Open Access

Probing unknown nonperturbative effects in $b \to s ℓ ℓ$ with inclusive and exclusive observables

P. Alvarez-Cartelle ^1,*, B. Capdevila ^2,†, E. Lunghi ^3,‡, and J. Matias ^4,§

¹Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain and Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
²Departament de Física Quántica i Astrofísica, Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí Franquès 1, E08028 Barcelona
³Physics Department, Indiana University, Bloomington, Indiana 47405, USA
⁴Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona and Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, Barcelona

^*Contact author: paula.alvarez@usc.es
^†Contact author: bcapdevila@icc.ub.edu
^‡Contact author: elunghi@iu.edu
^§Contact author: matias@ifae.es

Phys. Rev. D 114, 073009 – Published 30 October, 2026

DOI: https://doi.org/10.1103/zrp8-84fg

Abstract

In this paper we revisit, from a different perspective, a long-standing question: “Is the systematic deficit observed in all branching ratios mediated by a $b \to s μ μ$ transition due to new physics, or to a hypothetical constant unknown universal hadronic contribution that mimics new physics?” The key observation that allows us to distinguish between these two possibilities is that nonperturbative contributions associated with $c \bar{c}$ loops affect inclusive $B \to X_{s} ℓ ℓ$ and exclusive $B \to K^{(*)} ℓ ℓ$ modes differently. In inclusive decays, factorizable contributions are exactly determined from data on $e^{+} e^{-} \to hadrons$ , while nonfactorizable corrections are described by resolved-photon contributions at low $q^{2}$ and by local power corrections at high $q^{2}$ . In exclusive decays, by contrast, hypothetical charming-penguin effects, beyond those already included in current uncertainty estimates, could appear, in a worst-case scenario, as a constant, universal contribution that it seems, in principle, indistinguishable from genuine new physics. We identify two observables, constructed from ratios of exclusive to inclusive modes, that can discriminate between a new physics contribution and a constant hadronic contribution. Moreover, these ratios can be measured directly by LHCb, as they do not require any normalization to $J / ψ K^{(*)}$ branching fractions from B factories. A preliminary evaluation of these observables with present data shows some preference for the new physics interpretation. In a complementary test, a comparison between inclusive measurements and the corresponding sum of exclusive modes at high $q^{2}$ similarly disfavors an explanation based on a constant hadronic contribution. Finally, we provide projections for the new observables based on expected LHCb and Belle II measurements in the near future.

Physics Subject Headings (PhySH)

Article Text

References (69)

