Abstract
The Two-Higgs-Doublet model (2HDM) is a simple and viable extension of the Standard Model with a scalar potential complex enough that two minima may coexist. In this work we investigate if the procedure to identify our vacuum as the global minimum by tree-level formulas carries over to the one-loop corrected potential. In the CP conserving case, we identify two distinct types of coexisting minima — the regular ones (moderate tan β) and the non-regular ones (small or large tan β) — and conclude that the tree level expectation fails only for the non-regular type of coexisting minima. For the regular type, the sign of m 212 already precisely indicates which minima is the global one, even at one-loop.
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].
WMAP collaboration, C.L. Bennett et al., Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: final maps and results, Astrophys. J. Suppl. 208 (2013) 20 [arXiv:1212.5225] [INSPIRE].
G.C. Branco et al., Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].
H.P. Nilles, Supersymmetry, supergravity and particle physics, Phys. Rept. 110 (1984) 1 [INSPIRE].
H.E. Haber and G.L. Kane, The search for supersymmetry: probing physics beyond the standard model, Phys. Rept. 117 (1985) 75 [INSPIRE].
A.B. Lahanas and D.V. Nanopoulos, The road to no scale supergravity, Phys. Rept. 145 (1987) 1 [INSPIRE].
T.D. Lee, A theory of spontaneous T violation, Phys. Rev. D 8 (1973) 1226 [INSPIRE].
T.D. Lee, CP nonconservation and spontaneous symmetry breaking, Phys. Rept. 9 (1974) 143 [INSPIRE].
C.C. Nishi, CP violation conditions in N-Higgs-doublet potentials, Phys. Rev. D 74 (2006) 036003 [Erratum ibid. D 76 (2007) 119901] [hep-ph/0605153] [INSPIRE].
A.I. Bochkarev, S.V. Kuzmin and M.E. Shaposhnikov, Electroweak baryogenesis and the Higgs boson mass problem, Phys. Lett. B 244 (1990) 275 [INSPIRE].
A.I. Bochkarev, S.V. Kuzmin and M.E. Shaposhnikov, On the model dependence of the cosmological upper bound on the Higgs boson and top quark masses, Phys. Rev. D 43 (1991) 369 [INSPIRE].
L.D. McLerran, M.E. Shaposhnikov, N. Turok and M.B. Voloshin, Why the baryon asymmetry of the universe is ∼ 10−10, Phys. Lett. B 256 (1991) 451 [INSPIRE].
N. Turok and J. Zadrozny, Electroweak baryogenesis in the two doublet model, Nucl. Phys. B 358 (1991) 471 [INSPIRE].
N. Turok and J. Zadrozny, Phase transitions in the two doublet model, Nucl. Phys. B 369 (1992) 729 [INSPIRE].
A.G. Cohen, D.B. Kaplan and A.E. Nelson, Spontaneous baryogenesis at the weak phase transition, Phys. Lett. B 263 (1991) 86 [INSPIRE].
A.E. Nelson, D.B. Kaplan and A.G. Cohen, Why there is something rather than nothing: matter from weak interactions, Nucl. Phys. B 373 (1992) 453 [INSPIRE].
K. Funakubo, A. Kakuto and K. Takenaga, The effective potential of electroweak theory with two massless Higgs doublets at finite temperature, Prog. Theor. Phys. 91 (1994) 341 [hep-ph/9310267] [INSPIRE].
A.T. Davies, C.D. Froggatt, G. Jenkins and R.G. Moorhouse, Baryogenesis constraints on two Higgs doublet models, Phys. Lett. B 336 (1994) 464 [INSPIRE].
K. Funakubo, A. Kakuto, S. Otsuki, K. Takenaga and F. Toyoda, CP violating profile of the electroweak bubble wall, Prog. Theor. Phys. 94 (1995) 845 [hep-ph/9507452] [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].
G.C. Dorsch, S.J. Huber and J.M. No, A strong electroweak phase transition in the 2HDM after LHC8, JHEP 10 (2013) 029 [arXiv:1305.6610] [INSPIRE].
G.C. Dorsch, S.J. Huber, K. Mimasu and J.M. No, Echoes of the electroweak phase transition: discovering a second Higgs doublet through A 0 → ZH 0, Phys. Rev. Lett. 113 (2014) 211802 [arXiv:1405.5537] [INSPIRE].
K. Fuyuto and E. Senaha, Sphaleron and critical bubble in the scale invariant two Higgs doublet model, Phys. Lett. B 747 (2015) 152 [INSPIRE].
C.-W. Chiang, K. Fuyuto and E. Senaha, Electroweak baryogenesis with lepton flavor violation, Phys. Lett. B 762 (2016) 315 [arXiv:1607.07316] [INSPIRE].
G.C. Dorsch, S.J. Huber, T. Konstandin and J.M. No, A second Higgs doublet in the early universe: baryogenesis and gravitational waves, JCAP 05 (2017) 052 [arXiv:1611.05874] [INSPIRE].
G.C. Dorsch, S.J. Huber, K. Mimasu and J.M. No, The Higgs vacuum uplifted: revisiting the electroweak phase transition with a second Higgs doublet, arXiv:1705.09186 [INSPIRE].
