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Unraveling new physics effects in $b \to s ℓ_{1} ℓ_{2}$ transitions with a model-independent perspective

Aishwarya Bhatta ^1,*, Dhiren Panda ^2,†, and Rukmani Mohanta ^2,‡

¹National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha, India
²School of Physics, University of Hyderabad, Hyderabad-500046, India

^*Contact author: aishwaryabhatta@niser.ac.in
^†Contact author: pandadhiren530@gmail.com
^‡Contact author: rmsp@uohyd.ac.in

Phys. Rev. D 112, 075006 – Published 3 October, 2025

DOI: https://doi.org/10.1103/g2ck-lkmx

Abstract

Motivated by recent anomalies in observables associated with flavor-changing neutral current transitions, specifically $b \to s ℓ^{+} ℓ^{-}$ processes, we present a comprehensive analysis of lepton flavor-violating (LFV) decay modes mediated by $b \to s ℓ_{1} ℓ_{2}$ transitions with $ℓ_{1} \neq ℓ_{2}$ . While such LFV processes are forbidden within the standard model, they naturally arise in several of its extensions, including models featuring additional vectorlike fermions and extra $Z^{'}$ bosons. Employing the most general effective Hamiltonian for $b \to s ℓ_{1} ℓ_{2}$ transitions, we derive the angular distributions of the relevant decay modes. Adopting a model-independent framework, we systematically study the LFV decays $B \to K^{*} ℓ_{1} ℓ_{2}$ , $B_{s} \to ϕ ℓ_{1} ℓ_{2}$ , $B \to K_{2}^{*} ℓ_{1} ℓ_{2}$ , and $Λ_{b} \to Λ ℓ_{1} ℓ_{2}$ . Although LFV mesonic decays have been widely explored, the corresponding baryonic decays remain comparatively underinvestigated. We provide bounds on the branching ratio ( $B$ ), forward-backward asymmetry ( $A_{F B}$ ), and longitudinal lepton polarization fraction ( $F_{L}$ ). Furthermore, considering the projected sensitivities of the LHCb upgrade and Belle II experiments, we estimate upper limits for these observables, offering promising avenues for probing new physics in these LFV channels.

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References (102)

R. Aaij et al., Test of lepton universality in beauty-quark decays, Nat. Phys. 18, 277 (2022).
R. Aaij et al., Test of lepton universality with $B^{0} \to K^{* 0} ℓ^{+} ℓ^{-}$ decays, J. High Energy Phys. 08 (2017) 055.
R. Aaij et al., Measurement of $C P$ -averaged observables in the $B^{0} \to K^{* 0} μ^{+} μ^{-}$ decay, Phys. Rev. Lett. 125, 011802 (2020).
R. Aaij et al., Test of lepton universality in $b \to s ℓ^{+} ℓ^{-}$ decays, Phys. Rev. Lett. 131, 051803 (2023).
R. Aaij et al., Measurement of lepton universality parameters in $B^{+} \to K^{+} ℓ^{+} ℓ^{-}$ and $B^{0} \to K^{* 0} ℓ^{+} ℓ^{-}$ decays, Phys. Rev. D 108, 032002 (2023).
R. Aaij et al., Measurement of form-factor-independent observables in the decay $B^{0} \to K^{* 0} μ^{+} μ^{-}$ , Phys. Rev. Lett. 111, 191801 (2013).
R. Aaij et al., Angular analysis of the $B^{0} \to K^{* 0} μ^{+} μ^{-}$ decay using $3 {fb}^{- 1}$ of integrated luminosity, J. High Energy Phys. 02 (2016) 104.
M. Aaboud et al., Angular analysis of $B_{d}^{0} \to K^{*} μ^{+} μ^{-}$ decays in $p p$ collisions at $\sqrt{s} = 8 TeV$ with the ATLAS detector, J. High Energy Phys. 10 (2018) 047.
A. M. Sirunyan et al., Measurement of angular parameters from the decay $B^{0} \to K^{* 0} μ^{+} μ^{-}$ in proton-proton collisions at $\sqrt{s} = 8 TeV$ , Phys. Lett. B 781, 517 (2018).
A. Abdesselam et al., Angular analysis of $B^{0} \to K^{*} (892)^{0} ℓ^{+} ℓ^{-}$ , in LHC Ski 2016: A First Discussion of 13 TeV Results, arXiv:1607.01212.
R. Aaij et al., Test of lepton universality in beauty-quark decays, Nat. Phys. 18 277 (2022).
R. Aaij et al., Angular analysis of the $B^{+} \to K^{* +} μ^{+} μ^{-}$ decay, Phys. Rev. Lett. 126, 161802 (2021).
R. Aaij et al., Measurement of $C P$ -averaged observables in the $B^{0} \to K^{* 0} μ^{+} μ^{-}$ decay, Phys. Rev. Lett. 125, 011802 (2020).
R. Aaij et al., Test of lepton universality using $B^{+} \to K^{+} ℓ^{+} ℓ^{-}$ decays, Phys. Rev. Lett. 113, 151601 (2014).
R. Aaij et al., Test of lepton universality with $B^{0} \to K^{* 0} ℓ^{+} ℓ^{-}$ decays, J. High Energy Phys. 08 (2017) 055.
R. Aaij et al., Search for lepton-universality violation in $B^{+} \to K^{+} ℓ^{+} ℓ^{-}$ decays, Phys. Rev. Lett. 122, 191801 (2019).
R. Aaij et al., Angular analysis of the $B^{0} \to K^{* 0} μ^{+} μ^{-}$ decay using $3 {fb}^{- 1}$ of integrated luminosity, J. High Energy Phys. 02 (2016) 104.
J. P. Lees et al., Evidence for an excess of $\bar{B} \to D^{(*)} τ^{-} {\bar{ν}}_{τ}$ decays, Phys. Rev. Lett. 109, 101802 (2012).
J. P. Lees et al., Measurement of an excess of $\bar{B} \to D^{(*)} τ^{-} {\bar{ν}}_{τ}$ decays and implications for charged Higgs bosons, Phys. Rev. D 88, 072012 (2013).
R. Aaij et al., Measurement of the ratio of branching fractions $B ({\bar{B}}^{0} \to D^{* +} τ^{-} {\bar{ν}}_{τ}) / B ({\bar{B}}^{0} \to D^{* +} μ^{-} {\bar{ν}}_{μ})$ , Phys. Rev. Lett. 115, 111803 (2015); 115, 159901(E) (2015).
S. Hirose et al., Measurement of the $τ$ lepton polarization and $R (D^{*})$ in the decay $\bar{B} \to D^{*} τ^{-} {\bar{ν}}_{τ}$ , Phys. Rev. Lett. 118, 211801 (2017).
S. Hirose et al., Measurement of the $τ$ lepton polarization and $R (D^{*})$ in the decay $\bar{B} \to D^{*} τ^{-} {\bar{ν}}_{τ}$ with one-prong hadronic $τ$ decays at Belle, Phys. Rev. D 97, 012004 (2018).
R. Aaij et al., Measurement of the ratio of the $B^{0} \to D^{* -} τ^{+} ν_{τ}$ and $B^{0} \to D^{* -} μ^{+} ν_{μ}$ branching fractions using three-prong $τ$ -lepton decays, Phys. Rev. Lett. 120, 171802 (2018).
R. Aaij et al., Test of lepton flavor universality by the measurement of the $B^{0} \to D^{* -} τ^{+} ν_{τ}$ branching fraction using three-prong $τ$ decays, Phys. Rev. D 97, 072013 (2018).
G. Caria et al. (Belle Collaboration), Measurement of $ℛ (D)$ and $ℛ (D^{*})$ with a semileptonic tagging method, Phys. Rev. Lett. 124, 161803 (2020).
C.-J. Lee and J. Tandean, Minimal lepton flavor violation implications of the $b \to s$ anomalies, J. High Energy Phys. 08 (2015) 123.
W. Altmannshofer and I. Yavin, Predictions for lepton flavor universality violation in rare B decays in models with gauged $L_{μ} - L_{τ}$ , Phys. Rev. D 92, 075022 (2015).
A. Crivellin, G. D’Ambrosio, and J. Heeck, Explaining $h \to μ^{\pm} τ^{\mp}$ , $B \to K^{*} μ^{+} μ^{-}$ and $B \to K μ^{+} μ^{-} / B \to K e^{+} e^{-}$ in a two-Higgs-doublet model with gauged $L_{μ} - L_{τ}$ , Phys. Rev. Lett. 114, 151801 (2015).
R. Alonso, B. Grinstein, and J. Martin Camalich, Lepton universality violation and lepton flavor conservation in $B$ -meson decays, J. High Energy Phys. 10 (2015) 184.
D. Guadagnoli, D. Melikhov, and M. Reboud, More lepton flavor violating observables for LHCb’s Run 2, Phys. Lett. B 760, 442 (2016).
R. Aaij et al., Search for the lepton-flavour-violating decays $B_{s}^{0} \to τ^{\pm} μ^{\mp}$ and $B^{0} \to τ^{\pm} μ^{\mp}$ , Phys. Rev. Lett. 123, 211801 (2019).
R. Aaij et al., Search for lepton-flavor violating decays $B^{+} \to K^{+} μ^{\pm} e^{\mp}$ , Phys. Rev. Lett. 123, 241802 (2019).
S. Watanuki et al., Search for the lepton flavor violating decays $B^{+} \to K^{+} τ^{\pm} ℓ^{\mp}$ ( $ℓ = e, μ$ ) at Belle, Phys. Rev. Lett. 130, 261802 (2023).
R. Aaij et al., Search for the lepton-flavour violating decays $B^{0} \to K^{* 0} τ^{\pm} μ^{\mp}$ , J. High Energy Phys. 06 (2023) 143.
L. Calibbi, A. Crivellin, and T. Li, Model of vector leptoquarks in view of the $B$ -physics anomalies, Phys. Rev. D 98, 115002 (2018).
R. Barbieri and A. Tesi, $B$ -decay anomalies in Pati-Salam SU(4), Eur. Phys. J. C 78, 193 (2018).
M. Blanke and A. Crivellin, $B$ meson anomalies in a Pati-Salam model within the Randall-Sundrum background, Phys. Rev. Lett. 121, 011801 (2018).
L. Di Luzio, J. Fuentes-Martin, A. Greljo, M. Nardecchia, and S. Renner, Maximal flavour violation: A Cabibbo mechanism for leptoquarks, J. High Energy Phys. 11 (2018) 081.
T. Faber, M. Hudec, M. Malinský, P. Meinzinger, W. Porod, and F. Staub, A unified leptoquark model confronted with lepton non-universality in $B$ -meson decays, Phys. Lett. B 787, 159 (2018).
J. Heeck and D. Teresi, Pati-Salam explanations of the B-meson anomalies, J. High Energy Phys. 12 (2018) 103.
A. Angelescu, D. Bečirević, D. A. Faroughy, and O. Sumensari, Closing the window on single leptoquark solutions to the $B$ -physics anomalies, J. High Energy Phys. 10 (2018) 183.
M. Schmaltz and Y.-M. Zhong, The leptoquark Hunter’s guide: Large coupling, J. High Energy Phys. 01 (2019) 132.
