Abstract
This is the second of a series of papers that explores the physical parameterization, sum rules and unitarity bounds arising from a non-minimal scalar sector of the Standard Model (SM) that consists of N Higgs doublets. In this paper, we focus on the structure and implication of the Yukawa interactions that couple the N scalar doublets to the SM fermions. We employ the charged Higgs basis, which is defined as the basis of scalar fields such that the neutral scalar field vacuum expectation value resides entirely in one of the N scalar doublet fields, and the charged components of the remaining N − 1 scalar doublet fields are the physical (mass-eigenstate) charged Higgs fields. Based on the structure of the Yukawa Lagrangian of the model (and as a consequence of tree-level unitarity), one may deduce numerous sum rules, several of which have not appeared previously in the literature. These sum rules can be used to uncover intimate relations between the structure of the Higgs-fermion couplings and the scalar/gauge couplings. In particular, we show that the approximate alignment limit, in which the W+W− and ZZ couplings to the observed Higgs boson are approximately SM-like, imposes significant constraints on the Higgs-fermion couplings.
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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].
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].
T.D. Lee, A Theory of Spontaneous T Violation, Phys. Rev. D 8 (1973) 1226 [INSPIRE].
S.L. Glashow and S. Weinberg, Natural Conservation Laws for Neutral Currents, Phys. Rev. D 15 (1977) 1958 [INSPIRE].
E.A. Paschos, Diagonal Neutral Currents, Phys. Rev. D 15 (1977) 1966 [INSPIRE].
M.P. Bento, H.E. Haber, J.C. Romão and J.P. Silva, Multi-Higgs doublet models: physical parametrization, sum rules and unitarity bounds, JHEP 11 (2017) 095 [arXiv:1708.09408] [INSPIRE].
J.C. Romao and J.P. Silva, A resource for signs and Feynman diagrams of the Standard Model, Int. J. Mod. Phys. A 27 (2012) 1230025 [arXiv:1209.6213] [INSPIRE].
F.J. Botella and J.P. Silva, Jarlskog-like invariants for theories with scalars and fermions, Phys. Rev. D 51 (1995) 3870 [hep-ph/9411288] [INSPIRE].
G.C. Branco, L. Lavoura and J.P. Silva, CP Violation, Oxford University Press, Oxford U.K. (1999) [Int. Ser. Monogr. Phys. 103 (1999) 1] [INSPIRE].
C.C. Nishi, The Structure of potentials with N Higgs doublets, Phys. Rev. D 76 (2007) 055013 [arXiv:0706.2685] [INSPIRE].
H.E. Haber, O.M. Ogreid, P. Osland and M.N. Rebelo, Symmetries and Mass Degeneracies in the Scalar Sector, arXiv:1808.08629 [INSPIRE].
F.D. Murnaghan, The Unitary and Rotation Groups, Spartan Books, Washington, D.C. U.S.A. (1962).
H.E. Haber and D. O’Neil, Basis-independent methods for the two-Higgs-doublet model. II. The Significance of tanβ, Phys. Rev. D 74 (2006) 015018 [Erratum ibid. D 74 (2006) 059905] [hep-ph/0602242] [INSPIRE].
W. Grimus and L. Lavoura, Soft lepton flavor violation in a multi Higgs doublet seesaw model, Phys. Rev. D 66 (2002) 014016 [hep-ph/0204070] [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].
W. Grimus and H. Neufeld, Radiative Neutrino Masses in an SU(2) × U(1) Model, Nucl. Phys. B 325 (1989) 18 [INSPIRE].
H.G.J. Veltman, The Equivalence Theorem, Phys. Rev. D 41 (1990) 2294 [INSPIRE].
J.F. Gunion, H.E. Haber and J. Wudka, Sum rules for Higgs bosons, Phys. Rev. D 43 (1991) 904 [INSPIRE].
B. Grinstein, C.W. Murphy, D. Pirtskhalava and P. Uttayarat, Theoretical Constraints on Additional Higgs Bosons in Light of the 126 GeV Higgs, JHEP 05 (2014) 083 [arXiv:1401.0070] [INSPIRE].
I.F. Ginzburg, Multi-Higgs models. Perspectives for identification of wide set of models in future experiments at colliders in the SM-like situation, in proceedings of the 22th International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP 2015), Samara, Russia, 24 June-1 July 2015, arXiv:1502.07197 [INSPIRE].
J.F. Gunion, H.E. Haber, G. Kane and S. Dawson, The Higgs Hunter’s Guide, Westview Press, Boulder CO U.S.A. (2000) [Front. Phys. 80 (2000) 1] [INSPIRE].