LHCb Collaboration, Comprehensive analysis of the $B^{0} \to K^{* 0} μ^{+} μ^{-}$ decay, Phys. Rev. Lett. 137, 021802 (2026).
CMS Collaboration, Angular analysis of the $B^{0} \to K^{*} (892)^{0} μ^{+} μ^{-}$ decay in proton-proton collisions at $\sqrt{s} = 13 TeV$ , Phys. Lett. B 864, 139406 (2025).
A. Khodjamirian, T. Mannel, A. A. Pivovarov, and Y. M. Wang, Charm-loop effect in $B \to K^{(*)} ℓ^{+} ℓ^{-}$ and $B \to K^{*} γ$ , J. High Energy Phys. 09 (2010) 089.
N. Gubernari, A. Kokulu, and D. van Dyk, $B \to P$ and $B \to V$ form factors from $B$ -meson light-cone sum rules beyond leading twist, J. High Energy Phys. 01 (2019) 150.
A. Bharucha, D. M. Straub, and R. Zwicky, $B \to V ℓ^{+} ℓ^{-}$ in the standard model from light-cone sum rules, J. High Energy Phys. 08 (2016) 098.
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].
HPQCD Collaboration, $B \to K$ and $D \to K$ form factors from fully relativistic lattice QCD, Phys. Rev. D 107, 014510 (2023).
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).
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).
T. Hurth, F. Mahmoudi, Y. Monceaux, and S. Neshatpour, Data-driven analyses and model-independent fits for present $b \to s ℓ ℓ$ results, Phys. Rev. D 112, 113003 (2025).
N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, Improved theory predictions and global analysis of exclusive $b \to s μ^{+} μ^{-}$ processes, J. High Energy Phys. 09 (2022) 133.
N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, Dispersive analysis of $B \to K^{(*)}$ and $B_{s} \to ϕ$ form factors, J. High Energy Phys. 12 (2023) 153.
J. Matias, F. Mescia, M. Ramon, and J. Virto, Complete anatomy of ${\bar{B}}_{d} \to {\bar{K}}^{* 0} (\to K π) l^{+} l^{-}$ and its angular distribution, J. High Energy Phys. 04 (2012) 104.
S. Descotes-Genon, T. Hurth, J. Matias, and J. Virto, Optimizing the basis of $B \to K^{*} l l$ observables in the full kinematic range, J. High Energy Phys. 05 (2013) 137.
HPQCD Collaboration, Standard model predictions for $B \to K ℓ^{+} ℓ^{-}$ , $B \to K ℓ_{1}^{-} ℓ_{2}^{+}$ and $B \to K ν \bar{ν}$ using form factors from Nf = 2 + 1 + 1 lattice QCD, Phys. Rev. D 107, 014511 (2023).
G. Isidori, Z. Polonsky, and A. Tinari, Explicit estimate of charm rescattering in $B^{0} \to K^{0} \bar{ℓ} ℓ$ , Phys. Rev. D 111, 093007 (2025).
G. Isidori, Z. Polonsky, and A. Tinari, Charm rescattering in $B^{0} \to K^{0} \bar{ℓ} ℓ$ : An improved analysis, Eur. Phys. J. C 85, 1221 (2025).
H. M. Asatrian, C. Greub, and J. Virto, Exact NLO matching and analyticity in $b \to s ℓ ℓ$ , J. High Energy Phys. 04 (2020) 012.
M. Beylich, G. Buchalla, and T. Feldmann, Theory of $B \to K^{(*)} ℓ^{+} ℓ^{-}$ decays at high $q^{2}$ : OPE and quark-hadron duality, Eur. Phys. J. C 71, 1635 (2011).
M. Bordone, G. Isidori, S. Mächler, and A. Tinari, Short- vs long-distance physics in $B \to K^{(*)} ℓ^{+} ℓ^{-}$ : A data-driven analysis, Eur. Phys. J. C 84, 547 (2024).
M. Hoferichter, B. Kubis, and S. Mutke, Reconciling hadronic and partonic analyticity in $b \to s ℓ ℓ$ transitions, Phys. Lett. B 881, 140841 (2026).
W. Altmannshofer, S. G. Christensen, and P. Stangl, Large Hadronic Effects in $B \to K^{*} μ μ$ ?, arXiv:2603.27753.
T. Huber, T. Hurth, J. Jenkins, E. Lunghi, Q. Qin, and K. K. Vos, Phenomenology of inclusive $\bar{B} \to X_{s} ℓ^{+} ℓ^{-}$ for the Belle II era, J. High Energy Phys. 10 (2020) 088.
G. Isidori, Z. Polonsky, and A. Tinari, Semi-inclusive $b \to s ℓ^{-} ℓ$ transitions at high $q^{2}$ , Phys. Rev. D 108, 093008 (2023).
T. Huber, T. Hurth, J. Jenkins, E. Lunghi, Q. Qin, and K. K. Vos, Inclusive $\bar{B} \to X_{s} ℓ^{+} ℓ^{-}$ at the LHC: Theory predictions and new-physics reach, J. High Energy Phys. 11 (2024) 130.
G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68, 1125 (1996).
