MultiHiggs doublet models: physical parametrization, sum rules and unitarity bounds
Abstract
If the scalar sector of the Standard Model is nonminimal, one might expect multiple generations of the hypercharge1/2 scalar doublet analogous to the generational structure of the fermions. In this work, we examine the structure of a Higgs sector consisting of N Higgs doublets (where N ≥ 2). It is particularly convenient to work in the socalled charged Higgs basis, in which the neutral Higgs vacuum expectation value resides entirely in the first Higgs doublet, and the charged components of remaining N  1 Higgs doublets are masseigenstate fields. We elucidate the interactions of the gauge bosons with the physical Higgs scalars and the Goldstone bosons and show that they are determined by an N × 2N matrix. This matrix depends on (N  1)(2N  1) real parameters that are associated with the mixing of the neutral Higgs fields in the charged Higgs basis. Among these parameters, N  1 are unphysical (and can be removed by rephasing the physical charged Higgs fields), and the remaining 2(N  1)^{2} parameters are physical. We also demonstrate a particularly simple form for the cubic interaction and some of the quartic interactions of the Goldstone bosons with the physical Higgs scalars. These results are applied in the derivation of Higgs coupling sum rules and treelevel unitarity bounds that restrict the size of the quartic scalar couplings. In particular, new applications to three Higgs doublet models with an order4 CP symmetry and with a ${\mathbb{Z}}_{3}$ symmetry, respectively, are presented.
 Authors:

 Univ. of Lisbon (Portugal). Center for Theoretical Particle Physics (CFTP). Dept. of Physics. Inst. Superior Técnico
 Univ. of California, Santa Cruz, CA (United States). Santa Cruz Inst. for Particle Physics
 Publication Date:
 Research Org.:
 Univ. of California, Santa Cruz, CA (United States); Univ. of Lisbon (Portugal)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Foundation for Science and Technology (FCT) (Portugal)
 OSTI Identifier:
 1501931
 Grant/Contract Number:
 SC0010107; PHY1066293; CERN/FISNUC/0010/2015; UID/FIS/00777/2013
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 11; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Beyond Standard Model; Higgs physics; CP violation; discrete symmetries
Citation Formats
Bento, Miguel P., Haber, Howard E., Romão, J. C., and Silva, João P. MultiHiggs doublet models: physical parametrization, sum rules and unitarity bounds. United States: N. p., 2017.
Web. doi:10.1007/jhep11(2017)095.
Bento, Miguel P., Haber, Howard E., Romão, J. C., & Silva, João P. MultiHiggs doublet models: physical parametrization, sum rules and unitarity bounds. United States. doi:10.1007/jhep11(2017)095.
Bento, Miguel P., Haber, Howard E., Romão, J. C., and Silva, João P. Wed .
"MultiHiggs doublet models: physical parametrization, sum rules and unitarity bounds". United States. doi:10.1007/jhep11(2017)095. https://www.osti.gov/servlets/purl/1501931.
@article{osti_1501931,
title = {MultiHiggs doublet models: physical parametrization, sum rules and unitarity bounds},
author = {Bento, Miguel P. and Haber, Howard E. and Romão, J. C. and Silva, João P.},
abstractNote = {If the scalar sector of the Standard Model is nonminimal, one might expect multiple generations of the hypercharge1/2 scalar doublet analogous to the generational structure of the fermions. In this work, we examine the structure of a Higgs sector consisting of N Higgs doublets (where N ≥ 2). It is particularly convenient to work in the socalled charged Higgs basis, in which the neutral Higgs vacuum expectation value resides entirely in the first Higgs doublet, and the charged components of remaining N  1 Higgs doublets are masseigenstate fields. We elucidate the interactions of the gauge bosons with the physical Higgs scalars and the Goldstone bosons and show that they are determined by an N × 2N matrix. This matrix depends on (N  1)(2N  1) real parameters that are associated with the mixing of the neutral Higgs fields in the charged Higgs basis. Among these parameters, N  1 are unphysical (and can be removed by rephasing the physical charged Higgs fields), and the remaining 2(N  1)2 parameters are physical. We also demonstrate a particularly simple form for the cubic interaction and some of the quartic interactions of the Goldstone bosons with the physical Higgs scalars. These results are applied in the derivation of Higgs coupling sum rules and treelevel unitarity bounds that restrict the size of the quartic scalar couplings. In particular, new applications to three Higgs doublet models with an order4 CP symmetry and with a Z 3 symmetry, respectively, are presented.},
doi = {10.1007/jhep11(2017)095},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2017,
place = {United States},
year = {2017},
month = {11}
}
Web of Science
Works referenced in this record:
Properties of the general $N$ Higgsdoublet model. I. The orbit space
journal, July 2010
 Ivanov, I. P.; Nishi, C.