K. Kajantie, K. Rummukainen and M.E. Shaposhnikov, A lattice Monte Carlo study of the hot electroweak phase transition, Nucl. Phys. B 407 (1993) 356 [hep-ph/9305345] [INSPIRE].
Z. Fodor, J. Hein, K. Jansen, A. Jaster and I. Montvay, Simulating the electroweak phase transition in the SU(2) Higgs model, Nucl. Phys. B 439 (1995) 147 [hep-lat/9409017] [INSPIRE].
K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, The electroweak phase transition: a nonperturbative analysis, Nucl. Phys. B 466 (1996) 189 [hep-lat/9510020] [INSPIRE].
K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, Is there a hot electroweak phase transition at m H ≳ m W ?, Phys. Rev. Lett. 77 (1996) 2887 [hep-ph/9605288] [INSPIRE].
K. Jansen, Status of the finite temperature electroweak phase transition on the lattice, Nucl. Phys. Proc. Suppl. 47 (1996) 196 [hep-lat/9509018] [INSPIRE].
M. D’Onofrio, K. Rummukainen and A. Tranberg, Sphaleron rate in the minimal standard model, Phys. Rev. Lett. 113 (2014) 141602 [arXiv:1404.3565] [INSPIRE].
N.G. Deshpande and E. Ma, Pattern of symmetry breaking with two Higgs doublets, Phys. Rev. D 18 (1978) 2574 [INSPIRE].
I.P. Ivanov, Minkowski space structure of the Higgs potential in the two-Higgs-doublet model, Phys. Rev. D 75 (2007) 035001 [Erratum ibid. D 76 (2007) 039902] [hep-ph/0609018] [INSPIRE].
I.P. Ivanov, Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. II. Minima, symmetries and topology, Phys. Rev. D 77 (2008) 015017 [arXiv:0710.3490] [INSPIRE].
P.M. Ferreira, R. Santos and A. Barroso, Stability of the tree-level vacuum in two Higgs doublet models against charge or CP spontaneous violation, Phys. Lett. B 603 (2004) 219 [Erratum ibid. B 629 (2005) 114] [hep-ph/0406231] [INSPIRE].
A. Barroso, P.M. Ferreira and R. Santos, Charge and CP symmetry breaking in two Higgs doublet models, Phys. Lett. B 632 (2006) 684 [hep-ph/0507224] [INSPIRE].
A. Barroso, P.M. Ferreira and R. Santos, Neutral minima in two-Higgs doublet models, Phys. Lett. B 652 (2007) 181 [hep-ph/0702098] [INSPIRE].
R.A. Battye, G.D. Brawn and A. Pilaftsis, Vacuum topology of the two Higgs doublet model, JHEP 08 (2011) 020 [arXiv:1106.3482] [INSPIRE].
C.C. Nishi, The structure of potentials with N Higgs doublets, Phys. Rev. D 76 (2007) 055013 [arXiv:0706.2685] [INSPIRE].
I.P. Ivanov and C.C. Nishi, Symmetry breaking patterns in 3HDM, JHEP 01 (2015) 021 [arXiv:1410.6139] [INSPIRE].
I.P. Ivanov and C.C. Nishi, Properties of the general N-Higgs-doublet model. I. The orbit space, Phys. Rev. D 82 (2010) 015014 [arXiv:1004.1799] [INSPIRE].
I.P. Ivanov, Properties of the general NHDM. II. Higgs potential and its symmetries, JHEP 07 (2010) 020 [arXiv:1004.1802] [INSPIRE].
A. Barroso, P.M. Ferreira, I.P. Ivanov and R. Santos, Metastability bounds on the two Higgs doublet model, JHEP 06 (2013) 045 [arXiv:1303.5098] [INSPIRE].
A. Barroso, P.M. Ferreira, I.P. Ivanov, R. Santos and J.P. Silva, Evading death by vacuum, Eur. Phys. J. C 73 (2013) 2537 [arXiv:1211.6119] [INSPIRE].
I.P. Ivanov and J.P. Silva, Tree-level metastability bounds for the most general two Higgs doublet model, Phys. Rev. D 92 (2015) 055017 [arXiv:1507.05100] [INSPIRE].
P.M. Ferreira and B. Swiezewska, One-loop contributions to neutral minima in the inert doublet model, JHEP 04 (2016) 099 [arXiv:1511.02879] [INSPIRE].
S.P. Martin, Two loop effective potential for a general renormalizable theory and softly broken supersymmetry, Phys. Rev. D 65 (2002) 116003 [hep-ph/0111209] [INSPIRE].
S.P. Martin, Two-loop scalar self-energies in a general renormalizable theory at leading order in gauge couplings, Phys. Rev. D 70 (2004) 016005 [hep-ph/0312092] [INSPIRE].
N.K. Nielsen, On the gauge dependence of spontaneous symmetry breaking in gauge theories, Nucl. Phys. B 101 (1975) 173 [INSPIRE].
