Abstract
Leptoquarks with masses between 2 TeV and 50 TeV are commonly invoked to explain deviations between data and Standard-Model (SM) predictions of several observables in the decays \( b\to c\tau \overline{\nu} \) and b → sℓ+ℓ− with ℓ = e, μ. While Leptoquarks appear in theories unifying quarks and leptons, the corresponding unification scale MQLU is typically many orders of magnitude above this mass range. We study the case that the mass gap between the electroweak scale and MQLU is only populated by scalar Leptoquarks and SM particles, restricting ourselves to scenarios addressing the mentioned flavour anomalies, and determine the renormalisation-group evolution of Leptoquark couplings to fermions below MQLU. In the most general case, we consider three SU(2) triplet Leptoquarks \( {S}_3^{\ell } \), ℓ = e, μ, τ, which couple quark doublets to the lepton doublet (νℓ, ℓ−) to address the b → sℓ+ℓ− anomalies. In this case, we find a scenario in which the Leptoquark couplings to electrons and muons are driven to the same infrared fixed point, so that lepton flavour universality emerges dynamically. However, the corresponding fixed point for the couplings to taus is necessarily opposite in sign, leading to a unique signature in b → sτ+τ−. For \( b\to c\tau \overline{\nu} \) we complement these with either an SU(2) singlet \( {S}_1^{\tau } \) or doublet \( {R}_2^{\tau } \) and study further the cases that also these Leptoquarks come in three replicas. The fixed point solutions for the \( {S}_3^{\ell } \) couplings explain the b → sℓ+ℓ− data for \( {S}_3^{e,\mu } \) masses between 14 and 15 TeV, according to the scenario. \( b\to c\tau \overline{\nu} \) data can only be fully explained by couplings exceeding their fixed-point values and evolving into Landau poles at high energies, so that one can place an upper bound on MQLU between 108 and 1011 GeV.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
LHCb collaboration, Differential branching fractions and isospin asymmetries of B → K(∗)μ+μ− decays, JHEP 06 (2014) 133 [arXiv:1403.8044] [INSPIRE].
LHCb collaboration, Angular analysis and differential branching fraction of the decay \( {B}_s^0\to \phi {\mu}^{+}{\mu}^{-} \), JHEP 09 (2015) 179 [arXiv:1506.08777] [INSPIRE].
LHCb collaboration, Branching Fraction Measurements of the Rare \( {B}_s^0\to \phi {\mu}^{+}{\mu}^{-} \) and \( {B}_s^0\to {f}_2^{\prime } \) (1525)μ+μ− Decays, Phys. Rev. Lett. 127 (2021) 151801 [arXiv:2105.14007] [INSPIRE].
A. Khodjamirian, T. Mannel, A.A. Pivovarov and Y.M. Wang, Charm-loop effect in B → K(∗)ℓ+ℓ− and B → K∗γ, JHEP 09 (2010) 089 [arXiv:1006.4945] [INSPIRE].
A. Khodjamirian, T. Mannel and Y.M. Wang, B → Kℓ+ℓ− decay at large hadronic recoil, JHEP 02 (2013) 010 [arXiv:1211.0234] [INSPIRE].
LHCb collaboration, Measurement of Form-Factor-Independent Observables in the Decay B0 → K∗0μ+μ−, Phys. Rev. Lett. 111 (2013) 191801 [arXiv:1308.1707] [INSPIRE].
LHCb collaboration, Angular analysis of the B0 → K∗0μ+μ− decay using 3 fb−1 of integrated luminosity, JHEP 02 (2016) 104 [arXiv:1512.04442] [INSPIRE].
LHCb collaboration, Measurement of CP-Averaged Observables in the B0 → K∗0μ+μ− Decay, Phys. Rev. Lett. 125 (2020) 011802 [arXiv:2003.04831] [INSPIRE].
LHCb collaboration, Angular Analysis of the B+ → K∗+μ+μ− Decay, Phys. Rev. Lett. 126 (2021) 161802 [arXiv:2012.13241] [INSPIRE].
G. Hiller and F. Kruger, More model-independent analysis of b → s processes, Phys. Rev. D 69 (2004) 074020 [hep-ph/0310219] [INSPIRE].
LHCb collaboration, Test of lepton universality in b → sℓ+ℓ− decays, Phys. Rev. Lett. 131 (2023) 051803 [arXiv:2212.09152] [INSPIRE].
