Abstract
With the assumption of classical scale invariance at the Planck scale, the DFSZ axion model can generate the Higgs mass terms of the appropriate size through technically natural parameters and may be valid up to the Planck scale. We discuss the high scale validity of the Higgs sector, namely the absence of Landau poles and the vacuum stability. The Higgs sector is identical to that of the type-II two Higgs doublet model with a limited number of the Higgs quartic couplings. We utilize the state-of-the-art method to calculate vacuum decay rates and find that they are enhanced at most by 1010 compared with the tree level evaluation. We also discuss the constraints from flavor observables, perturbative unitarity, oblique parameters and collider searches. We find that the high scale validity tightly constrains the parameter region, but there is still a chance to observe at most about 10% deviation of the 125 GeV Higgs couplings to the fermions.
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References
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [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].
L.F. Abbott and P. Sikivie, A Cosmological Bound on the Invisible Axion, Phys. Lett. 120B (1983) 133 [INSPIRE].
M. Dine and W. Fischler, The Not So Harmless Axion, Phys. Lett. 120B (1983) 137 [INSPIRE].
J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the Invisible Axion, Phys. Lett. 120B (1983) 127 [INSPIRE].
M. Kuster, G. Raffelt and B. Beltran, Axions: Theory, cosmology, and experimental searches. Proceedings, 1st Joint ILIAS-CERN-CAST axion training, Geneva, Switzerland, November 30 – December 2, 2005, Lect. Notes Phys. 741 (2008) 1.
M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Can Confinement Ensure Natural CP Invariance of Strong Interactions?, Nucl. Phys. B 166 (1980) 493 [INSPIRE].
J.E. Kim, Weak Interaction Singlet and Strong CP Invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].
A.R. Zhitnitsky, On Possible Suppression of the Axion Hadron Interactions (in Russian), Sov. J. Nucl. Phys. 31 (1980) 260 [INSPIRE].
M. Dine, W. Fischler and M. Srednicki, A Simple Solution to the Strong CP Problem with a Harmless Axion, Phys. Lett. 104B (1981) 199 [INSPIRE].
W.A. Bardeen, On naturalness in the standard model, in Ontake Summer Institute on Particle Physics Ontake Mountain, Japan, August 27-September 2, 1995, FERMILAB-CONF-95-391 [INSPIRE].
C.T. Hill, Conjecture on the physical implications of the scale anomaly, hep-th/0510177 [INSPIRE].
H. Aoki and S. Iso, Revisiting the Naturalness Problem – Who is afraid of quadratic divergences? –, Phys. Rev. D 86 (2012) 013001 [arXiv:1201.0857] [INSPIRE].
K. Allison, C.T. Hill and G.G. Ross, An ultra-weak sector, the strong CP problem and the pseudo-Goldstone dilaton, Nucl. Phys. B 891 (2015) 613 [arXiv:1409.4029] [INSPIRE].
K. Allison, C.T. Hill and G.G. Ross, Ultra-weak sector, Higgs boson mass and the dilaton, Phys. Lett. B 738 (2014) 191 [arXiv:1404.6268] [INSPIRE].
F. Vissani, Do experiments suggest a hierarchy problem?, Phys. Rev. D 57 (1998) 7027 [hep-ph/9709409] [INSPIRE].
M. Farina, D. Pappadopulo and A. Strumia, A modified naturalness principle and its experimental tests, JHEP 08 (2013) 022 [arXiv:1303.7244] [INSPIRE].
R. Foot, A. Kobakhidze, K.L. McDonald and R.R. Volkas, Poincaré protection for a natural electroweak scale, Phys. Rev. D 89 (2014) 115018 [arXiv:1310.0223] [INSPIRE].
J.D. Clarke, R. Foot and R.R. Volkas, Natural leptogenesis and neutrino masses with two Higgs doublets, Phys. Rev. D 92 (2015) 033006 [arXiv:1505.05744] [INSPIRE].