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, 131803 (2019).
B. Fornal, S. A. Gadam, and B. Grinstein, Left-right SU(4) vector leptoquark model for flavor anomalies, Phys. Rev. D 99, 055025 (2019).
M. J. Baker, J. Fuentes-Martín, G. Isidori, and M. König, High- $p_{T}$ signatures in vector–leptoquark models, Eur. Phys. J. C 79, 334 (2019).
C. Cornella, J. Fuentes-Martin, and G. Isidori, Revisiting the vector leptoquark explanation of the B-physics anomalies, J. High Energy Phys. 07 (2019) 168.
L. Da Rold and F. Lamagna, A vector leptoquark for the B-physics anomalies from a composite GUT, J. High Energy Phys. 12 (2019) 112.
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, 317 (2018).
M. Bordone, C. Cornella, J. Fuentes-Martín, and G. Isidori, Low-energy signatures of the ${PS}^{3}$ model: From $B$ -physics anomalies to LFV, J. High Energy Phys. 10 (2018) 148.
M. Bordone, O. Catà, and T. Feldmann, Effective theory approach to new physics with flavour: General framework and a leptoquark example, J. High Energy Phys. 01 (2020) 067.
D. Marzocca, Addressing the B-physics anomalies in a fundamental Composite Higgs Model, J. High Energy Phys. 07 (2018) 121.
D. Bečirević, I. Doršner, S. Fajfer, N. Košnik, D. A. Faroughy, and O. Sumensari, Scalar leptoquarks from grand unified theories to accommodate the $B$ -physics anomalies, Phys. Rev. D 98, 055003 (2018).
I. Bigaran, J. Gargalionis, and R. R. Volkas, A near-minimal leptoquark model for reconciling flavour anomalies and generating radiative neutrino masses, J. High Energy Phys. 10 (2019) 106.
A. Crivellin, D. Müller, and F. Saturnino, Flavor phenomenology of the leptoquark singlet-triplet model, J. High Energy Phys. 06 (2020) 020.
S. Saad, Combined explanations of $(g - 2)_{μ}$ , $R_{D^{(*)}}$ , $R_{K^{(*)}}$ anomalies in a two-loop radiative neutrino mass model, Phys. Rev. D 102, 015019 (2020).
V. Gherardi, D. Marzocca, and E. Venturini, Low-energy phenomenology of scalar leptoquarks at one-loop accuracy, J. High Energy Phys. 01 (2021) 138.
K. S. Babu, P. S. B. Dev, S. Jana, and A. Thapa, Unified framework for $B$ -anomalies, muon $g - 2$ and neutrino masses, J. High Energy Phys. 03 (2021) 179.
A. Crivellin, D. Müller, and T. Ota, Simultaneous explanation of $R (D^{(*)})$ and $b \to s μ^{+} μ^{-}$ : The last scalar leptoquarks standing, J. High Energy Phys. 09 (2017) 040.
D. Buttazzo, A. Greljo, G. Isidori, and D. Marzocca, B-physics anomalies: A guide to combined explanations, J. High Energy Phys. 11 (2017) 044.
M. Bordone, O. Catà, T. Feldmann, and R. Mandal, Constraining flavour patterns of scalar leptoquarks in the effective field theory, J. High Energy Phys. 03 (2021) 122.
C. Cornella, D. A. Faroughy, J. Fuentes-Martin, G. Isidori, and M. Neubert, Reading the footprints of the B-meson flavor anomalies, J. High Energy Phys. 08 (2021) 050.
D. Marzocca and S. Trifinopoulos, Minimal explanation of flavor anomalies: B-meson decays, muon magnetic moment, and the Cabibbo angle, Phys. Rev. Lett. 127, 061803 (2021).
A. Greljo, P. Stangl, and A. E. Thomsen, A model of muon anomalies, Phys. Lett. B 820, 136554 (2021).
J. Davighi, Anomalous Z’ bosons for anomalous B decays, J. High Energy Phys. 08 (2021) 101.
J. S. Alvarado, S. F. Mantilla, R. Martinez, F. Ochoa, and C. Sierra, Gauged nonuniversal U(1)X model to study muon g-2 and B meson anomalies, Phys. Rev. D 108, 095040 (2023).
T. Blake, S. Meinel, and D. van Dyk, Bayesian analysis of $b \to s μ^{+} μ^{-}$ Wilson coefficients using the full angular distribution of $Λ_{b} \to Λ (\to p π^{-}) μ^{+} μ^{-}$ decays, Phys. Rev. D 101, 035023 (2020).
R. Aaij et al., Physics case for an LHCb upgrade II—Opportunities in flavour physics, and beyond, in the HL-LHC era, Report No. LHCB-PUB-2018-009, CERN-LHCC-2018-027 (2018), arXiv:1808.08865.
M. Algueró, B. Capdevila, S. Descotes-Genon, J. Matias, and M. Novoa-Brunet, $b \to s ℓ ℓ$ global fits after Moriond 2021 results, in 55th Rencontres de Moriond on Electroweak Interactions and Unified Theories (2021).
W. Altmannshofer and P. Stangl, New physics in rare B decays after Moriond 2021, Eur. Phys. J. C 81, 952 (2021).
T. Hurth, F. Mahmoudi, D. M. Santos, and S. Neshatpour, More indications for lepton nonuniversality in $b \to s ℓ^{+} ℓ^{-}$ , Phys. Lett. B 824, 136838 (2022).
M. Ciuchini, A. M. Coutinho, M. Fedele, E. Franco, A. Paul, L. Silvestrini, and M. Valli, New physics in $b \to s ℓ^{+} ℓ^{-}$ confronts new data on lepton universality, Eur. Phys. J. C 79, 719 (2019).
R. Mohanta, Effect of FCNC mediated Z boson on lepton flavor violating decays, Eur. Phys. J. C 71, 1625 (2011).
P. Nayek, S. Biswas, P. Maji, S. Sahoo, and S. Sahoo, Implication of Z-mediated FCNC on semileptonic decays $B_{s} \to ϕ ℓ^{+} ℓ^{-}$ and $B^{+} \to K^{+} ℓ^{+} ℓ^{-}$ , Int. J. Theor. Phys. 59, 1418 (2020).
A. Crivellin, L. Hofer, J. Matias, U. Nierste, S. Pokorski, and J. Rosiek, Lepton-flavour violating $B$ decays in generic $Z^{'}$ models, Phys. Rev. D 92, 054013 (2015).
Y. Farzan and I. M. Shoemaker, Lepton flavor violating non-standard interactions via light mediators, J. High Energy Phys. 07 (2016) 033.
D. Das, Lepton flavor violating $Λ_{b} \to Λ ℓ_{1} ℓ_{2}$ decay, Eur. Phys. J. C 79, 1005 (2019).
A. Crivellin, Z. Fabisiewicz, W. Materkowska, U. Nierste, S. Pokorski, and J. Rosiek, Lepton flavour violation in the MSSM: Exact diagonalization vs mass expansion, J. High Energy Phys. 06 (2018) 003.
A. Dedes, J. Rosiek, and P. Tanedo, Complete one-loop MSSM predictions for $B^{0} \to ℓ^{+} ℓ^{'}$ at the Tevatron and LHC, Phys. Rev. D 79, 055006 (2009).
B. M. Dassinger, T. Feldmann, T. Mannel, and S. Turczyk, Model-independent analysis of lepton flavour violating tau decays, J. High Energy Phys. 10 (2007) 039.
S. L. Glashow, D. Guadagnoli, and K. Lane, Lepton flavor violation in $B$ decays?, Phys. Rev. Lett. 114, 091801 (2015).
D. Bečirević, O. Sumensari, and R. Zukanovich Funchal, Lepton flavor violation in exclusive $b \to s$ decays, Eur. Phys. J. C 76, 134 (2016).
D. Guadagnoli and K. Lane, Charged-lepton mixing and lepton flavor violation, Phys. Lett. B 751, 54 (2015).
D. Bečirević, N. Košnik, O. Sumensari, and R. Zukanovich Funchal, Palatable leptoquark scenarios for lepton flavor violation in exclusive $b \to s ℓ_{1} ℓ_{2}$ modes, J. High Energy Phys. 11 (2016) 035.
