Abstract
A Z2 symmetry that extends the weak interaction, SU(2)L → SU(2)L ×SU(2)′, and the Higgs sector, H(2) → H(2, 1) + H′(1, 2), yields a Standard Model quartic coupling that vanishes at scale v′ = 〈H′〉 ≫ 〈H〉. Near v′, theories either have a “prime” sector, or possess “Left-Right” (LR) symmetry with SU(2)′ = SU(2)R. If the Z2 symmetry incorporates spacetime parity, these theories can solve the strong CP problem. The LR theories have all quark and lepton masses arising from operators of dimension 5 or more, requiring Froggatt-Nielsen structures. Two-loop contributions to \( \overline{\theta} \) are estimated and typically lead to a neutron electric dipole moment of order 10−27e cm that can be observed in future experiments. Minimal models, with gauge group SU(3) × SU(2)L × SU(2)L × U(1)B−L, have precise gauge coupling unification for v′ = 1010±1 GeV, successfully correlating gauge unification with the observed Higgs mass of 125 GeV. With SU(3) × U(1)B−L embedded in SU(4), the central value of the unification scale is reduced from 1016−17 GeV to below 1016 GeV, improving the likelihood of proton decay discovery. Unified theories based on SO(10) × CP are constructed that have H + H′ in a 16 or 144 and generate higher-dimensional flavor operators, while maintaining perturbative gauge couplings.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].
M. Lindner, M. Sher and H.W. Zaglauer, Probing Vacuum Stability Bounds at the Fermilab Collider, Phys. Lett. B 228 (1989) 139 [INSPIRE].
M. Sher, Precise vacuum stability bound in the standard model, Phys. Lett. B 317 (1993) 159 [hep-ph/9307342] [INSPIRE].
G. Altarelli and G. Isidori, Lower limit on the Higgs mass in the standard model: An Update, Phys. Lett. B 337 (1994) 141 [INSPIRE].
J.A. Casas, J.R. Espinosa and M. Quirós, Improved Higgs mass stability bound in the standard model and implications for supersymmetry, Phys. Lett. B 342 (1995) 171 [hep-ph/9409458] [INSPIRE].
J.R. Espinosa and M. Quirós, Improved metastability bounds on the standard model Higgs mass, Phys. Lett. B 353 (1995) 257 [hep-ph/9504241] [INSPIRE].
J.A. Casas, J.R. Espinosa and M. Quirós, Standard model stability bounds for new physics within LHC reach, Phys. Lett. B 382 (1996) 374 [hep-ph/9603227] [INSPIRE].
T. Hambye and K. Riesselmann, Matching conditions and Higgs mass upper bounds revisited, Phys. Rev. D 55 (1997) 7255 [hep-ph/9610272] [INSPIRE].
G. Isidori, G. Ridolfi and A. Strumia, On the metastability of the standard model vacuum, Nucl. Phys. B 609 (2001) 387 [hep-ph/0104016] [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
V. Agrawal, S.M. Barr, J.F. Donoghue and D. Seckel, The Anthropic principle and the mass scale of the standard model, Phys. Rev. D 57 (1998) 5480 [hep-ph/9707380] [INSPIRE].
L.J. Hall, D. Pinner and J.T. Ruderman, The Weak Scale from BBN, JHEP 12 (2014) 134 [arXiv:1409.0551] [INSPIRE].
M. Redi and A. Strumia, Axion-Higgs Unification, JHEP 11 (2012) 103 [arXiv:1208.6013] [INSPIRE].
L.J. Hall and Y. Nomura, Grand Unification and Intermediate Scale Supersymmetry, JHEP 02 (2014) 129 [arXiv:1312.6695] [INSPIRE].
M. Ibe, S. Matsumoto and T.T. Yanagida, Flat Higgs Potential from Planck Scale Supersymmetry Breaking, Phys. Lett. B 732 (2014) 214 [arXiv:1312.7108] [INSPIRE].
L.J. Hall, Y. Nomura and S. Shirai, Grand Unification, Axion and Inflation in Intermediate Scale Supersymmetry, JHEP 06 (2014) 137 [arXiv:1403.8138] [INSPIRE].
B. Feldstein, L.J. Hall and T. Watari, Landscape Prediction for the Higgs Boson and Top Quark Masses, Phys. Rev. D 74 (2006) 095011 [hep-ph/0608121] [INSPIRE].
G. ’t Hooft, Symmetry Breaking Through Bell-Jackiw Anomalies, Phys. Rev. Lett. 37 (1976) 8 [INSPIRE].
M.A.B. Beg and H.S. Tsao, Strong P, T Noninvariances in a Superweak Theory, Phys. Rev. Lett. 41 (1978) 278 [INSPIRE].
R.N. Mohapatra and G. Senjanovic, Natural Suppression of Strong P and T Noninvariance, Phys. Lett. B 79 (1978) 283.
S.M. Barr, D. Chang and G. Senjanović, Strong CP problem and parity, Phys. Rev. Lett. 67 (1991) 2765 [INSPIRE].
R. Kuchimanchi, Solution to the strong CP problem: Supersymmetry with parity, Phys. Rev. Lett. 76 (1996) 3486 [hep-ph/9511376] [INSPIRE].
R.N. Mohapatra and A. Rasin, Simple supersymmetric solution to the strong CP problem, Phys. Rev. Lett. 76 (1996) 3490 [hep-ph/9511391] [INSPIRE].
R.N. Mohapatra and A. Rasin, A Supersymmetric solution to CP problems, Phys. Rev. D 54 (1996) 5835 [hep-ph/9604445] [INSPIRE].
R. Kuchimanchi, P/CP Conserving CP/P Violation Solves Strong CP Problem, Phys. Rev. D 82 (2010) 116008 [arXiv:1009.5961] [INSPIRE].