 Physical Review D, Vol. 82, Issue 1
Theoretical constraints on additional Higgs bosons in light of the 126 GeV Higgs
journal, May 2014
 Grinstein, Benjamín; Murphy, Christopher W.; Pirtskhalava, David
 Journal of High Energy Physics, Vol. 2014, Issue 5
Jarlskoglike invariants for theories with scalars and fermions
journal, April 1995
 Botella, F. J.; Silva, João P.
 Physical Review D, Vol. 51, Issue 7
The anatomy of electroweak symmetry breaking Tome II: The Higgs bosons in the Minimal Supersymmetric Model
journal, April 2008
 Djouadi, A.
 Physics Reports, Vol. 459, Issue 16
Theory and phenomenology of twoHiggsdoublet models
journal, July 2012
 Branco, G. C.; Ferreira, P. M.; Lavoura, L.
 Physics Reports, Vol. 516, Issue 12
The anatomy of electroweak symmetry breaking
journal, February 2008
 Djouadi, Abdelhak
 Physics Reports, Vol. 457, Issue 14
Enhanced charged Higgs production through W Higgs fusion in W b scattering
journal, May 2016
 Arhrib, Abdesslam; Cheung, Kingman; Lee, Jae Sik
 Journal of High Energy Physics, Vol. 2016, Issue 5
Basisindependent methods for the twoHiggsdoublet model
journal, August 2005
 Davidson, Sacha; Haber, Howard E.
 Physical Review D, Vol. 72, Issue 3
The gauge hierarchy problem, technicolor, supersymmetry, and all that
journal, February 1984
 Susskind, Leonard
 Physics Reports, Vol. 104, Issue 24
Radiative neutrino masses in an SU(2) × U(1) model
journal, October 1989
 Grimus, W.; Neufeld, H.
 Nuclear Physics B, Vol. 325, Issue 1
Strength of Weak Interactions at Very High Energies and the Higgs Boson Mass
journal, April 1977
 Lee, Benjamin W.; Quigg, C.; Thacker, H. B.
 Physical Review Letters, Vol. 38, Issue 16
CP conserving twoHiggsdoublet model: The approach to the decoupling limit
journal, April 2003
 Gunion, John F.; Haber, Howard E.
 Physical Review D, Vol. 67, Issue 7
Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
journal, September 2012
 Chatrchyan, S.; Khachatryan, V.; Sirunyan, A. M.
 Physics Letters B, Vol. 716, Issue 1
Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
journal, September 2012
 Aad, G.; Abajyan, T.; Abbott, B.
 Physics Letters B, Vol. 716, Issue 1
Treelevel unitarity constraints in the most general two Higgs doublet model
journal, December 2005
 Ginzburg, I. F.; Ivanov, I. P.
 Physical Review D, Vol. 72, Issue 11
CP violation in charged Higgs production and decays in the Complex Two Higgs Doublet Model
journal, April 2011
 Arhrib, A.; Christova, E.; Eberl, H.
 Journal of High Energy Physics, Vol. 2011, Issue 4
Suppression of flavor changing effects from neutral spinless meson exchange in gauge theories
journal, March 1979
 Georgi, Howard; Nanopoulos, D. V.
 Physics Letters B, Vol. 82, Issue 1
Fundamental CP violating quantities in an SU(2)⊗U(1) model with many Higgs doublets
journal, October 1994
 Lavoura, L.; Silva, João P.