B. Grinstein, R. P. Springer, and M. B. Wise, Effective Hamiltonian for weak radiative B meson decay, Phys. Lett. B 202, 138 (1988).
B. Capdevila, A. Crivellin, S. Descotes-Genon, J. Matias, and J. Virto, Patterns of new physics in $b \to s ℓ^{+} ℓ^{-}$ transitions in the light of recent data, J. High Energy Phys. 01 (2018) 093.
A. Hardmeier, E. Lunghi, D. Pirjol, and D. Wyler, Subleading collinear operators and their matrix elements, Nucl. Phys. B682, 150 (2004).
T. Becher, R. J. Hill, and M. Neubert, Soft collinear messengers: A new mode in soft collinear effective theory, Phys. Rev. D 69, 054017 (2004).
S. Descotes-Genon, L. Hofer, J. Matias, and J. Virto, Global analysis of $b \to s ℓ ℓ$ anomalies, J. High Energy Phys. 06 (2016) 092.
M. Algueró, B. Capdevila, A. Crivellin, S. Descotes-Genon, P. Masjuan, J. Matias, and J. Virto, Emerging patterns of new physics with and without lepton flavor universal contributions, Eur. Phys. J. C 79, 714 (2019).
M. Beneke, T. Feldmann, and D. Seidel, Systematic approach to exclusive $B \to V l^{+} l^{-}$ , $V γ$ decays, Nucl. Phys. B612, 25 (2001).
C. Bobeth, M. Chrzaszcz, D. van Dyk, and J. Virto, Long-distance effects in $B \to K^{*} ℓ ℓ$ from analyticity, Eur. Phys. J. C 78, 451 (2018).
N. Gubernari, D. van Dyk, and J. Virto, Nonlocal matrix elements in $B_{(s)} \to {K^{(*)}, ϕ} ℓ^{+} ℓ^{-}$ , J. High Energy Phys. 02 (2021) 088.
B. Grinstein and D. Pirjol, Exclusive rare $B \to K^{*} ℓ^{+} ℓ^{-}$ decays at low recoil: Controlling the long-distance effects, Phys. Rev. D 70, 114005 (2004).
F. Kruger and L. M. Sehgal, Lepton polarization in the decays $b \to X_{d} μ^{+} μ^{-}$ and $B \to X_{s} τ^{+} τ^{-}$ , Phys. Lett. B 380, 199 (1996).
C. Bobeth, G. Hiller, and D. van Dyk, The benefits of $\bar{B} \to {\bar{K}}^{*} l^{+} l^{-}$ decays at low recoil, J. High Energy Phys. 07 (2010) 098.
M. Beneke, G. Buchalla, M. Neubert, and C. T. Sachrajda, Penguins with charm and quark-hadron duality, Eur. Phys. J. C 61, 439 (2009).
G. Buchalla, G. Isidori, and S. J. Rey, Corrections of order $Λ_{QCD}^{2} / m_{c}^{2}$ to inclusive rare B decays, Nucl. Phys. B511, 594 (1998).
T. Hurth, M. Fickinger, S. Turczyk, and M. Benzke, Resolved power corrections to the inclusive decay $\bar{B} \to X_{s} ℓ^{+} ℓ^{-}$ , Nucl. Part. Phys. Proc. 285–286, 57 (2017).
M. Benzke, T. Hurth, and S. Turczyk, Subleading power factorization in $\bar{B} \to X_{s} ℓ^{+} ℓ^{-}$ , J. High Energy Phys. 10 (2017) 031.
M. Benzke and T. Hurth, Resolved $1 / m_{b}$ contributions to $\bar{B} \to X_{s, d} ℓ^{+} ℓ^{-}$ and $\bar{B} \to X_{s} γ$ , Phys. Rev. D 102, 114024 (2020).
Z. Ligeti and F. J. Tackmann, Precise predictions for $B \to X_{s} l^{+} l^{-}$ in the large $q^{2}$ region, Phys. Lett. B 653, 404 (2007).
Belle Collaboration, Measurement of differential branching fractions of inclusive $B \to X_{u} ℓ^{+} ν_{ℓ}$ decays, Phys. Rev. Lett. 127, 261801 (2021).
BABAR Collaboration, Measurement of the $B \to X_{s} ℓ^{+} ℓ^{-}$ branching fraction with a sum over exclusive modes, Phys. Rev. Lett. 93, 081802 (2004).
BABAR Collaboration, Measurement of the $B \to X_{s} l^{+} l^{-}$ branching fraction and search for direct $C P$ violation from a sum of exclusive final states, Phys. Rev. Lett. 112, 211802 (2014).
Belle Collaboration, Improved measurement of the electroweak penguin process $B \to X_{s} l^{+} l^{-}$ , Phys. Rev. D 72, 092005 (2005).
Belle Collaboration, Measurement of the lepton forward-backward asymmetry in $B \to X_{s} ℓ^{+} ℓ^{-}$ decays with a sum of exclusive modes, Phys. Rev. D 93, 032008 (2016).
Z. Wang (Belle-II Collaboration), Measurement of inclusive $B \to X_{s} ℓ^{+} ℓ^{-}$ branching fractions at Belle II, in Talk at 2025 Rencontres de Moriond, Electroweak Interactions and Unified Theories.