K.S. Babu and R.N. Mohapatra, A Solution to the Strong CP Problem Without an Axion, Phys. Rev. D 41 (1990) 1286 [INSPIRE].
H. Georgi, The State of the Art-Gauge Theories, AIP Conf. Proc. 23 (1975) 575.
H. Fritzsch and P. Minkowski, Unified Interactions of Leptons and Hadrons, Annals Phys. 93 (1975) 193 [INSPIRE].
C.D. Froggatt and H.B. Nielsen, Hierarchy of Quark Masses, Cabibbo Angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].
R. Foot, Experimental implications of mirror matter-type dark matter, Int. J. Mod. Phys. A 19 (2004) 3807 [astro-ph/0309330] [INSPIRE].
Z. Berezhiani, Mirror world and its cosmological consequences, Int. J. Mod. Phys. A 19 (2004) 3775 [hep-ph/0312335] [INSPIRE].
J.C. Pati and A. Salam, Lepton Number as the Fourth Color, Phys. Rev. D 10 (1974) 275 [Erratum ibid. D 11 (1975) 703] [INSPIRE].
R.J. Crewther, P. Di Vecchia, G. Veneziano and E. Witten, Chiral Estimate of the Electric Dipole Moment of the Neutron in Quantum Chromodynamics, Phys. Lett. B 88 (1979) 123.
C.A. Baker et al., An Improved experimental limit on the electric dipole moment of the neutron, Phys. Rev. Lett. 97 (2006) 131801 [hep-ex/0602020] [INSPIRE].
B. Graner, Y. Chen, E.G. Lindahl and B.R. Heckel, Reduced Limit on the Permanent Electric Dipole Moment of Hg199, Phys. Rev. Lett. 116 (2016) 161601 [Erratum ibid. 119 (2017) 119901] [arXiv:1601.04339] [INSPIRE].
J.R. Ellis and M.K. Gaillard, Strong and Weak CP-violation, Nucl. Phys. B 150 (1979) 141 [INSPIRE].
Super-Kamiokande collaboration, K. Abe et al., Search for proton decay via p → e + π 0 and p→μ + π 0 in 0.31megaton·years exposure of the Super-Kamiokande water Cherenkov detector, Phys. Rev. D 95 (2017) 012004 [arXiv:1610.03597] [INSPIRE].
T.W.B. Kibble, G. Lazarides and Q. Shafi, Strings in SO(10), Phys. Lett. B 113 (1982) 237.
G. Lazarides and Q. Shafi, Superconducting Membranes, Phys. Lett. B 159 (1985) 261.
D. Chang, R.N. Mohapatra and M.K. Parida, Decoupling Parity and SU(2)-R Breaking Scales: A New Approach to Left-Right Symmetric Models, Phys. Rev. Lett. 52 (1984) 1072 [INSPIRE].
D. Chang, R.N. Mohapatra and M.K. Parida, A New Approach to Left-Right Symmetry Breaking in Unified Gauge Theories, Phys. Rev. D 30 (1984) 1052 [INSPIRE].
M. Yasue, Symmetry Breaking of SO(10) and Constraints on Higgs Potential. 1. Adjoint (45) and Spinorial (16), Phys. Rev. D 24 (1981) 1005 [INSPIRE].
M. Yasue, How to break SO(10) VIA SO(4) × SO(6) down to SU(2)L × SU(3)C × U(1), Phys. Lett. B 103 (1981) 33.
G. Anastaze, J.P. Derendinger and F. Buccella, Intermediate symmetries in the SO(10) model with (16 + 16) + 45 Higgses, Z. Phys. C 20 (1983) 269 [INSPIRE].
K.S. Babu and E. Ma, Symmetry Breaking in SO(10): Higgs Boson Structure, Phys. Rev. D 31 (1985) 2316 [INSPIRE].
S. Bertolini, L. Di Luzio and M. Malinsky, On the vacuum of the minimal nonsupersymmetric SO(10) unification, Phys. Rev. D 81 (2010) 035015 [arXiv:0912.1796] [INSPIRE].
M. Fukugita and T. Yanagida, Baryogenesis Without Grand Unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
R.D. Peccei and H.R. Quinn, Constraints Imposed by CP Conservation in the Presence of Instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].
S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].
K. Abe et al., Letter of Intent: The Hyper-Kamiokande Experiment — Detector Design and Physics Potential —, arXiv:1109.3262 [INSPIRE].
S.K. Lamoreaux and R. Golub, Experimental searches for the neutron electric dipole moment, J. Phys. G 36 (2009) 104002 [INSPIRE].
C.A. Baker et al., The search for the neutron electric dipole moment at the Paul Scherrer Institute, Phys. Procedia 17 (2011) 159 [INSPIRE].
nEDM collaboration, E.P. Tsentalovich, The nEDM experiment at the SNS, Phys. Part. Nucl. 45 (2014) 249 [INSPIRE].
A.E. Nelson, Naturally Weak CP Violation, Phys. Lett. B 136 (1984) 387.
S.M. Barr, Solving the Strong CP Problem Without the Peccei-Quinn Symmetry, Phys. Rev. Lett. 53 (1984) 329 [INSPIRE].
L. Bento, G.C. Branco and P.A. Parada, A Minimal model with natural suppression of strong CP-violation, Phys. Lett. B 267 (1991) 95 [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
ArXiv ePrint: 1803.08119
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Hall, L.J., Harigaya, K. Implications of Higgs discovery for the strong CP problem and unification. J. High Energ. Phys. 2018, 130 (2018). https://doi.org/10.1007/JHEP10(2018)130
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2018)130