V. Branchina, F. Contino and P.M. Ferreira, Electroweak vacuum lifetime in two Higgs doublet models, JHEP 11 (2018) 107 [arXiv:1807.10802] [INSPIRE].
M.E. Krauss, T. Opferkuch and F. Staub, The Ultraviolet Landscape of Two-Higgs Doublet Models, Eur. Phys. J. C 78 (2018) 1020 [arXiv:1807.07581] [INSPIRE].
P. Basler, P.M. Ferreira, M. Mühlleitner and R. Santos, High scale impact in alignment and decoupling in two-Higgs doublet models, Phys. Rev. D 97 (2018) 095024 [arXiv:1710.10410] [INSPIRE].
N. Chakrabarty and B. Mukhopadhyaya, High-scale validity of a two Higgs doublet scenario: predicting collider signals, Phys. Rev. D 96 (2017) 035028 [arXiv:1702.08268] [INSPIRE].
N. Chakrabarty and B. Mukhopadhyaya, High-scale validity of a two Higgs doublet scenario: metastability included, Eur. Phys. J. C 77 (2017) 153 [arXiv:1603.05883] [INSPIRE].
V. Cacchio, D. Chowdhury, O. Eberhardt and C.W. Murphy, Next-to-leading order unitarity fits in Two-Higgs-Doublet models with soft ℤ2 breaking, JHEP 11 (2016) 026 [arXiv:1609.01290] [INSPIRE].
E. Bagnaschi, F. Brümmer, W. Buchmüller, A. Voigt and G. Weiglein, Vacuum stability and supersymmetry at high scales with two Higgs doublets, JHEP 03 (2016) 158 [arXiv:1512.07761] [INSPIRE].
D. Chowdhury and O. Eberhardt, Global fits of the two-loop renormalized Two-Higgs-Doublet model with soft Z2 breaking, JHEP 11 (2015) 052 [arXiv:1503.08216] [INSPIRE].
P. Ferreira, H.E. Haber and E. Santos, Preserving the validity of the Two-Higgs Doublet Model up to the Planck scale, Phys. Rev. D 92 (2015) 033003 [Erratum ibid. D 94 (2016) 059903] [arXiv:1505.04001] [INSPIRE].
D. Das and I. Saha, Search for a stable alignment limit in two-Higgs-doublet models, Phys. Rev. D 91 (2015) 095024 [arXiv:1503.02135] [INSPIRE].
N. Chakrabarty, U.K. Dey and B. Mukhopadhyaya, High-scale validity of a two-Higgs doublet scenario: a study including LHC data, JHEP 12 (2014) 166 [arXiv:1407.2145] [INSPIRE].
B. Grzadkowski, O.M. Ogreid and P. Osland, Diagnosing CP properties of the 2HDM, JHEP 01 (2014) 105 [arXiv:1309.6229] [INSPIRE].
J. Shu and Y. Zhang, Impact of a CP-violating Higgs Sector: From LHC to Baryogenesis, Phys. Rev. Lett. 111 (2013) 091801 [arXiv:1304.0773] [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. D 16 (1977) 1248] [INSPIRE].
C.G. Callan Jr. and S.R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev. D 16 (1977) 1762 [INSPIRE].
M. Endo, T. Moroi, M.M. Nojiri and Y. Shoji, Renormalization-Scale Uncertainty in the Decay Rate of False Vacuum, JHEP 01 (2016) 031 [arXiv:1511.04860] [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].
M. Endo, T. Moroi, M.M. Nojiri and Y. Shoji, False Vacuum Decay in Gauge Theory, JHEP 11 (2017) 074 [arXiv:1704.03492] [INSPIRE].
A. Andreassen, W. Frost and M.D. Schwartz, Scale Invariant Instantons and the Complete Lifetime of the Standard Model, Phys. Rev. D 97 (2018) 056006 [arXiv:1707.08124] [INSPIRE].
S. Chigusa, T. Moroi and Y. Shoji, State-of-the-Art Calculation of the Decay Rate of Electroweak Vacuum in the Standard Model, Phys. Rev. Lett. 119 (2017) 211801 [arXiv:1707.09301] [INSPIRE].