LHCb collaboration, Measurement of lepton universality parameters in B+ → K+ℓ+ℓ− and B0 → K∗0ℓ+ℓ− decays, Phys. Rev. D 108 (2023) 032002 [arXiv:2212.09153] [INSPIRE].
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].
Belle collaboration, Measurement of \( \mathcal{R}(D) \) and \( \mathcal{R}\left({D}^{\ast}\right) \) with a semileptonic tagging method, Phys. Rev. Lett. 124 (2020) 161803 [arXiv:1910.05864] [INSPIRE].
LHCb collaboration, Measurement of the ratios of branching fractions \( \mathcal{R}\left({D}^{\ast}\right) \) and \( \mathcal{R}\left({D}^0\right) \), Phys. Rev. Lett. 131 (2023) 111802 [arXiv:2302.02886] [INSPIRE].
Belle collaboration, Measurement of the branching ratio of \( \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } \) relative to \( \overline{B}\to {D}^{\left(\ast \right)}{\ell}^{-}{\overline{\nu}}_{\ell } \) decays with hadronic tagging at Belle, Phys. Rev. D 92 (2015) 072014 [arXiv:1507.03233] [INSPIRE].
Belle collaboration, Measurement of the branching ratio of \( {\overline{B}}^0\to {D}^{\ast +}{\tau}^{-}{\overline{\nu}}_{\tau } \) relative to \( {\overline{B}}^0\to {D}^{\ast +}{\ell}^{-}{\overline{\nu}}_{\ell } \) decays with a semileptonic tagging method, Phys. Rev. D 94 (2016) 072007 [arXiv:1607.07923] [INSPIRE].
LHCb collaboration, Measurement of R(D∗) with hadronic τ + decays at \( \sqrt{s} \) = 13 TeV by the LHCb collaboration, https://indico.cern.ch/event/1231797/.
HFLAV collaboration, Averages of b-hadron, c-hadron, and τ-lepton properties as of 2021, Phys. Rev. D 107 (2023) 052008 [arXiv:2206.07501] [INSPIRE].
D. Bigi and P. Gambino, Revisiting B → Dℓν, Phys. Rev. D 94 (2016) 094008 [arXiv:1606.08030] [INSPIRE].
F.U. Bernlochner, Z. Ligeti, M. Papucci and D.J. Robinson, Combined analysis of semileptonic B decays to D and D∗: R(D(∗)), |Vcb|, and new physics, Phys. Rev. D 95 (2017) 115008 [arXiv:1703.05330] [Erratum ibid. 97 (2018) 059902] [INSPIRE].
S. Jaiswal, S. Nandi and S.K. Patra, Extraction of |Vcb| from B → D(∗)ℓνℓ and the Standard Model predictions of R(D(∗)), JHEP 12 (2017) 060 [arXiv:1707.09977] [INSPIRE].
P. Gambino, M. Jung and S. Schacht, The Vcb puzzle: An update, Phys. Lett. B 795 (2019) 386 [arXiv:1905.08209] [INSPIRE].
M. Bordone, M. Jung and D. van Dyk, Theory determination of \( \overline{B}\to {D}^{\left(\ast \right)}{\ell}^{-}\overline{\nu} \) form factors at \( \mathcal{O}\left(1/{m}_c^2\right) \), Eur. Phys. J. C 80 (2020) 74 [arXiv:1908.09398] [INSPIRE].
G. Martinelli, S. Simula and L. Vittorio, |Vcb| and R(D)(∗)) using lattice QCD and unitarity, Phys. Rev. D 105 (2022) 034503 [arXiv:2105.08674] [INSPIRE].
M. Blanke et al., Impact of polarization observables and Bc → τν on new physics explanations of the b → cτν anomaly, Phys. Rev. D 99 (2019) 075006 [arXiv:1811.09603] [INSPIRE].
M. Blanke, A. Crivellin, T. Kitahara, M. Moscati, U. Nierste and I. Nišandžić, Addendum to “Impact of polarization observables and Bc → τν on new physics explanations of the b → cτν anomaly”, Phys. Rev. D 100 (2019) 035035 [arXiv:1905.035035] [INSPIRE].
LHCb collaboration, Observation of the decay \( {\Lambda}_b^0\to {\Lambda}_c^{+}{\tau}^{-}{\overline{\nu}}_{\tau } \), Phys. Rev. Lett. 128 (2022) 191803 [arXiv:2201.03497] [INSPIRE].
M. Fedele et al., Impact of Λb → Λcτν measurement on new physics in b → cℓν transitions, Phys. Rev. D 107 (2023) 055005 [arXiv:2211.14172] [INSPIRE].
