  81. See Supplemental Material at http://link.aps.org/supplemental/10.1103/bc5h-8jm3 for the different sets of observables used.
  82. S. Banerjee et al. (Heavy Flavor Averaging Group (HFLAV) Collaboration), Averages of b-hadron, c-hadron, and τ-lepton properties as of 2023, arXiv:2411.18639.
  83. S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  84. R. Aaij et al. (LHCb Collaboration), Search for the rare decays Bs0→e+e− and B0→e+e−, Phys. Rev. Lett. 124, 211802 (2020).
  85. J. P. Lees et al. (BABAR Collaboration, Measurement of the B→Xsl+l− branching fraction and search for direct CP violation from a sum of exclusive final states, Phys. Rev. Lett. 112, 211802 (2014).
  86. A. Abdesselam et al. (Belle Collaboration), Test of lepton-flavor universality in B→K*ℓ+ℓ− decays at Belle, Phys. Rev. Lett. 126, 161801 (2021).
  87. R. Aaij et al. (LHCb Collaboration), Angular analysis of charged and neutral B→Kμ+μ− decays, J. High Energy Phys. 05 (2014) 082.
  88. R. Aaij et al. (LHCb Collaboration), Angular moments of the decay Λb0→Λμ+μ− at low hadronic recoil, J. High Energy Phys. 09 (2018) 146.
  89. R. Aaij et al. (LHCb Collaboration), Tests of lepton universality using B0→KS0ℓ+ℓ− and B+→K*+ℓ+ℓ− decays, Phys. Rev. Lett. 128, 191802 (2022).
  90. S. Choudhury et al. (BELLE Collaboration), Test of lepton flavor universality and search for lepton flavor violation in B→Kℓℓ decays, J. High Energy Phys. 03 (2019) 105.
  91. A. M. Sirunyan et al. (CMS Collaboration), Angular analysis of the decay B+→ K+μ+μ− in proton-proton collisions at s=8  TeV, Phys. Rev. D 98, 112011 (2018).
  92. R. Aaij et al. (LHCb Collaboration), Measurement of the B0→K*0e+e− branching fraction at low dilepton mass, J. High Energy Phys. 05 (2013) 159.
  93. R. Aaij et al. (LHCb Collaboration), Strong constraints on the b→sγ photon polarisation from B0→K*0e+e− decays, J. High Energy Phys. 12 (2020) 081.
  94. A. Hayrapetyan et al. (CMS Collaboration), Test of lepton flavor universality in B±→ K±μ+μ− and B±→ K±e+e− decays in proton-proton collisions at s=13  TeV, Rep. Prog. Phys. 87, 077802 (2024).
  95. R. Aaij et al. (LHCb Collaboration), Test of lepton flavour universality with Bs0→ϕℓ+ℓ− decays, Phys. Rev. Lett. 134, 121803 (2025).
  96. R. Aaij et al. (LHCb Collaboration), Constraints on the photon polarisation in b→sγ transitions using Bs0→ϕe+e− decays, J. High Energy Phys. 03 (2025) 047.
  97. D. Ferlewicz et al. (Belle Collaboration), Angular analysis of B→K*e+e− in the low-q2 region with new electron identification at Belle, Phys. Rev. D 110, 072005 (2024).
  98. R. Aaij et al. (LHCb Collaboration), Angular analysis of B0→K*0e+e− decays, J. High Energy Phys. 06 (2025) 140.
  99. J. A. Bailey et al., B→Kl+l− decay form factors from three-flavor lattice QCD, Phys. Rev. D 93, 025026 (2016).
  100. W. G. Parrott, C. Bouchard, and C. T. H. Davies (HPQCD Collaboration), B→K and D→K form factors from fully relativistic lattice QCD, Phys. Rev. D 107, 014510 (2023).
  101. A. Khodjamirian and A. V. Rusov, Bs→Kℓνℓ and B(s)→π(K)ℓ+ℓ− decays at large recoil and CKM matrix elements, J. High Energy Phys. 08 (2017) 112.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation