Abstract
Scalar triplet extensions of the Standard Model provide an interesting playground for the explanation of neutrino mass suppression through the type-II seesaw mechanism. Propelled by the possible connections with leptonic CP violation, we explore under which conditions spontaneous CP violation can arise in models with extra scalar triplets. The minimal model satisfying such conditions requires adding two such triplets to the SM field content. For this model, the scalar mass spectrum in both the CP-conserving and spontaneous CP-violating scenarios is studied. In the former case, a decoupling limit for the new scalars can be achieved, while this is not the case when CP is spontaneously broken. In particular, we show that the existence of two light neutral scalars with masses below a few tenths of GeVs is unavoidable in the CP-violating case. Using matrix theory theorems, we derive upper bounds for the masses of those light scalars and briefly examine whether they can still be experimentally viable. Other interesting features of the scalar mass spectrum are discussed as, e.g., the existence of relations among the charged and neutral scalar masses.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [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].
J. McDonald, Gauge singlet scalars as cold dark matter, Phys. Rev. D 50 (1994) 3637 [hep-ph/0702143] [INSPIRE].
V. Barger, P. Langacker, M. McCaskey, M. Ramsey-Musolf and G. Shaughnessy, Complex Singlet Extension of the Standard Model, Phys. Rev. D 79 (2009) 015018 [arXiv:0811.0393] [INSPIRE].
T.D. Lee, A Theory of Spontaneous T Violation, Phys. Rev. D 8 (1973) 1226 [INSPIRE].
N. Turok and J. Zadrozny, Dynamical generation of baryons at the electroweak transition, Phys. Rev. Lett. 65 (1990) 2331 [INSPIRE].
N. Turok and J. Zadrozny, Electroweak baryogenesis in the two doublet model, Nucl. Phys. B 358 (1991) 471 [INSPIRE].
J. McDonald, Electroweak baryogenesis and dark matter via a gauge singlet scalar, Phys. Lett. B 323 (1994) 339 [INSPIRE].
J.M. Cline, K. Kainulainen and A.P. Vischer, Dynamics of two Higgs doublet CP-violation and baryogenesis at the electroweak phase transition, Phys. Rev. D 54 (1996) 2451 [hep-ph/9506284] [INSPIRE].
B. Grzadkowski and D. Huang, Spontaneous CP-Violating Electroweak Baryogenesis and Dark Matter from a Complex Singlet Scalar, JHEP 08 (2018) 135 [arXiv:1807.06987] [INSPIRE].
G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].
M. Nebot, Bounded masses in two Higgs doublets models, spontaneous CP violation and symmetry, Phys. Rev. D 102 (2020) 115002 [arXiv:1911.02266] [INSPIRE].
W. Konetschny and W. Kummer, Nonconservation of Total Lepton Number with Scalar Bosons, Phys. Lett. B 70 (1977) 433 [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
M. Magg and C. Wetterich, Neutrino Mass Problem and Gauge Hierarchy, Phys. Lett. B 94 (1980) 61 [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].
J. Schechter and J.W.F. Valle, Neutrino Masses in SU(2) × U(1) Theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].
G. Lazarides, Q. Shafi and C. Wetterich, Proton Lifetime and Fermion Masses in an SO(10) Model, Nucl. Phys. B 181 (1981) 287 [INSPIRE].
S. Kanemura and H. Sugiyama, Dark matter and a suppression mechanism for neutrino masses in the Higgs triplet model, Phys. Rev. D 86 (2012) 073006 [arXiv:1202.5231] [INSPIRE].
G.C. Branco, R.G. Felipe and F.R. Joaquim, Leptonic CP-violation, Rev. Mod. Phys. 84 (2012) 515 [arXiv:1111.5332] [INSPIRE].
G.C. Branco, R. Gonzalez Felipe, F.R. Joaquim and H. Serodio, Spontaneous leptonic CP-violation and nonzero θ13, Phys. Rev. D 86 (2012) 076008 [arXiv:1203.2646] [INSPIRE].
E. Ma and U. Sarkar, Neutrino masses and leptogenesis with heavy Higgs triplets, Phys. Rev. Lett. 80 (1998) 5716 [hep-ph/9802445] [INSPIRE].
R. Gonzalez Felipe, F.R. Joaquim and H. Serodio, Flavoured CP asymmetries for type-II seesaw leptogenesis, Int. J. Mod. Phys. A 28 (2013) 1350165 [arXiv:1301.0288] [INSPIRE].