J. Gratrex, M. Hopfer, and R. Zwicky, Generalised helicity formalism, higher moments and the $B \to K_{J_{K}} (\to K π) {\bar{ℓ}}_{1} ℓ_{2}$ angular distributions, Phys. Rev. D 93, 054008 (2016).
P. Zyla et al., Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
http://www.utfit.org/UTfit/WebHome
R. Balasubramamian and B. Blossier, Decay constant of $B_{s}$ and $B_{s}^{*}$ mesons from $N_{f} = 2$ lattice QCD, Eur. Phys. J. C 80, 412 (2020).
C. Bouchard, G. P. Lepage, C. Monahan, H. Na, and J. Shigemitsu, Rare decay $B \to K ℓ^{+} ℓ^{-}$ form factors from lattice QCD, Phys. Rev. D 88, 054509 (2013); 88, 079901(E) (2013).
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.
R. Aaij et al., Search for the lepton flavour violating decay $B^{+} \to K^{+} μ^{-} τ^{+}$ using $B_{s 2}^{* 0}$ decays, J. High Energy Phys. 06 (2020) 129.
J. P. Lees et al., A search for the decay modes $B^{+ -} \to h^{+ -} τ^{+ -} l$ , Phys. Rev. D 86, 012004 (2012).
R. Aaij et al., Search for the lepton-flavour-violating decays $B_{s}^{0} \to τ^{\pm} μ^{\mp}$ and $B^{0} \to τ^{\pm} μ^{\mp}$ , Phys. Rev. Lett. 123, 211801 (2019).
D. Lancierini, G. Isidori, P. Owen, and N. Serra, On the significance of new physics in $b \to s ℓ^{+} ℓ^{-}$ decays, Phys. Lett. B 822, 136644 (2021).
W. Altmannshofer, P. Ball, A. Bharucha, A. J. Buras, D. M. Straub, and M. Wick, Symmetries and asymmetries of $B \to K^{*} μ^{+} μ^{-}$ decays in the standard model and beyond, J. High Energy Phys. 01 (2009) 019.
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.
P. Ball and R. Zwicky, $B_{d, s} \to ρ, ω, K^{*}, ϕ$ decay form-factors from light-cone sum rules revisited, Phys. Rev. D 71, 014029 (2005).
W. Wang, B to tensor meson form factors in the perturbative QCD approach, Phys. Rev. D 83, 014008 (2011).
T. M. Aliev, H. Dag, A. Kokulu, and A. Ozpineci, $B \to T$ transition form factors in light-cone sum rules, Phys. Rev. D 100, 094005 (2019).
Z.-G. Wang, Analysis of the $B \to K_{2}^{*} (1430), a_{2} (1320), f_{2} (1270)$ form-factors with light-cone QCD sum rules, Mod. Phys. Lett. A 26, 2761 (2011).
D. Das, Model independent new physics analysis in $Λ_{b} \to Λ μ^{+} μ^{-}$ decay, Eur. Phys. J. C 78, 230 (2018).
D. Das, On the angular distribution of $Λ_{b} \to Λ (\to N π) τ^{+} τ^{-}$ decay, J. High Energy Phys. 07 (2018) 063.
E. R. Berger, A. Donnachie, H. G. Dosch, and O. Nachtmann, Observing the odderon: Tensor meson photoproduction, Eur. Phys. J. C 14, 673 (2000).

Phys. Rev. D 112, 075006– Published 3 October, 2025

Vol. 112, Iss. 7 — 1 October 2025

Received 14 May 2025
Accepted 4 September 2025

DOI: https://doi.org/10.1103/g2ck-lkmx

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.

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Unraveling new physics effects in $b \to s ℓ_{1} ℓ_{2}$ transitions with a model-independent perspective

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Unraveling new physics effects in b→sℓ1ℓ2 transitions with a model-independent perspective

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Physics Subject Headings (PhySH)

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References (102)

Unraveling new physics effects in $b \to s ℓ_{1} ℓ_{2}$ transitions with a model-independent perspective