Abstract
The scotogenic neutrino seesaw model is a minimal extension of the standard model with three ℤ2-odd right-handed singlet fermions N and one ℤ2-odd Higgs doublet η that can accommodate the tiny neutrino mass and provide a dark matter candidate in a unified picture. Due to lack of experimental signatures for electroweak scale new physics, it is appealing to assume these new particles are well above the electroweak scale and take the effective field theory approach to study their effects on low energy observables. In this work we apply the recently developed functional matching formalism to the one-loop matching of the model onto the standard model effective field theory up to dimension seven for the case when all new states N and η are heavy to be integrated out. This is a realistic example which has no tree-level matching due to the ℤ2 symmetry. Using the matching results, we analyze their phenomenological implications for several physical processes, including the lepton number violating effect, the CDF W mass excess, and the lepton flavor violating decays like μ → eγ and μ → 3e.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73 (2006) 077301 [hep-ph/0601225] [INSPIRE].
J. Kubo, E. Ma and D. Suematsu, Cold dark matter, radiative neutrino mass, μ → eγ, and neutrinoless double beta decay, Phys. Lett. B 642 (2006) 18 [hep-ph/0604114] [INSPIRE].
D. Aristizabal Sierra, J. Kubo, D. Restrepo, D. Suematsu and O. Zapata, Radiative seesaw: Warm dark matter, collider and lepton flavour violating signals, Phys. Rev. D 79 (2009) 013011 [arXiv:0808.3340] [INSPIRE].
D. Suematsu, T. Toma and T. Yoshida, Reconciliation of CDM abundance and μ → eγ in a radiative seesaw model, Phys. Rev. D 79 (2009) 093004 [arXiv:0903.0287] [INSPIRE].
A. Adulpravitchai, M. Lindner and A. Merle, Confronting Flavour Symmetries and extended Scalar Sectors with Lepton Flavour Violation Bounds, Phys. Rev. D 80 (2009) 055031 [arXiv:0907.2147] [INSPIRE].
T. Toma and A. Vicente, Lepton Flavor Violation in the Scotogenic Model, JHEP 01 (2014) 160 [arXiv:1312.2840] [INSPIRE].
A. Vicente and C.E. Yaguna, Probing the scotogenic model with lepton flavor violating processes, JHEP 02 (2015) 144 [arXiv:1412.2545] [INSPIRE].
W.-C. Huang, H. Päs and S. Zeißner, Scalar Dark Matter, GUT baryogenesis and Radiative neutrino mass, Phys. Rev. D 98 (2018) 075024 [arXiv:1806.08204] [INSPIRE].
I.M. Ávila, V. De Romeri, L. Duarte and J.W.F. Valle, Phenomenology of scotogenic scalar dark matter, Eur. Phys. J. C 80 (2020) 908 [arXiv:1910.08422] [INSPIRE].
T. de Boer, R. Busse, A. Kappes, M. Klasen and S. Zeinstra, Indirect detection constraints on the scotogenic dark matter model, JCAP 08 (2021) 038 [arXiv:2105.04899] [INSPIRE].
I.M. Ávila, G. Cottin and M.A. Díaz, Revisiting the scotogenic model with scalar dark matter, J. Phys. G 49 (2022) 065001 [arXiv:2108.05103] [INSPIRE].
D. Schmidt, T. Schwetz and T. Toma, Direct Detection of Leptophilic Dark Matter in a Model with Radiative Neutrino Masses, Phys. Rev. D 85 (2012) 073009 [arXiv:1201.0906] [INSPIRE].
A. Ibarra, C.E. Yaguna and O. Zapata, Direct Detection of Fermion Dark Matter in the Radiative Seesaw Model, Phys. Rev. D 93 (2016) 035012 [arXiv:1601.01163] [INSPIRE].
A.G. Hessler, A. Ibarra, E. Molinaro and S. Vogl, Probing the scotogenic FIMP at the LHC, JHEP 01 (2017) 100 [arXiv:1611.09540] [INSPIRE].
M. Lindner, M. Platscher, C.E. Yaguna and A. Merle, Fermionic WIMPs and vacuum stability in the scotogenic model, Phys. Rev. D 94 (2016) 115027 [arXiv:1608.00577] [INSPIRE].
S. Baumholzer, V. Brdar and P. Schwaller, The New νMSM (ννMSM): Radiative Neutrino Masses, keV-Scale Dark Matter and Viable Leptogenesis with sub-TeV New Physics, JHEP 08 (2018) 067 [arXiv:1806.06864] [INSPIRE].
A. Merle and M. Platscher, Running of radiative neutrino masses: the scotogenic model — revisited, JHEP 11 (2015) 148 [arXiv:1507.06314] [INSPIRE].