Y. Sakaki, M. Tanaka, A. Tayduganov and R. Watanabe, Testing leptoquark models in \( \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} \), Phys. Rev. D 88 (2013) 094012 [arXiv:1309.0301] [INSPIRE].
G. Hiller and M. Schmaltz, RK and future b → sℓℓ physics beyond the standard model opportunities, Phys. Rev. D 90 (2014) 054014 [arXiv:1408.1627] [INSPIRE].
I. Doršner, S. Fajfer, A. Greljo, J.F. Kamenik and N. Košnik, Physics of leptoquarks in precision experiments and at particle colliders, Phys. Rept. 641 (2016) 1 [arXiv:1603.04993] [INSPIRE].
B. Dumont, K. Nishiwaki and R. Watanabe, LHC constraints and prospects for S1 scalar leptoquark explaining the \( \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} \) anomaly, Phys. Rev. D 94 (2016) 034001 [arXiv:1603.05248] [INSPIRE].
X.-Q. Li, Y.-D. Yang and X. Zhang, Revisiting the one leptoquark solution to the R(D(∗)) anomalies and its phenomenological implications, JHEP 08 (2016) 054 [arXiv:1605.09308] [INSPIRE].
G. Hiller, D. Loose and K. Schönwald, Leptoquark Flavor Patterns & B Decay Anomalies, JHEP 12 (2016) 027 [arXiv:1609.08895] [INSPIRE].
B. Bhattacharya, A. Datta, J.-P. Guévin, D. London and R. Watanabe, Simultaneous Explanation of the RK and \( {R}_{D^{\ast }} \) Puzzles: a Model Analysis, JHEP 01 (2017) 015 [arXiv:1609.09078] [INSPIRE].
C.-H. Chen, T. Nomura and H. Okada, Excesses of muon g – 2, \( {R}_{D^{\left(\ast \right)}} \), and RK in a leptoquark model, Phys. Lett. B 774 (2017) 456 [arXiv:1703.03251] [INSPIRE].
A. Crivellin, D. Müller and T. Ota, Simultaneous explanation of R(D(∗)) and and b → sμ+μ−: the last scalar leptoquarks standing, JHEP 09 (2017) 040 [arXiv:1703.09226] [INSPIRE].
M. Jung and D.M. Straub, Constraining new physics in b → cℓν transitions, JHEP 01 (2019) 009 [arXiv:1801.01112] [INSPIRE].
U. Aydemir, T. Mandal and S. Mitra, Addressing the \( {R}_{D^{\left(\ast \right)}} \) anomalies with an S1 leptoquark from SO(10) grand unification, Phys. Rev. D 101 (2020) 015011 [arXiv:1902.08108] [INSPIRE].
O. Popov, M.A. Schmidt and G. White, R2 as a single leptoquark solution to \( {R}_{D^{\left(\ast \right)}} \) and \( {R}_{K^{\left(\ast \right)}} \), Phys. Rev. D 100 (2019) 035028 [arXiv:1905.06339] [INSPIRE].
A. Crivellin, D. Müller and F. Saturnino, Flavor Phenomenology of the Leptoquark Singlet-Triplet Model, JHEP 06 (2020) 020 [arXiv:1912.04224] [INSPIRE].
S. Iguro, M. Takeuchi and R. Watanabe, Testing leptoquark/EFT in \( \overline{B}\to {D}^{\left(\ast \right)}l\overline{\nu} \) at the LHC, Eur. Phys. J. C 81 (2021) 406 [arXiv:2011.02486] [INSPIRE].
P. Athron, C. Balázs, D.H.J. Jacob, W. Kotlarski, D. Stöckinger and H. Stöckinger-Kim, New physics explanations of aμ in light of the FNAL muon g – 2 measurement, JHEP 09 (2021) 080 [arXiv:2104.03691] [INSPIRE].
B. Pendleton and G.G. Ross, Mass and Mixing Angle Predictions from Infrared Fixed Points, Phys. Lett. B 98 (1981) 291 [INSPIRE].
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 (2023) 055036 [arXiv:2212.10516] [INSPIRE].
A. Greljo, J. Salko, A. Smolkovič and P. Stangl, Rare b decays meet high-mass Drell-Yan, JHEP 05 (2023) 087 [arXiv:2212.10497] [INSPIRE].
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 (2023) 648 [arXiv:2304.07330] [INSPIRE].
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, JHEP 02 (2015) 184 [arXiv:1409.4557] [INSPIRE].