 Physical Review D, Vol. 50, Issue 7
Soft leptonflavor violation in a multiHiggsdoublet seesaw model
journal, July 2002
 Grimus, Walter; Lavoura, Luís
 Physical Review D, Vol. 66, Issue 1
Twocomponent spinor techniques and Feynman rules for quantum field theory and supersymmetry
journal, September 2010
 Dreiner, Herbi K.; Haber, Howard E.; Martin, Stephen P.
 Physics Reports, Vol. 494, Issue 12
High energy behaviour and gauge symmetry
journal, September 1973
 Llewellyn Smith, C. H.
 Physics Letters B, Vol. 46, Issue 2
$CP$ violation conditions in $N$ Higgsdoublet potentials
journal, August 2006
 Nishi, C. C.
 Physical Review D, Vol. 74, Issue 3
The oblique parameters in multiHiggsdoublet models
journal, September 2008
 Grimus, W.; Lavoura, L.; Ogreid, O. M.
 Nuclear Physics B, Vol. 801, Issue 12
Stability of the normal vacuum in multiHiggsdoublet models
journal, October 2006
 Barroso, A.; Ferreira, P. M.; Santos, R.
 Physical Review D, Vol. 74, Issue 8
Analysis of an extended scalar sector with ${S}_{3}$ symmetry
journal, May 2014
 Das, Dipankar; Dey, Ujjal Kumar
 Physical Review D, Vol. 89, Issue 9
Algebraic/combinatorial proofs of Cayleytype identities for derivatives of determinants and pfaffians
journal, April 2013
 Caracciolo, Sergio; Sokal, Alan D.; Sportiello, Andrea
 Advances in Applied Mathematics, Vol. 50, Issue 4
The symmetrybreaking pattern of scalars in low dimension representations
journal, June 1982
 Wu, Dandi
 Nuclear Physics B, Vol. 199, Issue 3
Derivation of gauge invariance from highenergy unitarity bounds on the $S$ matrix
journal, August 1974
 Cornwall, John M.; Levin, David N.; Tiktopoulos, George
 Physical Review D, Vol. 10, Issue 4
Building and testing models with extended Higgs sectors
journal, July 2017
 Ivanov, Igor P.
 Progress in Particle and Nuclear Physics, Vol. 95
Unitarity bound in the most general two Higgs doublet model
journal, December 2015
 Kanemura, Shinya; Yagyu, Kei
 Physics Letters B, Vol. 751
Is there a strong interaction sector in the standard lattice Higgs model?
journal, October 1988
 Lüscher, M.; Weisz, P.
 Physics Letters B, Vol. 212, Issue 4
A Resource for Signs and Feynman Diagrams of the Standard Model
journal, October 2012
 RomÃO, Jorge C.; Silva, JoÃO P.
 International Journal of Modern Physics A, Vol. 27, Issue 26
Works referencing / citing this record:
ThreeHiggsdoublet model under A4 symmetry implies alignment
journal, January 2018
 Pramanick, Soumita; Raychaudhuri, Amitava
 Journal of High Energy Physics, Vol. 2018, Issue 1
CP4 miracle: shaping Yukawa sector with CP symmetry of order four
journal, January 2018
 Ferreira, P. M.; Ivanov, Igor P.; Jiménez, Enrique
 Journal of High Energy Physics, Vol. 2018, Issue 1
Symmetries and mass degeneracies in the scalar sector
journal, January 2019
 Haber, Howard E.; Ogreid, O. M.; Osland, P.
 Journal of High Energy Physics, Vol. 2019, Issue 1
Systematic construction of basis invariants in the 2HDM
journal, May 2019
 Trautner, Andreas
 Journal of High Energy Physics, Vol. 2019, Issue 5
Alignment limit in three Higgsdoublet models
journal, August 2019
 Das, Dipankar; Saha, Ipsita
 Physical Review D, Vol. 100, Issue 3
Light charged Higgs boson with dominant decay to quarks and its search at the LHC and future colliders
journal, December 2018
 Akeroyd, A. G.; Moretti, Stefano; Song, Muyuan
 Physical Review D, Vol. 98, Issue 11