ATLAS and CMS collaborations, Combined Measurement of the Higgs Boson Mass in pp Collisions at \( \sqrt{s} \) = 7 and 8 TeV with the ATLAS and CMS Experiments, Phys. Rev. Lett. 114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].
ATLAS and CMS collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s} \) = 7 and 8 TeV, JHEP 08 (2016) 045 [arXiv:1606.02266] [INSPIRE].
H. Georgi and M. Machacek, Doubly Charged Higgs Bosons, Nucl. Phys. B 262 (1985) 463 [INSPIRE].
M.S. Chanowitz and M. Golden, Higgs Boson Triplets With MW = MZ cos θω, Phys. Lett. B 165 (1985) 105 [INSPIRE].
J.F. Gunion, R. Vega and J. Wudka, Higgs triplets in the standard model, Phys. Rev. D 42 (1990) 1673 [INSPIRE].
J.F. Gunion, R. Vega and J. Wudka, Naturalness problems for ρ = 1 and other large one loop effects for a standard model Higgs sector containing triplet fields, Phys. Rev. D 43 (1991) 2322 [INSPIRE].
K.-m. Cheung, R.J.N. Phillips and A. Pilaftsis, Signatures of Higgs triplet representations at TeV e+e− colliders, Phys. Rev. D 51 (1995) 4731 [hep-ph/9411333] [INSPIRE].
M. Aoki and S. Kanemura, Unitarity bounds in the Higgs model including triplet fields with custodial symmetry, Phys. Rev. D 77 (2008) 095009 [Erratum ibid. 89 (2014) 059902] [arXiv:0712.4053] [INSPIRE].
H.E. Logan and M.-A. Roy, Higgs couplings in a model with triplets, Phys. Rev. D 82 (2010) 115011 [arXiv:1008.4869] [INSPIRE].
C.-W. Chiang and K. Yagyu, Testing the custodial symmetry in the Higgs sector of the Georgi-Machacek model, JHEP 01 (2013) 026 [arXiv:1211.2658] [INSPIRE].
C. Englert, E. Re and M. Spannowsky, Pinning down Higgs triplets at the LHC, Phys. Rev. D 88 (2013) 035024 [arXiv:1306.6228] [INSPIRE].
C.-W. Chiang, A.-L. Kuo and K. Yagyu, Enhancements of weak gauge boson scattering processes at the CERN LHC, JHEP 10 (2013) 072 [arXiv:1307.7526] [INSPIRE].
S. Kanemura, K. Tsumura, K. Yagyu and H. Yokoya, Fingerprinting nonminimal Higgs sectors, Phys. Rev. D 90 (2014) 075001 [arXiv:1406.3294] [INSPIRE].
K. Hartling, K. Kumar and H.E. Logan, The decoupling limit in the Georgi-Machacek model, Phys. Rev. D 90 (2014) 015007 [arXiv:1404.2640] [INSPIRE].
C.-W. Chiang, S. Kanemura and K. Yagyu, Novel constraint on the parameter space of the Georgi-Machacek model with current LHC data, Phys. Rev. D 90 (2014) 115025 [arXiv:1407.5053] [INSPIRE].
C. Degrande, K. Hartling, H.E. Logan, A.D. Peterson and M. Zaro, Automatic predictions in the Georgi-Machacek model at next-to-leading order accuracy, Phys. Rev. D 93 (2016) 035004 [arXiv:1512.01243] [INSPIRE].
J. Chang, C.-R. Chen and C.-W. Chiang, Higgs boson pair productions in the Georgi-Machacek model at the LHC, JHEP 03 (2017) 137 [arXiv:1701.06291] [INSPIRE].
B. Keeshan, H.E. Logan and T. Pilkington, Custodial symmetry violation in the Georgi-Machacek model, Phys. Rev. D 102 (2020) 015001 [arXiv:1807.11511] [INSPIRE].
N. Ghosh, S. Ghosh and I. Saha, Charged Higgs boson searches in the Georgi-Machacek model at the LHC, Phys. Rev. D 101 (2020) 015029 [arXiv:1908.00396] [INSPIRE].
C.-W. Chiang, G. Cottin and O. Eberhardt, Global fits in the Georgi-Machacek model, Phys. Rev. D 99 (2019) 015001 [arXiv:1807.10660] [INSPIRE].
A. Ismail, H.E. Logan and Y. Wu, Updated constraints on the Georgi-Machacek model from LHC Run 2, arXiv:2003.02272 [INSPIRE].
