# The CP-violating 2HDM in light of a strong first order electroweak phase transition and implications for Higgs pair production

- 48 Downloads
- 6 Citations

## Abstract

We investigate the strength of the electroweak phase transition (EWPT) within the CP-violating 2-Higgs-Doublet Model (C2HDM). The 2HDM is a simple and well-studied model, which can feature CP violation at tree level in its extended scalar sector. This makes it, in contrast to the Standard Model (SM), a promising candidate for explaining the baryon asymmetry of the universe through electroweak baryogenesis. We apply a renormalisation scheme which allows efficient scans of the C2HDM parameter space by using the loop-corrected masses and mixing matrix as input parameters. This procedure enables us to investigate the possibility of a strong first order EWPT required for baryogenesis and study its phenomenological implications for the LHC. Like in the CP-conserving (real) 2HDM (R2HDM) we find that a strong EWPT favours mass gaps between the non-SM-like Higgs bosons. These lead to prominent final states comprised of gauge+Higgs bosons or pairs of Higgs bosons. In contrast to the R2HDM, the CP-mixing of the C2HDM also favours approximately mass degenerate spectra with dominant decays into SM particles. The requirement of a strong EWPT further allows us to distinguish the C2HDM from the R2HDM using the signal strengths of the SM-like Higgs boson. We additionally find that a strong EWPT requires an enhancement of the SM-like trilinear Higgs coupling at next-to-leading order (NLO) by up to a factor of 2.4 compared to the NLO SM coupling, establishing another link between cosmology and collider phenomenology. We provide several C2HDM benchmark scenarios compatible with a strong EWPT and all experimental and theoretical constraints. We include the dominant branching ratios of the non-SM-like Higgs bosons as well as the Higgs pair production cross section of the SM-like Higgs boson for every benchmark point. The pair production cross sections can be substantially enhanced compared to the SM and could be observable at the high-luminosity LHC, allowing access to the trilinear Higgs couplings.

## Keywords

Beyond Standard Model CP violation Higgs Physics## Notes

### **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.

## References

- [1]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]. - [2]ATLAS collaboration,
*Updated ATLAS results on the signal strength of the Higgs-like boson for decays into WW and heavy fermion final states*, ATLAS-CONF-2012-162 (2012). - [3]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]. - [4]CMS collaboration,
*Combination of standard model Higgs boson searches and measurements of the properties of the new boson with a mass near*125*GeV*, CMS-PAS-HIG-12-045 (2012). - [5]ATLAS collaboration,
*Study of the spin and parity of the Higgs boson in diboson decays with the ATLAS detector*,*Eur. Phys. J.***C 75**(2015) 476 [arXiv:1506.05669] [INSPIRE]. - [6]CMS collaboration,
*Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at*7*and*8*TeV*,*Phys. Rev.***D 92**(2015) 012004 [arXiv:1411.3441] [INSPIRE]. - [7]ATLAS collaboration,
*Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at*\( \sqrt{s}=7 \)*and*8*TeV in the ATLAS experiment*,*Eur. Phys. J.***C 76**(2016) 6 [arXiv:1507.04548] [INSPIRE]. - [8]CMS collaboration,
*Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at*7*and*8*TeV*,*Eur. Phys. J.***C 75**(2015) 212 [arXiv:1412.8662] [INSPIRE]. - [9]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]. - [10]V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov,
*On the anomalous electroweak baryon number nonconservation in the early universe*,*Phys. Lett.***155B**(1985) 36 [INSPIRE].ADSCrossRefGoogle Scholar - [11]A.G. Cohen, D.B. Kaplan and A.E. Nelson,
*Baryogenesis at the weak phase transition*,*Nucl. Phys.***B 349**(1991) 727 [INSPIRE].ADSCrossRefGoogle Scholar - [12]A.G. Cohen, D.B. Kaplan and A.E. Nelson,
*Progress in electroweak baryogenesis*,*Ann. Rev. Nucl. Part. Sci.***43**(1993) 27 [hep-ph/9302210] [INSPIRE]. - [13]M. Quirós,
*Field theory at finite temperature and phase transitions*,*Helv. Phys. Acta***67**(1994) 451 [INSPIRE].MathSciNetMATHGoogle Scholar - [14]V.A. Rubakov and M.E. Shaposhnikov,
*Electroweak baryon number nonconservation in the early universe and in high-energy collisions*,*Usp. Fiz. Nauk***166**(1996) 493 [hep-ph/9603208] [INSPIRE]. - [15]K. Funakubo,
*CP violation and baryogenesis at the electroweak phase transition*,*Prog. Theor. Phys.***96**(1996) 475 [hep-ph/9608358] [INSPIRE]. - [16]
- [17]W. Bernreuther,
*CP violation and baryogenesis*,*Lect. Notes Phys.***591**(2002) 237 [hep-ph/0205279] [INSPIRE]. - [18]D.E. Morrissey and M.J. Ramsey-Musolf,
*Electroweak baryogenesis*,*New J. Phys.***14**(2012) 125003 [arXiv:1206.2942] [INSPIRE].ADSCrossRefGoogle Scholar - [19]A.D. Sakharov,
*Violation of CP Invariance, c asymmetry, and baryon asymmetry of the universe*,*Pisma Zh. Eksp. Teor. Fiz.***5**(1967) 32 [*JETP Lett.***5**(1967) 24] [*Sov. Phys. Usp.***34**(1991) 392] [*Usp. Fiz. Nauk***161**(1991) 61].Google Scholar - [20]N.S. Manton,
*Topology in the Weinberg-Salam theory*,*Phys. Rev.***D 28**(1983) 2019 [INSPIRE].ADSMathSciNetGoogle Scholar - [21]F.R. Klinkhamer and N.S. Manton,
*A saddle point solution in the Weinberg-Salam theory*,*Phys. Rev.***D 30**(1984) 2212 [INSPIRE].ADSGoogle Scholar - [22]C. Grojean and G. Servant,
*Gravitational waves from phase transitions at the electroweak scale and beyond*,*Phys. Rev.***D 75**(2007) 043507 [hep-ph/0607107] [INSPIRE]. - [23]C. Caprini et al.,
*Science with the space-based interferometer eLISA. II: gravitational waves from cosmological phase transitions*,*JCAP***04**(2016) 001 [arXiv:1512.06239] [INSPIRE]. - [24]M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir,
*Numerical simulations of acoustically generated gravitational waves at a first order phase transition*,*Phys. Rev.***D 92**(2015) 123009 [arXiv:1504.03291] [INSPIRE].ADSGoogle Scholar - [25]S.J. Huber, T. Konstandin, G. Nardini and I. Rues,
*Detectable gravitational waves from very strong phase transitions in the general NMSSM*,*JCAP***03**(2016) 036 [arXiv:1512.06357] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [26]F.P. Huang, Y. Wan, D.-G. Wang, Y.-F. Cai and X. Zhang,
*Hearing the echoes of electroweak baryogenesis with gravitational wave detectors*,*Phys. Rev.***D 94**(2016) 041702 [arXiv:1601.01640] [INSPIRE].ADSGoogle Scholar - [27]K. Hashino, M. Kakizaki, S. Kanemura and T. Matsui,
*Synergy between measurements of gravitational waves and the triple-Higgs coupling in probing the first-order electroweak phase transition*,*Phys. Rev.***D 94**(2016) 015005 [arXiv:1604.02069] [INSPIRE].ADSGoogle Scholar - [28]M. Chala, G. Nardini and I. Sobolev,