S. Chigusa, T. Moroi and Y. Shoji, Decay Rate of Electroweak Vacuum in the Standard Model and Beyond, Phys. Rev. D 97 (2018) 116012 [arXiv:1803.03902] [INSPIRE].
R.D. Peccei, The strong CP problem and axions, Lect. Notes Phys. 741 (2008) 3 [hep-ph/0607268] [INSPIRE].
M.S. Turner, Windows on the Axion, Phys. Rept. 197 (1990) 67 [INSPIRE].
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209 [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].
M. Misiak and M. Steinhauser, Weak radiative decays of the B meson and bounds on MH ± in the Two-Higgs-Doublet Model, Eur. Phys. J. C 77 (2017) 201 [arXiv:1702.04571] [INSPIRE].
J. Haller, A. Hoecker, R. Kogler, K. Mönig, T. Peiffer and J. Stelzer, Update of the global electroweak fit and constraints on two-Higgs-doublet models, Eur. Phys. J. C 78 (2018) 675 [arXiv:1803.01853] [INSPIRE].
T. Enomoto and R. Watanabe, Flavor constraints on the Two Higgs Doublet Models of Z2 symmetric and aligned types, JHEP 05 (2016) 002 [arXiv:1511.05066] [INSPIRE].
S. Kanemura, T. Kubota and E. Takasugi, Lee-Quigg-Thacker bounds for Higgs boson masses in a two doublet model, Phys. Lett. B 313 (1993) 155 [hep-ph/9303263] [INSPIRE].
A.G. Akeroyd, A. Arhrib and E.-M. Naimi, Note on tree level unitarity in the general two Higgs doublet model, Phys. Lett. B 490 (2000) 119 [hep-ph/0006035] [INSPIRE].
W. Grimus, L. Lavoura, O.M. Ogreid and P. Osland, A precision constraint on multi-Higgs-doublet models, J. Phys. G 35 (2008) 075001 [arXiv:0711.4022] [INSPIRE].
W. Grimus, L. Lavoura, O.M. Ogreid and P. Osland, The oblique parameters in multi-Higgs-doublet models, Nucl. Phys. B 801 (2008) 81 [arXiv:0802.4353] [INSPIRE].
D. Eriksson, J. Rathsman and O. Stal, 2HDMC: Two-Higgs-Doublet Model Calculator Physics and Manual, Comput. Phys. Commun. 181 (2010) 189 [arXiv:0902.0851] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
P. Bechtle et al., HiggsBounds-4: Improved Tests of Extended Higgs Sectors against Exclusion Bounds from LEP, the Tevatron and the LHC, Eur. Phys. J. C 74 (2014) 2693 [arXiv:1311.0055] [INSPIRE].
P. Bechtle et al., Recent Developments in HiggsBounds and a Preview of HiggsSignals, PoS(CHARGED 2012)024 [arXiv:1301.2345] [INSPIRE].
P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein and K.E. Williams, HiggsBounds 2.0.0: Confronting Neutral and Charged Higgs Sector Predictions with Exclusion Bounds from LEP and the Tevatron, Comput. Phys. Commun. 182 (2011) 2605 [arXiv:1102.1898] [INSPIRE].
P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein and K.E. Williams, HiggsBounds: Confronting Arbitrary Higgs Sectors with Exclusion Bounds from LEP and the Tevatron, Comput. Phys. Commun. 181 (2010) 138 [arXiv:0811.4169] [INSPIRE].
P. Bechtle, S. Heinemeyer, O. Stal, T. Stefaniak and G. Weiglein, Applying Exclusion Likelihoods from LHC Searches to Extended Higgs Sectors, Eur. Phys. J. C 75 (2015) 421 [arXiv:1507.06706] [INSPIRE].
F. Staub, T. Ohl, W. Porod and C. Speckner, A Tool Box for Implementing Supersymmetric Models, Comput. Phys. Commun. 183 (2012) 2165 [arXiv:1109.5147] [INSPIRE].