K. Hartling, K. Kumar and H.E. Logan, GMCALC: a calculator for the Georgi-Machacek model, arXiv:1412.7387 [INSPIRE].
A. Arhrib et al., The Higgs Potential in the Type II Seesaw Model, Phys. Rev. D 84 (2011) 095005 [arXiv:1105.1925] [INSPIRE].
A. Arhrib, R. Benbrik, M. Chabab, G. Moultaka and L. Rahili, Higgs boson decay into 2 photons in the type II Seesaw Model, JHEP 04 (2012) 136 [arXiv:1112.5453] [INSPIRE].
M. Aoki, S. Kanemura, M. Kikuchi and K. Yagyu, Renormalization of the Higgs Sector in the Triplet Model, Phys. Lett. B 714 (2012) 279 [arXiv:1204.1951] [INSPIRE].
M. Aoki, S. Kanemura, M. Kikuchi and K. Yagyu, Radiative corrections to the Higgs boson couplings in the triplet model, Phys. Rev. D 87 (2013) 015012 [arXiv:1211.6029] [INSPIRE].
P.M. Ferreira and B.L. Gonçalves, Stability of neutral minima against charge breaking in the Higgs triplet model, JHEP 02 (2020) 182 [arXiv:1911.09746] [INSPIRE].
P.M. Ferreira, M. Maniatis, O. Nachtmann and J.P. Silva, CP properties of symmetry-constrained two-Higgs-doublet models, JHEP 08 (2010) 125 [arXiv:1004.3207] [INSPIRE].
ATLAS collaboration, Search for doubly charged scalar bosons decaying into same-sign W boson pairs with the ATLAS detector, Eur. Phys. J. C 79 (2019) 58 [arXiv:1808.01899] [INSPIRE].
CMS collaboration, Observation of electroweak production of same-sign W boson pairs in the two jet and two same-sign lepton final state in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Phys. Rev. Lett. 120 (2018) 081801 [arXiv:1709.05822] [INSPIRE].
R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, New York, U.S.A. (2013).
LEP Working Group for Higgs boson searches, ALEPH, DELPHI, L3 and OPAL collaborations, Search for the standard model Higgs boson at LEP, Phys. Lett. B 565 (2003) 61 [hep-ex/0306033] [INSPIRE].
A. Arbey, F. Mahmoudi, O. Stal and T. Stefaniak, Status of the Charged Higgs Boson in Two Higgs Doublet Models, Eur. Phys. J. C 78 (2018) 182 [arXiv:1706.07414] [INSPIRE].
CMS collaboration, Search for a standard model-like Higgs boson in the mass range between 70 and 110 GeV in the diphoton final state in proton-proton collisions at \( \sqrt{s} \) = 8 and 13 TeV, Phys. Lett. B 793 (2019) 320 [arXiv:1811.08459] [INSPIRE].
P.J. Fox and N. Weiner, Light Signals from a Lighter Higgs, JHEP 08 (2018) 025 [arXiv:1710.07649] [INSPIRE].
T. Biekötter, S. Heinemeyer and C. Muñoz, Precise prediction for the Higgs-boson masses in the μν SSM, Eur. Phys. J. C 78 (2018) 504 [arXiv:1712.07475] [INSPIRE].
U. Haisch and A. Malinauskas, Let there be light from a second light Higgs doublet, JHEP 03 (2018) 135 [arXiv:1712.06599] [INSPIRE].
L. Liu, H. Qiao, K. Wang and J. Zhu, A Light Scalar in the Minimal Dilaton Model in Light of LHC Constraints, Chin. Phys. C 43 (2019) 023104 [arXiv:1812.00107] [INSPIRE].
T. Biekötter, M. Chakraborti and S. Heinemeyer, A 96 GeV Higgs boson in the N2HDM, Eur. Phys. J. C 80 (2020) 2 [arXiv:1903.11661] [INSPIRE].
J.A. Aguilar-Saavedra and F.R. Joaquim, Multiphoton signals of a (96 GeV?) stealth boson, Eur. Phys. J. C 80 (2020) 403 [arXiv:2002.07697] [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: 2109.13179
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
Ferreira, P.M., Gonçalves, B.L. & Joaquim, F.R. The hidden side of scalar-triplet models with spontaneous CP violation. J. High Energ. Phys. 2022, 105 (2022). https://doi.org/10.1007/JHEP05(2022)105
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2022)105