*Unified explanation for dark matter and electroweak baryogenesis with direct detection and gravitational wave signatures*,*Phys. Rev.***D 94**(2016) 055006 [arXiv:1605.08663] [INSPIRE].ADSGoogle Scholar - [29]A. Addazi,
*Limiting first order phase transitions in dark gauge sectors from gravitational waves experiments*,*Mod. Phys. Lett.***A 32**(2017) 1750049 [arXiv:1607.08057] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar - [30]P. Huang, A.J. Long and L.-T. Wang,
*Probing the electroweak phase transition with Higgs factories and gravitational waves*,*Phys. Rev.***D 94**(2016) 075008 [arXiv:1608.06619] [INSPIRE].ADSGoogle Scholar - [31]K. Hashino, M. Kakizaki, S. Kanemura, P. Ko and T. Matsui,
*Gravitational waves and Higgs boson couplings for exploring first order phase transition in the model with a singlet scalar field*,*Phys. Lett.***B 766**(2017) 49 [arXiv:1609.00297] [INSPIRE].ADSCrossRefGoogle Scholar - [32]V. Vaskonen,
*Electroweak baryogenesis and gravitational waves from a real scalar singlet*,*Phys. Rev.***D 95**(2017) 123515 [arXiv:1611.02073] [INSPIRE].ADSGoogle Scholar - [33]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].ADSCrossRefGoogle Scholar - [34]M. Saeedhosini and A. Tofighi,
*Strong electroweak phase transition in a model with extended scalar sector*,*Adv. High Energy Phys.***2017**(2017) 7638204 [arXiv:1701.02074] [INSPIRE].Google Scholar - [35]F.P. Huang and X. Zhang,
*Probing the hidden gauge symmetry breaking through the phase transition gravitational waves*, arXiv:1701.04338 [INSPIRE]. - [36]W. Chao, H.-K. Guo and J. Shu,
*Gravitational wave signals of electroweak phase transition triggered by dark matter*,*JCAP***09**(2017) 009 [arXiv:1702.02698] [INSPIRE].ADSCrossRefGoogle Scholar - [37]L. Marzola, A. Racioppi and V. Vaskonen,
*Phase transition and gravitational wave phenomenology of scalar conformal extensions of the Standard Model*,*Eur. Phys. J.***C 77**(2017) 484 [arXiv:1704.01034] [INSPIRE].ADSCrossRefGoogle Scholar - [38]L. Bian, H.-K. Guo and J. Shu,
*Gravitational waves, baryon asymmetry of the universe and electric dipole moment in the CP-violating NMSSM*, arXiv:1704.02488 [INSPIRE]. - [39]M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir,
*Shape of the acoustic gravitational wave power spectrum from a first order phase transition*,*Phys. Rev.***D 96**(2017) 103520 [arXiv:1704.05871] [INSPIRE].ADSGoogle Scholar - [40]D.J. Weir,
*Gravitational waves from a first order electroweak phase transition: a brief review*,*Phil. Trans. Roy. Soc. Lond.***A 376**(2018) 20170126 [arXiv:1705.01783] [INSPIRE].ADSCrossRefGoogle Scholar - [41]Z. Kang, P. Ko and T. Matsui,
*Strong first order EWPT & strong gravitational waves in Z*_{3}*-symmetric singlet scalar extension*,*JHEP***02**(2018) 115 [arXiv:1706.09721] [INSPIRE].ADSCrossRefGoogle Scholar - [42]R.-G. Cai, M. Sasaki and S.-J. Wang,
*The gravitational waves from the first-order phase transition with a dimension-six operator*,*JCAP***08**(2017) 004 [arXiv:1707.03001] [INSPIRE].ADSCrossRefGoogle Scholar - [43]C.-W. Chiang and E. Senaha,
*On gauge dependence of gravitational waves from a first-order phase transition in classical scale-invariant U*(1)^{′}*models*,*Phys. Lett.***B 774**(2017) 489 [arXiv:1707.06765] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [44]R. Jinno, S. Lee, H. Seong and M. Takimoto,