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].
N. Craig, J. Galloway and S. Thomas, Searching for Signs of the Second Higgs Doublet, arXiv:1305.2424 [INSPIRE].
H.E. Haber, The Higgs data and the Decoupling Limit, in proceedings of the 1st Toyama International Workshop on Higgs as a Probe of New Physics 2013 (HPNP2013), Toyama, Japan, 13-16 February 2013, arXiv:1401.0152 [INSPIRE].
D.M. Asner et al., ILC Higgs White Paper, in proceedings of the 2013 Community Summer Study on the Future of U.S. Particle Physics: Snowmass on the Mississippi (CSS2013), Minneapolis, MN, U.S.A., 29 July-6 August 2013, arXiv:1310.0763 [INSPIRE].
M. Carena, I. Low, N.R. Shah and C.E.M. Wagner, Impersonating the Standard Model Higgs Boson: Alignment without Decoupling, JHEP 04 (2014) 015 [arXiv:1310.2248] [INSPIRE].
M. Carena, H.E. Haber, I. Low, N.R. Shah and C.E.M. Wagner, Complementarity between Nonstandard Higgs Boson Searches and Precision Higgs Boson Measurements in the MSSM, Phys. Rev. D 91 (2015) 035003 [arXiv:1410.4969] [INSPIRE].
P.S. Bhupal Dev and A. Pilaftsis, Maximally Symmetric Two Higgs Doublet Model with Natural Standard Model Alignment, JHEP 12 (2014) 024 [Erratum JHEP 11 (2015) 147] [arXiv:1408.3405] [INSPIRE].
J. Bernon, J.F. Gunion, H.E. Haber, Y. Jiang and S. Kraml, Scrutinizing the alignment limit in two-Higgs-doublet models: m h = 125 GeV, Phys. Rev. D 92 (2015) 075004 [arXiv:1507.00933] [INSPIRE].
J. Bernon, J.F. Gunion, H.E. Haber, Y. Jiang and S. Kraml, Scrutinizing the alignment limit in two-Higgs-doublet models. II. m H = 125 GeV, Phys. Rev. D 93 (2016) 035027 [arXiv:1511.03682] [INSPIRE].
I.F. Ginzburg, M. Krawczyk and P. Osland, Two Higgs doublet models with CP-violation, in proceedings of the 10th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY02), Seogwipo, Jeju Island, Korea, 26-30 August 2002, pp. 703-706 [hep-ph/0211371] [INSPIRE].
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].
A. Arhrib, E. Christova, H. Eberl and E. Ginina, CP violation in charged Higgs production and decays in the Complex Two Higgs Doublet Model, JHEP 04 (2011) 089 [arXiv:1011.6560] [INSPIRE].
A. Barroso, P.M. Ferreira, R. Santos and J.P. Silva, Probing the scalar-pseudoscalar mixing in the 125 GeV Higgs particle with current data, Phys. Rev. D 86 (2012) 015022 [arXiv:1205.4247] [INSPIRE].
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].
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].
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].
D. Fontes, M. Mühlleitner, J.C. Romão, R. Santos, J.P. Silva and J. Wittbrodt, The C2HDM revisited, JHEP 02 (2018) 073 [arXiv:1711.09419] [INSPIRE].
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].
A. Dery, C. Frugiuele and Y. Nir, Large Higgs-electron Yukawa coupling in 2HDM, JHEP 04 (2018) 044 [arXiv:1712.04514] [INSPIRE].
C.H. Llewellyn Smith, High-Energy Behavior and Gauge Symmetry, Phys. Lett. B 46 (1973) 233 [INSPIRE].
J.M. Cornwall, D.N. Levin and G. Tiktopoulos, Derivation of Gauge Invariance from High-Energy Unitarity Bounds on the S Matrix, Phys. Rev. D 10 (1974) 1145 [Erratum ibid. D 11 (1975) 972] [INSPIRE].
H.A. Weldon, The Effects of Multiple Higgs Bosons on Tree Unitarity, Phys. Rev. D 30 (1984) 1547 [INSPIRE].
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Bento, M.P., Haber, H.E., Romão, J.C. et al. Multi-Higgs doublet models: the Higgs-fermion couplings and their sum rules. J. High Energ. Phys. 2018, 143 (2018). https://doi.org/10.1007/JHEP10(2018)143
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DOI: https://doi.org/10.1007/JHEP10(2018)143