F. Staub, Exploring new models in all detail with SARAH, Adv. High Energy Phys. 2015 (2015) 840780 [arXiv:1503.04200] [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New Developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, RunDec: A mathematica package for running and decoupling of the strong coupling and quark masses, Comput. Phys. Commun. 133 (2000) 43 [hep-ph/0004189] [INSPIRE].
F. Herren and M. Steinhauser, Version 3 of RunDec and CRunDec, Comput. Phys. Commun. 224 (2018) 333 [arXiv:1703.03751] [INSPIRE].
N.G. Deshpande and E. Ma, Pattern of Symmetry Breaking with Two Higgs Doublets, Phys. Rev. D 18 (1978) 2574 [INSPIRE].
LCC Physics Working Group collaboration, Tests of the Standard Model at the International Linear Collider, arXiv:1908.11299 [INSPIRE].
ATLAS collaboration, Combined measurements of Higgs boson production and decay using up to 80 fb−1 of proton-proton collision data at \( \sqrt{s} \) = 13 TeV collected with the ATLAS experiment, Phys. Rev. D 101 (2020) 012002 [arXiv:1909.02845] [INSPIRE].
J. Hardy and I.S. Towner, |Vud| from nuclear 𝛽 decays, PoS(CKM2016)028.
HFLAV collaboration, Averages of b-hadron, c-hadron and 𝜏 -lepton properties as of 2018, arXiv:1909.12524 [INSPIRE].
M. Misiak et al., Updated NNLO QCD predictions for the weak radiative B-meson decays, Phys. Rev. Lett. 114 (2015) 221801 [arXiv:1503.01789] [INSPIRE].
M. Czakon, P. Fiedler, T. Huber, M. Misiak, T. Schutzmeier and M. Steinhauser, The (Q7, Q1,2) contribution to \( \overline{B} \) → Xs𝛾 at \( \mathcal{O}\left({\alpha}_{\mathrm{s}}^2\right) \), JHEP 04 (2015) 168 [arXiv:1503.01791] [INSPIRE].
Flavour Lattice Averaging Group collaboration, FLAG Review 2019, Eur. Phys. J. C 80 (2020) 113 [arXiv:1902.08191] [INSPIRE].
Fermilab Lattice and MILC collaborations, \( {B}_{(s)}^0 \) -mixing matrix elements from lattice QCD for the Standard Model and beyond, Phys. Rev. D 93 (2016) 113016 [arXiv:1602.03560] [INSPIRE].
S.R. Coleman, V. Glaser and A. Martin, Action Minima Among Solutions to a Class of Euclidean Scalar Field Equations, Commun. Math. Phys. 58 (1978) 211 [INSPIRE].
A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys. 41 (1993) 307 [arXiv:0709.1075] [INSPIRE].
L. Altenkamp, S. Dittmaier and H. Rzehak, Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → W W/Z Z → 4 fermions, JHEP 09 (2017) 134 [arXiv:1704.02645] [INSPIRE].
A. Djouadi, J. Kalinowski and P.M. Zerwas, Two and three-body decay modes of SUSY Higgs particles, Z. Phys. C 70 (1996) 435 [hep-ph/9511342] [INSPIRE].
A. Djouadi, The anatomy of electro-weak symmetry breaking. II. The Higgs bosons in the minimal supersymmetric model, Phys. Rept. 459 (2008) 1 [hep-ph/0503173] [INSPIRE].
M. Spira, Higgs Boson Production and Decay at Hadron Colliders, Prog. Part. Nucl. Phys. 95 (2017) 98 [arXiv:1612.07651] [INSPIRE].
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Oda, S., Shoji, Y. & Takahashi, Ds. High scale validity of the DFSZ axion model with precision. J. High Energ. Phys. 2020, 11 (2020). https://doi.org/10.1007/JHEP03(2020)011
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DOI: https://doi.org/10.1007/JHEP03(2020)011