Abstract
The Scotogenic model is an economical setup that induces Majorana neutrino masses at the 1-loop level and includes a dark matter candidate. We discuss a generalization of the original Scotogenic model with arbitrary numbers of generations of singlet fermion and inert doublet scalar fields. First, the full form of the light neutrino mass matrix is presented, with some comments on its derivation and with special attention to some particular cases. The behavior of the theory at high energies is explored by solving the Renormalization Group Equations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Zee, A Theory of Lepton Number Violation, Neutrino Majorana Mass and Oscillation, Phys. Lett. B 93 (1980) 389 [Erratum ibid. 95 (1980) 461] [INSPIRE].
T.P. Cheng and L.-F. Li, Neutrino Masses, Mixings and Oscillations in SU(2) × U(1) Models of Electroweak Interactions, Phys. Rev. D 22 (1980) 2860 [INSPIRE].
A. Zee, Quantum Numbers of Majorana Neutrino Masses, Nucl. Phys. B 264 (1986) 99 [INSPIRE].
K.S. Babu, Model of ‘Calculable’ Majorana Neutrino Masses, Phys. Lett. B 203 (1988) 132 [INSPIRE].
Y. Cai, J. Herrero-García, M.A. Schmidt, A. Vicente and R.R. Volkas, From the trees to the forest: a review of radiative neutrino mass models, Front. in Phys. 5 (2017) 63 [arXiv:1706.08524] [INSPIRE].
D. Restrepo, O. Zapata and C.E. Yaguna, Models with radiative neutrino masses and viable dark matter candidates, JHEP 11 (2013) 011 [arXiv:1308.3655] [INSPIRE].
E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73 (2006) 077301 [hep-ph/0601225] [INSPIRE].
P. Fileviez Perez and M.B. Wise, On the Origin of Neutrino Masses, Phys. Rev. D 80 (2009) 053006 [arXiv:0906.2950] [INSPIRE].
Y. Liao and J.-Y. Liu, Radiative and flavor-violating transitions of leptons from interactions with color-octet particles, Phys. Rev. D 81 (2010) 013004 [arXiv:0911.3711] [INSPIRE].
M. Reig, D. Restrepo, J.W.F. Valle and O. Zapata, Bound-state dark matter and Dirac neutrino masses, Phys. Rev. D 97 (2018) 115032 [arXiv:1803.08528] [INSPIRE].
M. Reig, D. Restrepo, J.W.F. Valle and O. Zapata, Bound-state dark matter with Majorana neutrinos, Phys. Lett. B 790 (2019) 303 [arXiv:1806.09977] [INSPIRE].
Y. Farzan and E. Ma, Dirac neutrino mass generation from dark matter, Phys. Rev. D 86 (2012) 033007 [arXiv:1204.4890] [INSPIRE].
W. Wang, R. Wang, Z.-L. Han and J.-Z. Han, The B − L Scotogenic Models for Dirac Neutrino Masses, Eur. Phys. J. C 77 (2017) 889 [arXiv:1705.00414] [INSPIRE].
Z.-L. Han and W. Wang, Z′ Portal Dark Matter in B − L Scotogenic Dirac Model, Eur. Phys. J. C 78 (2018) 839 [arXiv:1805.02025] [INSPIRE].
J. Calle, D. Restrepo, C.E. Yaguna and Ó. Zapata, Minimal radiative Dirac neutrino mass models, Phys. Rev. D 99 (2019) 075008 [arXiv:1812.05523] [INSPIRE].
E. Ma, Scotogenic U(1)χ Dirac neutrinos, Phys. Lett. B 793 (2019) 411 [arXiv:1901.09091] [INSPIRE].
E. Ma, Scotogenic cobimaximal Dirac neutrino mixing from ∆(27) and U(1)χ , Eur. Phys. J. C 79 (2019) 903 [arXiv:1905.01535] [INSPIRE].
S. Centelles Chuliá, R. Cepedello, E. Peinado and R. Srivastava, Scotogenic Dark Symmetry as a residual subgroup of Standard Model Symmetries, arXiv:1901.06402 [INSPIRE].
S. Jana, V.P.K. and S. Saad, Minimal Dirac neutrino mass models from U(1)R gauge symmetry and left-right asymmetry at colliders, Eur. Phys. J. C 79 (2019) 916 [arXiv:1904.07407] [INSPIRE].
S. Jana, P.K. Vishnu and S. Saad, Minimal Realizations of Dirac Neutrino Mass from Generic One-loop and Two-loop Topologies at d = 5, JCAP 04 (2020) 018 [arXiv:1910.09537] [INSPIRE].