L. Leskovec, S. Meinel, M. Petschlies, J. Negele, S. Paul, and A. Pochinsky, $B \to ρ ℓ ν^{-}$ resonance form factors from $B \to π π ℓ ν^{-}$ in lattice QCD, Phys. Rev. Lett. 134, 161901 (2025).
P. Boyle, F. Erben, V. Gülpers, M. T. Hansen, F. Joswig, M. Marshall, N. P. Lachini, and A. Portelli, Light and strange vector resonances from lattice QCD at physical quark masses, Phys. Rev. Lett. 134, 111901 (2025).
Q.-Z. Li, C. Liu, L. Liu, P. Sun, J.-J. Wu, Z. Xiao et al., Lattice QCD study of the $K^{*} (892)$ resonance at the physical point, arXiv:2603.16266.
Belle-II Collaboration, Measurement of inclusive $B \to X_{u} ℓ ν$ partial branching fractions and $| V_{u b} |$ at Belle II, Phys. Rev. D 113, 032004 (2026).
A. Broggio, B. Capdevila, A. Ferroglia, and P. Gambino, Structure functions for the inclusive semileptonic $b$ -quark decay at NNLO: A semi-analytic calculation, J. High Energy Phys. 06 (2026) 121.
L. Chen, X. Chen, X. Guan, and Y.-Q. Ma, Triple differential heavy-to-light semi-leptonic decays at next-to-next-to-next-to-leading order in QCD, arXiv:2602.11537.
M. Black, R. V. Harlander, J. T. Kohnen, F. Lange, A. Rago, A. Shindler et al., Bag parameters for heavy meson lifetimes, arXiv:2603.28516.
M. Black, R. V. Harlander, J. T. Kohnen, F. Lange, A. Rago, A. Shindler et al., Heavy-meson bag parameters using gradient flow, arXiv:2603.28517.
Particle Data Group, Review of particle physics, Phys. Rev. D 110, 030001 (2024).
Heavy Flavor Averaging Group (HFLAV, Averages of $b$ -hadron, $c$ -hadron, and $τ$ -lepton properties as of 2023, Phys. Rev. D 113, 012008 (2026).
F. Bernlochner, M. Jung, M. Khan, G. Landsberg, and Z. Ligeti, Novel approaches to determine $B^{\pm}$ and $B^{0}$ meson production fractions, Phys. Rev. D 110, 014007 (2024).
M. Jung and S. Schacht, $\bar{B} \to D^{(*)} ℓ \bar{ν}$ branching ratios and evidence for isospin breaking in $ϒ (4 S)$ decays, arXiv:2604.08391.
Belle Collaboration, Measurement of the $B^{+} / B^{0}$ production ratio in $e^{+} e^{-}$ collisions at the $ϒ (4 S)$ resonance using $B \to J / ψ (ℓ ℓ) K$ decays at Belle, Phys. Rev. D 107, L031102 (2023).
R. Fleischer and T. Mannel, General analysis of new physics in $B \to J / ψ K$ , Phys. Lett. B 506, 311 (2001).
LHCb Collaboration, Differential branching fractions and isospin asymmetries of $B \to K^{(*)} μ^{+} μ^{-}$ decays, J. High Energy Phys. 06 (2014) 133.
LHCb Collaboration, Measurements of the S-wave fraction in $B^{0} \to K^{+} π^{-} μ^{+} μ^{-}$ decays and the $B^{0} \to K^{*} (892)^{0} μ^{+} μ^{-}$ differential branching fraction, J. High Energy Phys. 11 (2016) 047.
CMS Collaboration, Test of lepton flavor universality in $B^{\pm} \to K^{\pm} μ^{+} μ^{-}$ and $B^{\pm} \to K^{\pm} e^{+} e^{-}$ decays in proton-proton collisions at $\sqrt{s} = 13 TeV$ , Rep. Prog. Phys. 87, 077802 (2024).
Belle Collaboration, Observation of a new charged charmoniumlike state in ${\bar{B}}^{0} \to J / ψ K^{-} π^{+}$ decays, Phys. Rev. D 90, 112009 (2014).
LHCb Collaboration, First observations of the rare decays $B^{+} \to K^{+} π^{+} π^{-} μ^{+} μ^{-}$ and $B^{+} \to ϕ K^{+} μ^{+} μ^{-}$ , J. High Energy Phys. 10 (2014) 064.

Phys. Rev. D 114, 073009– Published 30 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 12 May 2026
Accepted 4 September 2026

DOI: https://doi.org/10.1103/zrp8-84fg

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Probing unknown nonperturbative effects in $b \to s ℓ ℓ$ with inclusive and exclusive observables

Abstract

Physics Subject Headings (PhySH)

Article Text

References (69)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Probing unknown nonperturbative effects in b→sℓℓ with inclusive and exclusive observables

Abstract

Physics Subject Headings (PhySH)

Article Text

References (69)

Probing unknown nonperturbative effects in $b \to s ℓ ℓ$ with inclusive and exclusive observables