*Gravitational waves from first-order phase transitions: towards model separation by bubble nucleation rate*,*JCAP***11**(2017) 050 [arXiv:1708.01253] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [45]F.P. Huang and C.S. Li,
*Probing the baryogenesis and dark matter relaxed in phase transition by gravitational waves and colliders*,*Phys. Rev.***D 96**(2017) 095028 [arXiv:1709.09691] [INSPIRE].ADSGoogle Scholar - [46]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]. - [47]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]. - [48]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]. - [49]K. Jansen,
*Status of the finite temperature electroweak phase transition on the lattice*,*Nucl. Phys. Proc. Suppl.***47**(1996) 196 [hep-lat/9509018] [INSPIRE]. - [50]K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov,
*Is there a hot electroweak phase transition at m*(*H*)*larger or equal to m*(*W*)*?*,*Phys. Rev. Lett.***77**(1996) 2887 [hep-ph/9605288] [INSPIRE]. - [51]F. Csikor, Z. Fodor and J. Heitger,
*Endpoint of the hot electroweak phase transition*,*Phys. Rev. Lett.***82**(1999) 21 [hep-ph/9809291] [INSPIRE]. - [52]M.B. Gavela, P. Hernández, J. Orloff and O. Pene,
*Standard model CP-violation and baryon asymmetry*,*Mod. Phys. Lett.***A 9**(1994) 795 [hep-ph/9312215] [INSPIRE]. - [53]T. Konstandin,
*Quantum transport and electroweak baryogenesis*,*Phys. Usp.***56**(2013) 747 [arXiv:1302.6713] [INSPIRE].ADSCrossRefGoogle Scholar - [54]
- [55]T.D. Lee,
*A theory of spontaneous T violation*,*Phys. Rev.***D 8**(1973) 1226 [INSPIRE].ADSGoogle Scholar - [56]G.C. Branco et al.,
*Theory and phenomenology of two-Higgs-doublet models*,*Phys. Rept.***516**(2012) 1 [arXiv:1106.0034] [INSPIRE].ADSCrossRefGoogle Scholar - [57]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].ADSCrossRefGoogle Scholar - [58]L.D. McLerran, M.E. Shaposhnikov, N. Turok and M.B. Voloshin,
*Why the baryon asymmetry of the universe is approximately*10^{−10},*Phys. Lett.***B 256**(1991) 451 [INSPIRE].ADSGoogle Scholar - [59]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].ADSGoogle Scholar - [60]N. Turok and J. Zadrozny,
*Electroweak baryogenesis in the two doublet model*,*Nucl. Phys.***B 358**(1991) 471 [INSPIRE].ADSCrossRefGoogle Scholar - [61]A.G. Cohen, D.B. Kaplan and A.E. Nelson,
*Spontaneous baryogenesis at the weak phase transition*,*Phys. Lett.***B 263**(1991) 86 [INSPIRE].ADSCrossRefGoogle Scholar - [62]N. Turok and J. Zadrozny,
*Phase transitions in the two doublet model*,*Nucl. Phys.***B 369**(1992) 729 [INSPIRE].ADSCrossRefGoogle Scholar - [63]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].ADSCrossRefGoogle Scholar - [64]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]. - [65]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]. - [66]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]. - [67]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].ADSCrossRefGoogle Scholar - [68]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]. - [69]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].ADSCrossRefGoogle Scholar - [70]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*,*JHEP***12**(2017) 086 [arXiv:1705.09186] [INSPIRE].ADSCrossRefGoogle Scholar - [71]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]. - [72]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]. - [73]K. Funakubo, A. Kakuto, S. Otsuki and F. Toyoda,
*Explicit CP breaking and electroweak baryogenesis*,*Prog. Theor. Phys.***96**(1996) 771 [hep-ph/9606282] [INSPIRE]. - [74]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]. - [75]L. Fromme, S.J. Huber and M. Seniuch,