T. Kitabayashi, Scotogenic dark matter and single-zero textures of the neutrino mass matrix, Phys. Rev. D 98 (2018) 083011 [arXiv:1808.01060] [INSPIRE].
T. Hugle, M. Platscher and K. Schmitz, Low-Scale Leptogenesis in the Scotogenic Neutrino Mass Model, Phys. Rev. D 98 (2018) 023020 [arXiv:1804.09660] [INSPIRE].
D. Borah, P.S.B. Dev and A. Kumar, TeV scale leptogenesis, inflaton dark matter and neutrino mass in a scotogenic model, Phys. Rev. D 99 (2019) 055012 [arXiv:1810.03645] [INSPIRE].
S. Baumholzer, V. Brdar, P. Schwaller and A. Segner, Shining Light on the Scotogenic Model: Interplay of Colliders and Cosmology, JHEP 09 (2020) 136 [arXiv:1912.08215] [INSPIRE].
J. Liu, Z.-L. Han, Y. Jin and H. Li, Unraveling the Scotogenic Model at Muon Collider, arXiv:2207.07382 [INSPIRE].
D. Borah, A. Dasgupta, K. Fujikura, S.K. Kang and D. Mahanta, Observable Gravitational Waves in Minimal Scotogenic Model, JCAP 08 (2020) 046 [arXiv:2003.02276] [INSPIRE].
R.S. Hundi, Lepton flavor violating Z and Higgs decays in the scotogenic model, Eur. Phys. J. C 82 (2022) 505 [arXiv:2201.03779] [INSPIRE].
S. Weinberg, Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett. 43 (1979) 1566 [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].
L. Lehman, Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators, Phys. Rev. D 90 (2014) 125023 [arXiv:1410.4193] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485, . . . : Higher dimension operators in the SM EFT, JHEP 08 (2017) 016 [Erratum JHEP 09 (2019) 019] [arXiv:1512.03433] [INSPIRE].
Y. Liao and X.-D. Ma, Renormalization Group Evolution of Dimension-seven Baryon- and Lepton-number-violating Operators, JHEP 11 (2016) 043 [arXiv:1607.07309] [INSPIRE].
H.-L. Li, Z. Ren, J. Shu, M.-L. Xiao, J.-H. Yu and Y.-H. Zheng, Complete set of dimension-eight operators in the standard model effective field theory, Phys. Rev. D 104 (2021) 015026 [arXiv:2005.00008] [INSPIRE].
C.W. Murphy, Dimension-8 operators in the Standard Model Eective Field Theory, JHEP 10 (2020) 174 [arXiv:2005.00059] [INSPIRE].
H.-L. Li, Z. Ren, M.-L. Xiao, J.-H. Yu and Y.-H. Zheng, Complete set of dimension-nine operators in the standard model effective field theory, Phys. Rev. D 104 (2021) 015025 [arXiv:2007.07899] [INSPIRE].
Y. Liao and X.-D. Ma, An explicit construction of the dimension-9 operator basis in the standard model effective field theory, JHEP 11 (2020) 152 [arXiv:2007.08125] [INSPIRE].
B. Henning, X. Lu and H. Murayama, How to use the Standard Model effective field theory, JHEP 01 (2016) 023 [arXiv:1412.1837] [INSPIRE].
A. Drozd, J. Ellis, J. Quevillon and T. You, The Universal One-Loop Effective Action, JHEP 03 (2016) 180 [arXiv:1512.03003] [INSPIRE].
B. Henning, X. Lu and H. Murayama, One-loop Matching and Running with Covariant Derivative Expansion, JHEP 01 (2018) 123 [arXiv:1604.01019] [INSPIRE].
S.A.R. Ellis, J. Quevillon, T. You and Z. Zhang, Mixed heavy-light matching in the Universal One-Loop Effective Action, Phys. Lett. B 762 (2016) 166 [arXiv:1604.02445] [INSPIRE].
J. Fuentes-Martin, J. Portoles and P. Ruiz-Femenia, Integrating out heavy particles with functional methods: a simplified framework, JHEP 09 (2016) 156 [arXiv:1607.02142] [INSPIRE].
Z. Zhang, Covariant diagrams for one-loop matching, JHEP 05 (2017) 152 [arXiv:1610.00710] [INSPIRE].
S.A.R. Ellis, J. Quevillon, T. You and Z. Zhang, Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients, JHEP 08 (2017) 054 [arXiv:1706.07765] [INSPIRE].
M. Krämer, B. Summ and A. Voigt, Completing the scalar and fermionic Universal One-Loop Effective Action, JHEP 01 (2020) 079 [arXiv:1908.04798] [INSPIRE].
T. Cohen, M. Freytsis and X. Lu, Functional Methods for Heavy Quark Effective Theory, JHEP 06 (2020) 164 [arXiv:1912.08814] [INSPIRE].
T. Cohen, X. Lu and Z. Zhang, Functional Prescription for EFT Matching, JHEP 02 (2021) 228 [arXiv:2011.02484] [INSPIRE].
S. Dittmaier, S. Schuhmacher and M. Stahlhofen, Integrating out heavy fields in the path integral using the background-field method: general formalism, Eur. Phys. J. C 81 (2021) 826 [arXiv:2102.12020] [INSPIRE].
J.C. Criado, MatchingTools: a Python library for symbolic effective field theory calculations, Comput. Phys. Commun. 227 (2018) 42 [arXiv:1710.06445] [INSPIRE].
S. Das Bakshi, J. Chakrabortty and S.K. Patra, CoDEx: Wilson coefficient calculator connecting SMEFT to UV theory, Eur. Phys. J. C 79 (2019) 21 [arXiv:1808.04403] [INSPIRE].
A. Carmona, A. Lazopoulos, P. Olgoso and J. Santiago, Matchmakereft: automated tree-level and one-loop matching, SciPost Phys. 12 (2022) 198 [arXiv:2112.10787] [INSPIRE].
T. Cohen, X. Lu and Z. Zhang, STrEAMlining EFT Matching, SciPost Phys. 10 (2021) 098 [arXiv:2012.07851] [INSPIRE].
J. Fuentes-Martin, M. König, J. Pagès, A.E. Thomsen and F. Wilsch, SuperTracer: A Calculator of Functional Supertraces for One-Loop EFT Matching, JHEP 04 (2021) 281 [arXiv:2012.08506] [INSPIRE].
D. Zhang and S. Zhou, Complete one-loop matching of the type-I seesaw model onto the Standard Model effective field theory, JHEP 09 (2021) 163 [arXiv:2107.12133] [INSPIRE].
R. Coy and M. Frigerio, Effective comparison of neutrino-mass models, Phys. Rev. D 105 (2022) 115041 [arXiv:2110.09126] [INSPIRE].
T. Ohlsson and M. Pernow, One-loop matching conditions in neutrino effective theory, Nucl. Phys. B 978 (2022) 115729 [arXiv:2201.00840] [INSPIRE].
Y. Du, X.-X. Li and J.-H. Yu, Neutrino seesaw models at one-loop matching: discrimination by effective operators, JHEP 09 (2022) 207 [arXiv:2201.04646] [INSPIRE].
X. Li, D. Zhang and S. Zhou, One-loop matching of the type-II seesaw model onto the Standard Model effective field theory, JHEP 04 (2022) 038 [arXiv:2201.05082] [INSPIRE].
V. Gherardi, D. Marzocca and E. Venturini, Matching scalar leptoquarks to the SMEFT at one loop, JHEP 07 (2020) 225 [Erratum JHEP 01 (2021) 006] [arXiv:2003.12525] [INSPIRE].
A. Dedes and K. Mantzaropoulos, Universal scalar leptoquark action for matching, JHEP 11 (2021) 166 [arXiv:2108.10055] [INSPIRE].
U. Haisch, M. Ruhdorfer, E. Salvioni, E. Venturini and A. Weiler, Singlet night in Feynman-ville: one-loop matching of a real scalar, JHEP 04 (2020) 164 [Erratum JHEP 07 (2020) 066] [arXiv:2003.05936] [INSPIRE].
M. Jiang, N. Craig, Y.-Y. Li and D. Sutherland, Complete one-loop matching for a singlet scalar in the Standard Model EFT, JHEP 02 (2019) 031 [Erratum JHEP 01 (2021) 135] [arXiv:1811.08878] [INSPIRE].
M. Chala and A. Titov, One-loop matching in the SMEFT extended with a sterile neutrino, JHEP 05 (2020) 139 [arXiv:2001.07732] [INSPIRE].
I. Brivio et al., From models to SMEFT and back?, SciPost Phys. 12 (2022) 036 [arXiv:2108.01094] [INSPIRE].
R. Cepedello, F. Esser, M. Hirsch and V. Sanz, Mapping the SMEFT to discoverable models, JHEP 09 (2022) 229 [arXiv:2207.13714] [INSPIRE].
D. Zhang, Complete One-loop Structure of the Type-(I+II) Seesaw Effective Field Theory, arXiv:2208.07869 [INSPIRE].
Anisha et al., Effective limits on single scalar extensions in the light of recent LHC data, arXiv:2111.05876 [INSPIRE].
Y. Liao, X.-D. Ma and H.-L. Wang, Effective field theory approach to lepton number violating decays K± → π∓\( {l}_{\upalpha}^{\pm }{l}_{\upbeta}^{\pm } \): long-distance contribution, JHEP 03 (2020) 120 [arXiv:2001.07378] [INSPIRE].
M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
V.A. Smirnov, Applied asymptotic expansions in momenta and masses, in Springer Tracts in Modern Physics 177, Springer (2002) [INSPIRE].
M.K. Gaillard, The Effective One Loop Lagrangian With Derivative Couplings, Nucl. Phys. B 268 (1986) 669 [INSPIRE].
L.-H. Chan, Derivative Expansion for the One Loop Effective Actions With Internal Symmetry, Phys. Rev. Lett. 57 (1986) 1199 [INSPIRE].
O. Cheyette, Effective Action for the Standard Model With Large Higgs Mass, Nucl. Phys. B 297 (1988) 183 [INSPIRE].
Y. Liao and X.-D. Ma, Operators up to Dimension Seven in Standard Model Effective Field Theory Extended with Sterile Neutrinos, Phys. Rev. D 96 (2017) 015012 [arXiv:1612.04527] [INSPIRE].
J.C. Criado, A. Djouadi, M. Pérez-Victoria and J. Santiago, A complete effective field theory for dark matter, JHEP 07 (2021) 081 [arXiv:2104.14443] [INSPIRE].
E.E. Jenkins, A.V. Manohar and P. Stoffer, Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching, JHEP 03 (2018) 016 [arXiv:1709.04486] [INSPIRE].
Y. Liao, X.-D. Ma and Q.-Y. Wang, Extending low energy effective field theory with a complete set of dimension-7 operators, JHEP 08 (2020) 162 [arXiv:2005.08013] [INSPIRE].
P. Escribano, M. Reig and A. Vicente, Generalizing the Scotogenic model, JHEP 07 (2020) 097 [arXiv:2004.05172] [INSPIRE].
V. Cirigliano, W. Dekens, J. de Vries, M.L. Graesser and E. Mereghetti, Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven, JHEP 12 (2017) 082 [arXiv:1708.09390] [INSPIRE].
Y. Liao and X.-D. Ma, Renormalization Group Evolution of Dimension-seven Operators in Standard Model Effective Field Theory and Relevant Phenomenology, JHEP 03 (2019) 179 [arXiv:1901.10302] [INSPIRE].
CDF collaboration, High-precision measurement of the W boson mass with the CDF II detector, Science 376 (2022) 170 [INSPIRE].
Particle Data collaboration, Review of Particle Physics, Prog. Theor. Exp. Phys. 2022 (2022) 083C01 [INSPIRE].
Y.-Z. Fan, T.-P. Tang, Y.-L.S. Tsai and L. Wu, Inert Higgs Dark Matter for CDF II W-Boson Mass and Detection Prospects, Phys. Rev. Lett. 129 (2022) 091802 [arXiv:2204.03693] [INSPIRE].
A. Strumia, Interpreting electroweak precision data including the W-mass CDF anomaly, JHEP 08 (2022) 248 [arXiv:2204.04191] [INSPIRE].
J. de Blas, M. Pierini, L. Reina and L. Silvestrini, Impact of the recent measurements of the top-quark and W-boson masses on electroweak precision fits, arXiv:2204.04204 [INSPIRE].
E. Bagnaschi, J. Ellis, M. Madigan, K. Mimasu, V. Sanz and T. You, SMEFT analysis of mW , JHEP 08 (2022) 308 [arXiv:2204.05260] [INSPIRE].
A. Batra, ShivaSankar K.A., S. Mandal, H. Prajapati and R. Srivastava, CDF-II W Boson Mass Anomaly in the Canonical Scotogenic Neutrino-Dark Matter Model, arXiv:2204.11945 [INSPIRE].
R. Alonso, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization Group Evolution of the Standard Model Dimension Six Operators. Part III. Gauge Coupling Dependence and Phenomenology, JHEP 04 (2014) 159 [arXiv:1312.2014] [INSPIRE].
M.E. Peskin and T. Takeuchi, A New constraint on a strongly interacting Higgs sector, Phys. Rev. Lett. 65 (1990) 964 [INSPIRE].
Muon g – 2 collaboration, Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm, Phys. Rev. Lett. 126 (2021) 141801 [arXiv:2104.03281] [INSPIRE].
Muon g – 2 collaboration, Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL, Phys. Rev. D 73 (2006) 072003 [hep-ex/0602035] [INSPIRE].
A. Crivellin, S. Davidson, G.M. Pruna and A. Signer, Renormalisation-group improved analysis of μ → e processes in a systematic effective-field-theory approach, JHEP 05 (2017) 117 [arXiv:1702.03020] [INSPIRE].
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: 2210.04270
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
Liao, Y., Ma, XD. One-loop matching of scotogenic model onto standard model effective field theory up to dimension 7. J. High Energ. Phys. 2022, 53 (2022). https://doi.org/10.1007/JHEP12(2022)053
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2022)053