P. Basler, M. Krause, M. Muhlleitner, J. Wittbrodt and A. Wlotzka, Strong first order electroweak phase transition in the CP-conserving 2HDM revisited, JHEP 02 (2017) 121 [arXiv:1612.04086] [INSPIRE].
J.M. Cline and P.-A. Lemieux, Electroweak phase transition in two Higgs doublet models, Phys. Rev. D 55 (1997) 3873 [hep-ph/9609240] [INSPIRE].
J.M. Cline, K. Kainulainen and M. Trott, Electroweak baryogenesis in two Higgs doublet models and B meson anomalies, JHEP 11 (2011) 089 [arXiv:1107.3559] [INSPIRE].
S.P. Martin, Taming the Goldstone contributions to the effective potential, Phys. Rev. D 90 (2014) 016013 [arXiv:1406.2355] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
M. Krause, R. Lorenz, M. Mühlleitner, R. Santos and H. Ziesche, Gauge-independent renormalization of the 2-Higgs-doublet model, JHEP 09 (2016) 143 [arXiv:1605.04853] [INSPIRE].
M. Krause, M. Mühlleitner, R. Santos and H. Ziesche, Higgs-to-Higgs boson decays in a 2HDM at next-to-leading order, Phys. Rev. D 95 (2017) 075019 [arXiv:1609.04185] [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].
D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].
C. Ford, D.R.T. Jones, P.W. Stephenson and M.B. Einhorn, The effective potential and the renormalization group, Nucl. Phys. B 395 (1993) 17 [hep-lat/9210033] [INSPIRE].
J.A. Casas, A. Lleyda and C. Muñoz, Strong constraints on the parameter space of the MSSM from charge and color breaking minima, Nucl. Phys. B 471 (1996) 3 [hep-ph/9507294] [INSPIRE].
E.J. Weinberg and A.-q. Wu, Understanding complex perturbative effective potentials, Phys. Rev. D 36 (1987) 2474 [INSPIRE].
S. Nie and M. Sher, Vacuum stability bounds in the two Higgs doublet model, Phys. Lett. B 449 (1999) 89 [hep-ph/9811234] [INSPIRE].
P.M. Ferreira and D.R.T. Jones, Bounds on scalar masses in two Higgs doublet models, JHEP 08 (2009) 069 [arXiv:0903.2856] [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].
F. Staub, Reopen parameter regions in two-Higgs doublet models, arXiv:1705.03677 [INSPIRE].
D. Eriksson, J. Rathsman and O. Stål, 2HDMC — two-Higgs-doublet model calculator, Comput. Phys. Commun. 181 (2010) 189 [arXiv:0902.0851] [INSPIRE].
D. Eriksson, J. Rathsman and O. Stål, 2HDMC — two-Higgs-doublet model calculator, Comput. Phys. Commun. 181 (2010) 833 [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, 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 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, S. Heinemeyer, O. Stål, T. Stefaniak and G. Weiglein, HiggsSignals: confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC, Eur. Phys. J. C 74 (2014) 2711 [arXiv:1305.1933] [INSPIRE].
H.E. Haber and H.E. Logan, Radiative corrections to the \( Zb\overline{b} \) vertex and constraints on extended Higgs sectors, Phys. Rev. D 62 (2000) 015011 [hep-ph/9909335] [INSPIRE].
O. Deschamps et al., The two Higgs doublet of type II facing flavour physics data, Phys. Rev. D 82 (2010) 073012 [arXiv:0907.5135] [INSPIRE].
T. Hermann, M. Misiak and M. Steinhauser, \( \overline{B}\to {X}_s\gamma \) in the two Higgs doublet model up to next-to-next-to-leading order in QCD, JHEP 11 (2012) 036 [arXiv:1208.2788] [INSPIRE].
M. Misiak et al., Updated next-to-next-to-leading-order QCD predictions for the weak radiative B-meson decays, Phys. Rev. Lett. 114 (2015) 221801 [arXiv:1503.01789] [INSPIRE].
T. Enomoto and R. Watanabe, Flavor constraints on the two Higgs doublet models of Z 2 symmetric and aligned types, JHEP 05 (2016) 002 [arXiv:1511.05066] [INSPIRE].
F. Mahmoudi and O. St al, Flavor constraints on two-Higgs-doublet models with general diagonal Yukawa couplings, Phys. Rev. D 81 (2010) 035016 [arXiv:0907.1791] [INSPIRE].
X.-D. Cheng, Y.-D. Yang and X.-B. Yuan, Phenomenological discriminations of the Yukawa interactions in two-Higgs doublet models with Z 2 symmetry, Eur. Phys. J. C 74 (2014) 3081 [arXiv:1401.6657] [INSPIRE].
J.F. Gunion and H.E. Haber, CP-conserving two-Higgs-doublet model: the approach to the decoupling limit, Phys. Rev. D 67 (2003) 075019 [hep-ph/0207010] [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: 1707.04595
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
Cherchiglia, A.L., Nishi, C.C. One-loop considerations for coexisting vacua in the CP conserving 2HDM. J. High Energ. Phys. 2017, 106 (2017). https://doi.org/10.1007/JHEP11(2017)106
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2017)106