E. Ma and D. Suematsu, Fermion Triplet Dark Matter and Radiative Neutrino Mass, Mod. Phys. Lett. A 24 (2009) 583 [arXiv:0809.0942] [INSPIRE].
E. Ma, Dark Scalar Doublets and Neutrino Tribimaximal Mixing from A4 Symmetry, Phys. Lett. B 671 (2009) 366 [arXiv:0808.1729] [INSPIRE].
Y. Farzan, A Minimal model linking two great mysteries: neutrino mass and dark matter, Phys. Rev. D 80 (2009) 073009 [arXiv:0908.3729] [INSPIRE].
C.-H. Chen, C.-Q. Geng and D.V. Zhuridov, Neutrino Masses, Leptogenesis and Decaying Dark Matter, JCAP 10 (2009) 001 [arXiv:0906.1646] [INSPIRE].
A. Adulpravitchai, M. Lindner, A. Merle and R.N. Mohapatra, Radiative Transmission of Lepton Flavor Hierarchies, Phys. Lett. B 680 (2009) 476 [arXiv:0908.0470] [INSPIRE].
Y. Farzan, S. Pascoli and M.A. Schmidt, AMEND: A model explaining neutrino masses and dark matter testable at the LHC and MEG, JHEP 10 (2010) 111 [arXiv:1005.5323] [INSPIRE].
M. Aoki, S. Kanemura and K. Yagyu, Doubly-charged scalar bosons from the doublet, Phys. Lett. B 702 (2011) 355 [Erratum ibid. 706 (2012) 495] [arXiv:1105.2075] [INSPIRE].
Y. Cai, X.-G. He, M. Ramsey-Musolf and L.-H. Tsai, RνMDM and Lepton Flavor Violation, JHEP 12 (2011) 054 [arXiv:1108.0969] [INSPIRE].
C.-H. Chen and S.S.C. Law, Exotic fermion multiplets as a solution to baryon asymmetry, dark matter and neutrino masses, Phys. Rev. D 85 (2012) 055012 [arXiv:1111.5462] [INSPIRE].
W. Chao, Dark matter, LFV and neutrino magnetic moment in the radiative seesaw model with fermion triplet, Int. J. Mod. Phys. A 30 (2015) 1550007 [arXiv:1202.6394] [INSPIRE].
E. Ma, A. Natale and A. Rashed, Scotogenic A4 Neutrino Model for Nonzero θ13 and Large δCP , Int. J. Mod. Phys. A 27 (2012) 1250134 [arXiv:1206.1570] [INSPIRE].
M. Hirsch, R.A. Lineros, S. Morisi, J. Palacio, N. Rojas and J.W.F. Valle, WIMP dark matter as radiative neutrino mass messenger, JHEP 10 (2013) 149 [arXiv:1307.8134] [INSPIRE].
S. Bhattacharya, E. Ma, A. Natale and A. Rashed, Radiative Scaling Neutrino Mass with A4 Symmetry, Phys. Rev. D 87 (2013) 097301 [arXiv:1302.6266] [INSPIRE].
E. Ma, Neutrino Mixing and Geometric CP-violation with ∆(27) Symmetry, Phys. Lett. B 723 (2013) 161 [arXiv:1304.1603] [INSPIRE].
E. Ma, Unified Framework for Matter, Dark Matter and Radiative Neutrino Mass, Phys. Rev. D 88 (2013) 117702 [arXiv:1307.7064] [INSPIRE].
V. Brdar, I. Picek and B. Radovcic, Radiative Neutrino Mass with Scotogenic Scalar Triplet, Phys. Lett. B 728 (2014) 198 [arXiv:1310.3183] [INSPIRE].
S.S.C. Law and K.L. McDonald, A Class of Inert N-tuplet Models with Radiative Neutrino Mass and Dark Matter, JHEP 09 (2013) 092 [arXiv:1305.6467] [INSPIRE].
S. Patra, N. Sahoo and N. Sahu, Dipolar dark matter in light of the 3.5 keV x-ray line, neutrino mass and LUX data, Phys. Rev. D 91 (2015) 115013 [arXiv:1412.4253] [INSPIRE].
E. Ma and A. Natale, Scotogenic Z2 or U(1)D Model of Neutrino Mass with ∆(27) Symmetry, Phys. Lett. B 734 (2014) 403 [arXiv:1403.6772] [INSPIRE].
S. Fraser, E. Ma and O. Popov, Scotogenic Inverse Seesaw Model of Neutrino Mass, Phys. Lett. B 737 (2014) 280 [arXiv:1408.4785] [INSPIRE].
H. Okada and Y. Orikasa, Radiative neutrino model with an inert triplet scalar, Phys. Rev. D 94 (2016) 055002 [arXiv:1512.06687] [INSPIRE].
T.A. Chowdhury and S. Nasri, Lepton Flavor Violation in the Inert Scalar Model with Higher Representations, JHEP 12 (2015) 040 [arXiv:1506.00261] [INSPIRE].
M.A. Díaz, N. Rojas, S. Urrutia-Quiroga and J.W.F. Valle, Heavy Higgs Boson Production at Colliders in the Singlet-Triplet Scotogenic Dark Matter Model, JHEP 08 (2017) 017 [arXiv:1612.06569] [INSPIRE].
P.M. Ferreira, W. Grimus, D. Jurciukonis and L. Lavoura, Scotogenic model for co-bimaximal mixing, JHEP 07 (2016) 010 [arXiv:1604.07777] [INSPIRE].
A. Ahriche, K.L. McDonald and S. Nasri, The Scale-Invariant Scotogenic Model, JHEP 06 (2016) 182 [arXiv:1604.05569] [INSPIRE].
F. von der Pahlen, G. Palacio, D. Restrepo and O. Zapata, Radiative Type III Seesaw Model and its collider phenomenology, Phys. Rev. D 94 (2016) 033005 [arXiv:1605.01129] [INSPIRE].
W.-B. Lu and P.-H. Gu, Mixed Inert Scalar Triplet Dark Matter, Radiative Neutrino Masses and Leptogenesis, Nucl. Phys. B 924 (2017) 279 [arXiv:1611.02106] [INSPIRE].
A. Merle, M. Platscher, N. Rojas, J.W.F. Valle and A. Vicente, Consistency of WIMP Dark Matter as radiative neutrino mass messenger, JHEP 07 (2016) 013 [arXiv:1603.05685] [INSPIRE].
P. Rocha-Moran and A. Vicente, Lepton Flavor Violation in the singlet-triplet scotogenic model, JHEP 07 (2016) 078 [arXiv:1605.01915] [INSPIRE].
T.A. Chowdhury and S. Nasri, The Sommerfeld Enhancement in the Scotogenic Model with Large Electroweak Scalar Multiplets, JCAP 01 (2017) 041 [arXiv:1611.06590] [INSPIRE].
E.C.F.S. Fortes, A.C.B. Machado, J. Montan˜o and V. Pleitez, Lepton masses and mixing in a scotogenic model, Phys. Lett. B 803 (2020) 135289 [arXiv:1705.09414] [INSPIRE].
Y.-L. Tang, Some Phenomenologies of a Simple Scotogenic Inverse Seesaw Model, Phys. Rev. D 97 (2018) 035020 [arXiv:1709.07735] [INSPIRE].
C. Guo, S.-Y. Guo and Y. Liao, Dark matter and LHC phenomenology of a scale invariant scotogenic model, Chin. Phys. C 43 (2019) 103102 [arXiv:1811.01180] [INSPIRE].
N. Rojas, R. Srivastava and J.W.F. Valle, Simplest Scoto-Seesaw Mechanism, Phys. Lett. B 789 (2019) 132 [arXiv:1807.11447] [INSPIRE].
A. Aranda, C. Bonilla and E. Peinado, Dynamical generation of neutrino mass scales, Phys. Lett. B 792 (2019) 40 [arXiv:1808.07727] [INSPIRE].
Z.-L. Han and W. Wang, Predictive Scotogenic Model with Flavor Dependent Symmetry, Eur. Phys. J. C 79 (2019) 522 [arXiv:1901.07798] [INSPIRE].
D. Suematsu, Low scale leptogenesis in a hybrid model of the scotogenic type-I and III seesaw models, Phys. Rev. D 100 (2019) 055008 [arXiv:1906.12008] [INSPIRE].
S.K. Kang, O. Popov, R. Srivastava, J.W.F. Valle and C.A. Vaquera-Araujo, Scotogenic dark matter stability from gauged matter parity, Phys. Lett. B 798 (2019) 135013 [arXiv:1902.05966] [INSPIRE].
S. Pramanick, Scotogenic S3 symmetric generation of realistic neutrino mixing, Phys. Rev. D 100 (2019) 035009 [arXiv:1904.07558] [INSPIRE].
T. Nomura, H. Okada and O. Popov, A modular A4 symmetric scotogenic model, Phys. Lett. B 803 (2020) 135294 [arXiv:1908.07457] [INSPIRE].
D. Restrepo and A. Rivera, Phenomenological consistency of the singlet-triplet scotogenic model, JHEP 04 (2020) 134 [arXiv:1907.11938] [INSPIRE].
N. Rojas, R. Srivastava and J.W.F. Valle, Scotogenic origin of the Inverse Seesaw Mechanism, arXiv:1907.07728 [INSPIRE].
I.M. Ávila, V. De Romeri, L. Duarte and J.W.F. Valle, Minimalistic scotogenic scalar dark matter, arXiv:1910.08422 [INSPIRE].
N. Kumar, T. Nomura and H. Okada, Scotogenic neutrino mass with large SU(2)L multiplet fields, arXiv:1912.03990 [INSPIRE].
C.A. R, G. Cottin, J.C. Helo and M. Hirsch, Long-lived charged particles and multi-lepton signatures from neutrino mass models, Phys. Rev. D 101 (2020) 095033 [arXiv:2003.11494] [INSPIRE].
E. Ma, I. Picek and B. Radovčić, New Scotogenic Model of Neutrino Mass with U(1)D Gauge Interaction, Phys. Lett. B 726 (2013) 744 [arXiv:1308.5313] [INSPIRE].
J.-H. Yu, Hidden Gauged U(1) Model: Unifying Scotogenic Neutrino and Flavor Dark Matter, Phys. Rev. D 93 (2016) 113007 [arXiv:1601.02609] [INSPIRE].
J. Kubo and D. Suematsu, Neutrino masses and CDM in a non-supersymmetric model, Phys. Lett. B 643 (2006) 336 [hep-ph/0610006] [INSPIRE].
D. Aristizabal Sierra, M. Dhen, C.S. Fong and A. Vicente, Dynamical flavor origin of ℤN symmetries, Phys. Rev. D 91 (2015) 096004 [arXiv:1412.5600] [INSPIRE].
C. Hagedorn, J. Herrero-García, E. Molinaro and M.A. Schmidt, Phenomenology of the Generalised Scotogenic Model with Fermionic Dark Matter, JHEP 11 (2018) 103 [arXiv:1804.04117] [INSPIRE].
C. Bonilla, L.M.G. de la Vega, J.M. Lamprea, R.A. Lineros and E. Peinado, Fermion Dark Matter and Radiative Neutrino Masses from Spontaneous Lepton Number Breaking, New J. Phys. 22 (2020) 033009 [arXiv:1908.04276] [INSPIRE].
E. Ma, D. Restrepo and Ó. Zapata, Anomalous leptonic U(1) symmetry: Syndetic origin of the QCD axion, weak-scale dark matter and radiative neutrino mass, Mod. Phys. Lett. A 33 (2018) 1850024 [arXiv:1706.08240] [INSPIRE].
C.D.R. Carvajal and Ó. Zapata, One-loop Dirac neutrino mass and mixed axion-WIMP dark matter, Phys. Rev. D 99 (2019) 075009 [arXiv:1812.06364] [INSPIRE].
L.M.G. de la Vega, N. Nath and E. Peinado, Dirac neutrinos from Peccei-Quinn symmetry: two examples, Nucl. Phys. B 957 (2020) 115099 [arXiv:2001.01846] [INSPIRE].
M.K. Parida, Radiative Seesaw in SO(10) with Dark Matter, Phys. Lett. B 704 (2011) 206 [arXiv:1106.4137] [INSPIRE].
J. Leite, O. Popov, R. Srivastava and J.W.F. Valle, A theory for scotogenic dark matter stabilised by residual gauge symmetry, arXiv:1909.06386 [INSPIRE].
Z.-L. Han, R. Ding, S.-J. Lin and B. Zhu, Gauged U(1)Lμ −Lτ scotogenic model in light of RK (∗) anomaly and AMS-02 positron excess, Eur. Phys. J. C 79 (2019) 1007 [arXiv:1908.07192] [INSPIRE].
W. Wang and Z.-L. Han, U(1)B−3Lα extended scotogenic models and single-zero textures of neutrino mass matrices, Phys. Rev. D 101 (2020) 115040 [arXiv:1911.00819] [INSPIRE].
D. Hehn and A. Ibarra, A radiative model with a naturally mild neutrino mass hierarchy, Phys. Lett. B 718 (2013) 988 [arXiv:1208.3162] [INSPIRE].
J. Fuentes-Martín, M. Reig and A. Vicente, Strong C P problem with low-energy emergent QCD: The 4321 case, Phys. Rev. D 100 (2019) 115028 [arXiv:1907.02550] [INSPIRE].
G. ’t Hooft, Naturalness, chiral symmetry and spontaneous chiral symmetry breaking, NATO Sci. Ser. B 59 (1980) 135 [INSPIRE].
G. Passarino and M.J.G. Veltman, One Loop Corrections for e+ e− Annihilation Into μ+ μ− in the Weinberg Model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].
A. Merle and M. Platscher, Parity Problem of the Scotogenic Neutrino Model, Phys. Rev. D 92 (2015) 095002 [arXiv:1502.03098] [INSPIRE].
A. Vicente, Computer tools in particle physics, arXiv:1507.06349 [INSPIRE].
A. Merle and M. Platscher, Running of radiative neutrino masses: the scotogenic model — revisited, JHEP 11 (2015) 148 [arXiv:1507.06314] [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].
J.A. Casas and A. Ibarra, Oscillating neutrinos and μ → e, γ, Nucl. Phys. B 618 (2001) 171 [hep-ph/0103065] [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].
I. Cordero-Carri´on, M. Hirsch and A. Vicente, Master Majorana neutrino mass parametrization, Phys. Rev. D 99 (2019) 075019 [arXiv:1812.03896] [INSPIRE].
I. Cordero-Carrión, M. Hirsch and A. Vicente, General parametrization of Majorana neutrino mass models, Phys. Rev. D 101 (2020) 075032 [arXiv:1912.08858] [INSPIRE].
P.F. de Salas, D.V. Forero, C.A. Ternes, M. Tortola and J.W.F. Valle, Status of neutrino oscillations 2018: 3σ hint for normal mass ordering and improved CP sensitivity, Phys. Lett. B 782 (2018) 633 [arXiv:1708.01186] [INSPIRE].
M. Quirós, Finite temperature field theory and phase transitions, in ICTP Summer School in High-Energy Physics and Cosmology, pp. 187–259 (1999) [hep-ph/9901312] [INSPIRE].
G. Gil, P. Chankowski and M. Krawczyk, Inert Dark Matter and Strong Electroweak Phase Transition, Phys. Lett. B 717 (2012) 396 [arXiv:1207.0084] [INSPIRE].
N. Blinov, S. Profumo and T. Stefaniak, The Electroweak Phase Transition in the Inert Doublet Model, JCAP 07 (2015) 028 [arXiv:1504.05949] [INSPIRE].
A.D. Linde, Particle physics and inflationary cosmology, vol. 5 (1990) [hep-th/0503203] [INSPIRE].
F. Staub, SARAH, arXiv:0806.0538 [INSPIRE].
F. Staub, From Superpotential to Model Files for FeynArts and CalcHep/CompHEP, Comput. Phys. Commun. 181 (2010) 1077 [arXiv:0909.2863] [INSPIRE].
F. Staub, Automatic Calculation of supersymmetric Renormalization Group Equations and Self Energies, Comput. Phys. Commun. 182 (2011) 808 [arXiv:1002.0840] [INSPIRE].
F. Staub, SARAH 3.2: Dirac Gauginos, UFO output and more, Comput. Phys. Commun. 184 (2013) 1792 [arXiv:1207.0906] [INSPIRE].
F. Staub, SARAH 4: A tool for (not only SUSY) model builders, Comput. Phys. Commun. 185 (2014) 1773 [arXiv:1309.7223] [INSPIRE].
K. Kannike, Vacuum Stability of a General Scalar Potential of a Few Fields, Eur. Phys. J. C 76 (2016) 324 [Erratum ibid. 78 (2018) 355] [arXiv:1603.02680] [INSPIRE].
I.P. Ivanov, M. Köpke and M. Mühlleitner, Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials, Eur. Phys. J. C 78 (2018) 413 [arXiv:1802.07976] [INSPIRE].
K. Kannike, Vacuum Stability Conditions From Copositivity Criteria, Eur. Phys. J. C 72 (2012) 2093 [arXiv:1205.3781] [INSPIRE].
W. Kaplan, A test for copositive matrices, Linear Algebra Appl. 313 (2000) 203.
S.-j. Yang and X.-x. Li, Algorithms for determining the copositivity of a given symmetric matrix, Linear Algebra Appl. 430 (2009) 609.
S.-J. Yang, C.-Q. Xu and X.-X. Li, A note on algorithms for determining the copositivity of a given symmetric matrix, J. Inequal. Appl. 2010 (2009) 498631.
F.S. Faro and I.P. Ivanov, Boundedness from below in the U(1) × U(1) three-Higgs-doublet model, Phys. Rev. D 100 (2019) 035038 [arXiv:1907.01963] [INSPIRE].
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
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: 2004.05172
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
Escribano, P., Reig, M. & Vicente, A. Generalizing the Scotogenic model. J. High Energ. Phys. 2020, 97 (2020). https://doi.org/10.1007/JHEP07(2020)097
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2020)097