Belle collaboration, Search for \( B\to h\nu \overline{\nu} \) decays with semileptonic tagging at Belle, Phys. Rev. D 96 (2017) 091101 [arXiv:1702.03224] [Addendum ibid. 97 (2018) 099902] [INSPIRE].
Belle collaboration, Recent belle ii results on radiative and electroweak penguin decays, at EPS-HEP2023 conference, Hamburg, Germany (2023), https://indico.desy.de/event/34916/contributions/146877.
Belle-II collaboration, The Belle II Physics Book, PTEP 2019 (2019) 123C01 [arXiv:1808.10567] [Erratum ibid. 2020 (2020) 029201] [INSPIRE].
W. Buchmuller and D. Wyler, Effective Lagrangian Analysis of New Interactions and Flavor Conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-Six Terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
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].
J. Aebischer, A. Crivellin, M. Fael and C. Greub, Matching of gauge invariant dimension-six operators for b → s and b → c transitions, JHEP 05 (2016) 037 [arXiv:1512.02830] [INSPIRE].
S. Iguro, T. Kitahara and R. Watanabe, Global fit to b → cτν anomalies 2022 mid-autumn, arXiv:2210.10751 [INSPIRE].
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 (2018) 055003 [arXiv:1806.05689] [INSPIRE].
W. Buchmuller, R. Ruckl and D. Wyler, Leptoquarks in Lepton-Quark Collisions, Phys. Lett. B 191 (1987) 442 [Erratum ibid. 448 (1999) 320] [INSPIRE].
A. Angelescu, D. Bečirević, D.A. Faroughy and O. Sumensari, Closing the window on single leptoquark solutions to the B-physics anomalies, JHEP 10 (2018) 183 [arXiv:1808.08179] [INSPIRE].
M. González-Alonso, J. Martin Camalich and K. Mimouni, Renormalization-group evolution of new physics contributions to (semi)leptonic meson decays, Phys. Lett. B 772 (2017) 777 [arXiv:1706.00410] [INSPIRE].
J. Aebischer, A. Crivellin and C. Greub, QCD improved matching for semileptonic B decays with leptoquarks, Phys. Rev. D 99 (2019) 055002 [arXiv:1811.08907] [INSPIRE].
A. Angelescu, D. Bečirević, D.A. Faroughy, F. Jaffredo and O. Sumensari, Single leptoquark solutions to the B-physics anomalies, Phys. Rev. D 104 (2021) 055017 [arXiv:2103.12504] [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two Loop Renormalization Group Equations in a General Quantum Field Theory. 1. Wave Function Renormalization, Nucl. Phys. B 222 (1983) 83 [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two Loop Renormalization Group Equations in a General Quantum Field Theory. 2. Yukawa Couplings, Nucl. Phys. B 236 (1984) 221 [INSPIRE].
S. Banik and A. Crivellin, Renormalization Group Evolution with Scalar Leptoquarks, arXiv:2307.06800 [INSPIRE].
P. Bandyopadhyay, S. Jangid and A. Karan, Constraining scalar doublet and triplet leptoquarks with vacuum stability and perturbativity, Eur. Phys. J. C 82 (2022) 516 [arXiv:2111.03872] [INSPIRE].
K. Kowalska, E.M. Sessolo and Y. Yamamoto, Flavor anomalies from asymptotically safe gravity, Eur. Phys. J. C 81 (2021) 272 [arXiv:2007.03567] [INSPIRE].
D. Marzocca, Addressing the B-physics anomalies in a fundamental Composite Higgs Model, JHEP 07 (2018) 121 [arXiv:1803.10972] [INSPIRE].
P. Fileviez Perez and M.B. Wise, Low Scale Quark-Lepton Unification, Phys. Rev. D 88 (2013) 057703 [arXiv:1307.6213] [INSPIRE].
I. de Medeiros Varzielas and G. Hiller, Clues for flavor from rare lepton and quark decays, JHEP 06 (2015) 072 [arXiv:1503.01084] [INSPIRE].
Acknowledgments
This research was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the Collaborative Research Center Particle Physics Phenomenology after the Higgs Discovery (P3H) (project no. 396021762 — TRR 257).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2307.15117
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Fedele, M., Nierste, U. & Wuest, F. Renormalisation group analysis of scalar Leptoquark couplings addressing flavour anomalies: emergence of lepton-flavour universality. J. High Energ. Phys. 2023, 131 (2023). https://doi.org/10.1007/JHEP11(2023)131
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2023)131