*Baryogenesis in the two-Higgs doublet model*,*JHEP***11**(2006) 038 [hep-ph/0605242] [INSPIRE]. - [76]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].ADSCrossRefMATHGoogle Scholar - [77]A. Haarr, A. Kvellestad and T.C. Petersen,
*Disfavouring electroweak baryogenesis and a hidden Higgs in a CP-violating Two-Higgs-Doublet Model*, arXiv:1611.05757 [INSPIRE]. - [78]I.F. Ginzburg, M. Krawczyk and P. Osland,
*Two Higgs Doublet Models with CP-violation*, hep-ph/0211371 [INSPIRE]. - [79]S. Inoue, M.J. Ramsey-Musolf and Y. Zhang,
*CP-violating phenomenology of flavor conserving Two Higgs Doublet Models*,*Phys. Rev.***D 89**(2014) 115023 [arXiv:1403.4257] [INSPIRE].ADSGoogle Scholar - [80]ACME collaboration, J. Baron et al.,
*Order of magnitude smaller limit on the electric dipole moment of the electron*,*Science***343**(2014) 269 [arXiv:1310.7534] [INSPIRE]. - [81]M. Jiang, L. Bian, W. Huang and J. Shu,
*Impact of a complex singlet: Electroweak baryogenesis and dark matter*,*Phys. Rev.***D 93**(2016) 065032 [arXiv:1502.07574] [INSPIRE].ADSGoogle Scholar - [82]A. Ayala, L.A. Hernández and J. Salinas,
*Charge asymmetry from CP-violating fermion scattering off bubble walls during the electroweak phase transition*,*Phys. Rev.***D 95**(2017) 123004 [arXiv:1704.05510] [INSPIRE].ADSGoogle Scholar - [83]
- [84]S. Bruggisser, T. Konstandin and G. Servant,
*CP-violation for electroweak baryogenesis from dynamical CKM matrix*,*JCAP***11**(2017) 034 [arXiv:1706.08534] [INSPIRE].ADSCrossRefGoogle Scholar - [85]F.P. Huang et al.,
*Testing the electroweak phase transition and electroweak baryogenesis at the LHC and a circular electron-positron collider*,*Phys. Rev.***D 93**(2016) 103515 [arXiv:1511.03969] [INSPIRE].ADSGoogle Scholar - [86]T. Huang et al.,
*Resonant di-Higgs boson production in the*\( b\overline{b}WW \)*channel: Probing the electroweak phase transition at the LHC*,*Phys. Rev.***D 96**(2017) 035007 [arXiv:1701.04442] [INSPIRE].ADSGoogle Scholar - [87]B. Jain, S.J. Lee and M. Son,
*On the validity of the effective potential and the precision of Higgs self couplings*, arXiv:1709.03232 [INSPIRE]. - [88]M. Reichert et al.,
*Probing baryogenesis through the Higgs self-coupling*, arXiv:1711.00019 [INSPIRE]. - [89]S.R. Coleman and E.J. Weinberg,
*Radiative corrections as the origin of spontaneous symmetry breaking*,*Phys. Rev.***D 7**(1973) 1888 [INSPIRE].ADSGoogle Scholar - [90]L. Dolan and R. Jackiw,
*Symmetry behavior at finite temperature*,*Phys. Rev.***D 9**(1974) 3320 [INSPIRE].ADSGoogle Scholar - [91]
- [92]M.E. Carrington,
*The effective potential at finite temperature in the Standard Model*,*Phys. Rev.***D 45**(1992) 2933 [INSPIRE].ADSGoogle Scholar - [93]G.D. Moore,
*Measuring the broken phase sphaleron rate nonperturbatively*,*Phys. Rev.***D 59**(1999) 014503 [hep-ph/9805264] [INSPIRE]. - [94]H.H. Patel and M.J. Ramsey-Musolf,
*Baryon washout, electroweak phase transition and perturbation theory*,*JHEP***07**(2011) 029 [arXiv:1101.4665] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [95]C. Wainwright, S. Profumo and M.J. Ramsey-Musolf,
*Gravity waves from a cosmological phase transition: gauge artifacts and daisy resummations*,*Phys. Rev.***D 84**(2011) 023521 [arXiv:1104.5487] [INSPIRE].ADSGoogle Scholar - [96]M. Garny and T. Konstandin,
*On the gauge dependence of vacuum transitions at finite temperature*,*JHEP***07**(2012) 189 [arXiv:1205.3392] [INSPIRE].ADSCrossRefGoogle Scholar - [97]D. Land and E.D. Carlson,
*Two stage phase transition in two Higgs models*,*Phys. Lett.***B 292**(1992) 107 [hep-ph/9208227] [INSPIRE]. - [98]A. Hammerschmitt, J. Kripfganz and M.G. Schmidt,
*Baryon asymmetry from a two stage electroweak phase transition?*,*Z. Phys.***C 64**(1994) 105 [hep-ph/9404272] [INSPIRE]. - [99]D. Fontes, J.C. Romão and J.P. Silva,
*h*→*Zγ in the complex two Higgs doublet model*,*JHEP***12**(2014) 043 [arXiv:1408.2534] [INSPIRE]. - [100]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]. - [101]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]. - [102]I.P. Ivanov,
*Minkowski space structure of the Higgs potential in 2HDM. II. Minima, symmetries and topology*,*Phys. Rev.***D 77**(2008) 015017 [arXiv:0710.3490] [INSPIRE]. - [103]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].ADSGoogle Scholar - [104]A.W. El Kaffas, P. Osland and O.M. Ogreid,
*CP violation, stability and unitarity of the Two Higgs Doublet Model*,*Nonlin. Phenom. Complex Syst.***10**(2007) 347 [hep-ph/0702097] [INSPIRE]. - [105]W. Khater and P. Osland,
*CP violation in top quark production at the LHC and Two Higgs Doublet Models*,*Nucl. Phys.***B 661**(2003) 209 [hep-ph/0302004] [INSPIRE]. - [106]D. Fontes, J.C. Romão, R. Santos and J.P. Silva,
*Large pseudoscalar Yukawa couplings in the complex 2HDM*,*JHEP***06**(2015) 060 [arXiv:1502.01720] [INSPIRE].ADSCrossRefGoogle Scholar - [107]M. Mühlleitner, M.O.P. Sampaio, R. Santos and J. Wittbrodt,
*Phenomenological comparison of models with extended Higgs sectors*,*JHEP***08**(2017) 132 [arXiv:1703.07750] [INSPIRE].ADSCrossRefGoogle Scholar - [108]R. Grober, M. Muhlleitner and M. Spira,
*Higgs pair production at NLO QCD for CP-violating Higgs Sectors*,*Nucl. Phys.***B 925**(2017) 1 [arXiv:1705.05314] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar - [109]M. Carena, G. Nardini, M. Quirós and C.E.M. Wagner,
*The baryogenesis window in the MSSM*,*Nucl. Phys.***B 812**(2009) 243 [arXiv:0809.3760] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [110]P.B. Arnold and O. Espinosa,
*The effective potential and first order phase transitions: beyond leading-order*,*Phys. Rev.***D 47**(1993) 3546 [*Erratum ibid.***D 50**(1994) 6662] [hep-ph/9212235] [INSPIRE]. - [111]R.R. Parwani,
*Resummation in a hot scalar field theory*,*Phys. Rev.***D 45**(1992) 4695 [*Erratum ibid.***D 48**(1993) 5965] [hep-ph/9204216] [INSPIRE]. - [112]E.J. Weinberg and A.-q. Wu,
*Understanding complex perturbative effective potentials*,*Phys. Rev.***D 36**(1987) 2474 [INSPIRE].ADSMathSciNetGoogle Scholar - [113]J.E. Camargo-Molina et al.,
*All one-loop scalar vertices in the effective potential approach*,*JHEP***08**(2016) 073 [arXiv:1606.07069] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [114]S.P. Martin,
*Taming the Goldstone contributions to the effective potential*,*Phys. Rev.***D 90**(2014) 016013 [arXiv:1406.2355] [INSPIRE].ADSGoogle Scholar - [115]J. Elias-Miro, J.R. Espinosa and T. Konstandin,
*Taming infrared divergences in the effective potential*,*JHEP***08**(2014) 034 [arXiv:1406.2652] [INSPIRE].ADSCrossRefGoogle Scholar - [116]J.A. Casas, J.R. Espinosa, M. Quirós and A. Riotto,
*The lightest Higgs boson mass in the minimal supersymmetric standard model*,*Nucl. Phys.***B 436**(1995) 3 [*Erratum ibid.***B 439**(1995) 466] [hep-ph/9407389] [INSPIRE]. - [117]R. Coimbra, M.O.P. Sampaio and R. Santos,
*ScannerS: constraining the phase diagram of a complex scalar singlet at the LHC*,*Eur. Phys. J.***C 73**(2013) 2428 [arXiv:1301.2599] [INSPIRE].ADSCrossRefGoogle Scholar - [118]P.M. Ferreira, R. Guedes, M.O.P. Sampaio and R. Santos,
*Wrong sign and symmetric limits and non-decoupling in 2HDMs*,*JHEP***12**(2014) 067 [arXiv:1409.6723] [INSPIRE].ADSCrossRefGoogle Scholar - [119]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].ADSGoogle Scholar - [120]H.E. Haber and H.E. Logan,
*Radiative corrections to the Zbb vertex and constraints on extended Higgs sectors*,*Phys. Rev.***D 62**(2000) 015011 [hep-ph/9909335] [INSPIRE]. - [121]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].ADSGoogle Scholar - [122]F. Mahmoudi and O. Stal,
*Flavor constraints on the Two-Higgs-Doublet Model with general Yukawa couplings*,*Phys. Rev.***D 81**(2010) 035016 [arXiv:0907.1791] [INSPIRE].ADSGoogle Scholar - [123]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].ADSCrossRefGoogle Scholar - [124]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].ADSCrossRefGoogle Scholar - [125]M. Misiak and M. Steinhauser,
*Weak radiative decays of the B meson and bounds on M*_{H}±*in the Two-Higgs-Doublet Model*,*Eur. Phys. J.***C 77**(2017) 201 [arXiv:1702.04571] [INSPIRE].ADSCrossRefGoogle Scholar - [126]Gfitter Group collaboration, M. Baa et al.,
*The global electroweak fit at NNLO and prospects for the LHC and ILC*,*Eur. Phys. J.***C 74**(2014) 3046 [arXiv:1407.3792] [INSPIRE]. - [127]ATLAS, CMS collaboration,
*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]. - [128]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].ADSCrossRefMATHGoogle Scholar - [129]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]. - [130]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].ADSCrossRefGoogle Scholar - [131]ATLAS, CMS collaboration,
*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]. - [132]A. Djouadi, J. Kalinowski and M. Spira,
*HDECAY: a program for Higgs boson decays in the standard model and its supersymmetric extension*,*Comput. Phys. Commun.***108**(1998) 56 [hep-ph/9704448] [INSPIRE]. - [133]J.M. Butterworth et al.,
*The tools and Monte Carlo working group summary report from the Les Houches 2009 Workshop on TeV Colliders*, talk given at the 6^{th}*Workshop, dedicated to Thomas Binoth*, June 8-26, Les Houches, France (2009), arXiv:1003.1643 [INSPIRE]. - [134]T. Abe, J. Hisano, T. Kitahara and K. Tobioka,
*Gauge invariant Barr-Zee type contributions to fermionic EDMs in the Two-Higgs Doublet Models*,*JHEP***01**(2014) 106 [*Erratum ibid.***04**(2016) 161] [arXiv:1311.4704] [INSPIRE]. - [135]Particle Data Group collaboration, K.A. Olive et al.,
*Review of particle physics*,*Chin. Phys.***C 38**(2014) 090001 [INSPIRE]. - [136]A. Denner et al.,
*Standard Model input parameters for Higgs physics*, LHCHXSWG-INT-2015-006 (2015). - [137]LHC Higgs Cross Section Working Group, https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWG
- [138]LHC Higgs Cross Section Working Group collaboration, S. Dittmaier et al.,
*Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables*, arXiv:1101.0593 [INSPIRE]. - [139]J. Baglio, O. Eberhardt, U. Nierste and M. Wiebusch,
*Benchmarks for Higgs pair production and heavy Higgs boson searches in the Two-Higgs-Doublet Model of type II*,*Phys. Rev.***D 90**(2014) 015008 [arXiv:1403.1264] [INSPIRE].ADSGoogle Scholar - [140]B. Hespel, D. Lopez-Val and E. Vryonidou,
*Higgs pair production via gluon fusion in the Two-Higgs-Doublet Model*,*JHEP***09**(2014) 124 [arXiv:1407.0281] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [141]L. Bian and N. Chen,
*Higgs pair productions in the CP-violating Two-Higgs-Doublet Model*,*JHEP***09**(2016) 069 [arXiv:1607.02703] [INSPIRE].ADSCrossRefGoogle Scholar - [142]J.F. Gunion and H.E. Haber,
*The CP conserving Two Higgs Doublet Model: the approach to the decoupling limit*,*Phys. Rev.***D 67**(2003) 075019 [hep-ph/0207010] [INSPIRE]. - [143]Gfitter collaboration, R. Kogler and T. Peiffer,
*Update of the global electroweak fit by Gfitter*, talk given at*(**EPS 2016**)*. - [144]S. Dawson, S. Dittmaier and M. Spira,
*Neutral Higgs boson pair production at hadron colliders: QCD corrections*,*Phys. Rev.***D 58**(1998) 115012 [hep-ph/9805244] [INSPIRE]. - [145]G.C. Branco, L. Lavoura and J.P. Silva,
*CP violation*,*Int. Ser. Monogr. Phys.***103**(1999) 1 [INSPIRE].Google Scholar - [146]D. Fontes, J.C. Romão, R. Santos and J.P. Silva,
*Undoubtable signs of CP -violation in Higgs boson decays at the LHC run 2*,*Phys. Rev.***D 92**(2015) 055014 [arXiv:1506.06755] [INSPIRE].ADSGoogle Scholar - [147]S.F. King, M. Muhlleitner, R. Nevzorov and K. Walz,
*Exploring the CP-violating NMSSM: EDM constraints and phenomenology*,*Nucl. Phys.***B 901**(2015) 526 [arXiv:1508.03255] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar - [148]S. Kanemura, S. Kiyoura, Y. Okada, E. Senaha and C.P. Yuan,
*New physics effect on the Higgs selfcoupling*,*Phys. Lett.***B 558**(2003) 157 [hep-ph/0211308] [INSPIRE]. - [149]J. Baglio et al.,
*The measurement of the Higgs self-coupling at the LHC: theoretical status*,*JHEP***04**(2013) 151 [arXiv:1212.5581] [INSPIRE].ADSCrossRefGoogle Scholar - [150]M. Krause, M. Muhlleitner, 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].ADSGoogle Scholar - [151]E.W.N. Glover and J.J. van der Bij,
*Higgs boson pair production via gluon fusion*,*Nucl. Phys.***B 309**(1988) 282 [INSPIRE].ADSCrossRefGoogle Scholar - [152]T. Plehn, M. Spira and P.M. Zerwas,
*Pair production of neutral Higgs particles in gluon-gluon collisions*,*Nucl. Phys.***B 479**(1996) 46 [*Erratum ibid.***B 531**(1998) 655] [hep-ph/9603205] [INSPIRE]. - [153]
*M. Spira’s website*, http://tiger.web.psi.ch/proglist.html. - [154]S. Borowka et al.,
*Higgs boson pair production in gluon fusion at next-to-leading order with full top-quark mass dependence*,*Phys. Rev. Lett.***117**(2016) 012001 [arXiv:1604.06447] [INSPIRE].ADSCrossRefGoogle Scholar - [155]S. Borowka et al.,
*Full top quark mass dependence in Higgs boson pair production at NLO*,*JHEP***10**(2016) 107 [arXiv:1608.04798] [INSPIRE].ADSCrossRefGoogle Scholar - [156]G. Heinrich, S.P. Jones, M. Kerner, G. Luisoni and E. Vryonidou,
*NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers*,*JHEP***08**(2017) 088 [arXiv:1703.09252] [INSPIRE].ADSCrossRefGoogle Scholar - [157]P.M. Ferreira, J.F. Gunion, H.E. Haber and R. Santos,
*Probing wrong-sign Yukawa couplings at the LHC and a future linear collider*,*Phys. Rev.***D 89**(2014) 115003 [arXiv:1403.4736] [INSPIRE].ADSGoogle Scholar - [158]D. Fontes, J.C. Romão and J.P. Silva,
*A reappraisal of the wrong-sign*\( hb\overline{b} \)*coupling and the study of h*→*Zγ*,*Phys. Rev.***D 90**(2014) 015021 [arXiv:1406.6080] [INSPIRE].