# Measuring the triple Higgs self-couplings in two Higgs doublet model

- 35 Downloads

## Abstract

The determination of the Higgs self-coupling in the Standard Model is one of the primary motivations among all the future lepton colliders. Extending the scalar sector of the Standard Model by a new Higgs doublet with a quadratic Higgs potential gives many new features to the model, and most importantly additional Higgs self-couplings emerge. Measuring these couplings is the only way to reconstruct the shape of the scalar potential. In this study, the numerical analysis of several scattering processes is carried out for the two-Higgs-doublet model to determine Higgs self-couplings. These processes are selected among various possible combinations of additional Higgs states. The computation is carried out in the exact alignment limit (*s*_{βα} = 1). The distribution of the cross sections is presented regarding the polarization of the incoming beams and up to \( \sqrt{s}=3 \) TeV. A strategy for extracting the Higgs self-couplings is considered in 2HDM and at the future lepton colliders. Possible final states that could be used for each of the processes are investigated using the decays of the final state particles.

## Keywords

Beyond Standard Model 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]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]. - [3]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]. - [4]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]. - [5]J. Gao,
*CEPC-SppC towards CDR*, in*Proceedings,*8^{th}*International Particle Accelerator Conference (IPAC*2017*)*, Copenhagen, Denmark, 14–19 May 2017, WEPIK016 [INSPIRE]. - [6]CEPC-SPPC Study Group collaboration, Z. Liang,
*Electroweak physics at CEPC*, PoS(ICHEP2016)692 [INSPIRE]. - [7]M. Xiao et al.,
*Study of CEPC performance with different collision energies and geometric layouts*,*Chin. Phys.***C 40**(2016) 087001 [arXiv:1512.07348] [INSPIRE].ADSCrossRefGoogle Scholar - [8]
*Future circular collider study webpage*, http://cern.ch/fcc-ee, November 2017. - [9]TLEP Design Study Working Group collaboration, M. Bicer et al.,
*First look at the physics case of TLEP*,*JHEP***01**(2014) 164 [arXiv:1308.6176] [INSPIRE]. - [10]LCC collaboration, A. Yamamoto,
*International Linear Collider (ILC)*—*technical progress and prospect*, PoS(ICHEP2016)067 [INSPIRE]. - [11]A. Gutierrez-Rodriguez, M.A. Hernandez-Ruiz, O.A. Sampayo, A. Chubykalo and A. Espinoza-Garrido,
*The triple Higgs boson self-coupling at future linear e*^{+}*e*^{−}*colliders energies: ILC and CLIC*,*J. Phys. Soc. Jap.***77**(2008) 094101 [arXiv:0807.0663] [INSPIRE].ADSCrossRefGoogle Scholar - [12]M. Battaglia, E. Boos and W.-M. Yao,
*Studying the Higgs potential at the e*^{+}*e*^{−}*linear collider*,*eConf***C 010630**(2001) E3016 [hep-ph/0111276] [INSPIRE]. - [13]D. d’Enterria,
*Physics at the FCC-ee*, in*Proceedings,*17^{th}*Lomonosov Conference on Elementary Particle Physics*, Moscow, Russia, 20–26 August 2015, World Scientific, Singapore, (2017), pg. 182 [arXiv:1602.05043] [INSPIRE]. - [14]C. Castanier, P. Gay, P. Lutz and J. Orloff,
*Higgs self coupling measurement in e*^{+}*e*^{−}*collisions at center-of-mass energy of*500*GeV*, hep-ex/0101028 [INSPIRE]. - [15]A. Arhrib, R. Benbrik and C.-W. Chiang,
*Probing triple Higgs couplings of the two Higgs doublet model at linear collider*,*Phys. Rev.***D 77**(2008) 115013 [arXiv:0802.0319] [INSPIRE].ADSGoogle Scholar - [16]G. Ferrera, J. Guasch, D. Lopez-Val and J. Solà,
*Triple Higgs boson production at the ILC within a generic two-Higgs-doublet model*, PoS(RADCOR2007)043, (2007) [arXiv:0801.3907] [INSPIRE]. - [17]G. Ferrera, J. Guasch, D. Lopez-Val and J. Solà,
*Triple Higgs boson production in the linear collider*,*Phys. Lett.***B 659**(2008) 297 [arXiv:0707.3162] [INSPIRE].ADSCrossRefGoogle Scholar - [18]A. Djouadi, W. Kilian, M. Muhlleitner and P.M. Zerwas,
*Testing Higgs selfcouplings at e*^{+}*e*^{−}*linear colliders*,*Eur. Phys. J.***C 10**(1999) 27 [hep-ph/9903229] [INSPIRE]. - [19]M.N. Dubinin and A.V. Semenov,
*Triple and quartic interactions of Higgs bosons in the general two Higgs doublet model*, hep-ph/9812246 [INSPIRE]. - [20]M.N. Dubinin and A.V. Semenov,
*Triple and quartic interactions of Higgs bosons in the two Higgs doublet model with CP-violation*,*Eur. Phys. J.***C 28**(2003) 223 [hep-ph/0206205] [INSPIRE]. - [21]G. Chalons, A. Djouadi and J. Quevillon,
*The neutral Higgs self-couplings in the (h)MSSM*,*Phys. Lett.***B 780**(2018) 74 [arXiv:1709.02332] [INSPIRE].ADSCrossRefGoogle Scholar - [22]F. Boudjema and A. Semenov,
*Measurements of the SUSY Higgs selfcouplings and the reconstruction of the Higgs potential*,*Phys. Rev.***D 66**(2002) 095007 [hep-ph/0201219] [INSPIRE]. - [23]M.M. Muhlleitner,
*Testing Higgs selfcouplings at high-energy linear colliders*, hep-ph/0101262 [INSPIRE]. - [24]H. Baer et al.,
*The International Linear Collider technical design report*—*volume*2*: physics*, arXiv:1306.6352 [INSPIRE]. - [25]S.F. Novaes,
*Standard Model: an introduction*, in*Particles and fields. Proceedings,*10^{th}*Jorge Andre Swieca Summer School*, Sao Paulo, Brazil, 6–12 February 1999, pg. 5 [hep-ph/0001283] [INSPIRE]. - [26]G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva,
*Theory and phenomenology of two-Higgs-doublet models*,*Phys. Rept.***516**(2012) 1 [arXiv:1106.0034] [INSPIRE].ADSCrossRefGoogle Scholar - [27]J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson,
*The Higgs hunter*’*s guide*,*Front. Phys.***80**(2000) 1 [INSPIRE].Google Scholar - [28]H.E. Haber and D. O’Neil,
*Basis-independent methods for the two-Higgs-doublet model. II. The significance of*tan*β*,*Phys. Rev.***D 74**(2006) 015018 [*Erratum ibid.***D 74**(2006) 059905] [hep-ph/0602242] [INSPIRE]. - [29]S. Davidson and H.E. Haber,
*Basis-independent methods for the two-Higgs-doublet model*,*Phys. Rev.***D 72**(2005) 035004 [*Erratum ibid.***D 72**(2005) 099902] [hep-ph/0504050] [INSPIRE]. - [30]M. Carena and H.E. Haber,
*Higgs boson theory and phenomenology*,*Prog. Part. Nucl. Phys.***50**(2003) 63 [hep-ph/0208209] [INSPIRE]. - [31]S.L. Glashow and S. Weinberg,
*Natural conservation laws for neutral currents*,*Phys. Rev.***D 15**(1977) 1958 [INSPIRE].ADSGoogle Scholar - [32]S. Kanemura and K. Yagyu,
*Unitarity bound in the most general two Higgs doublet model*,*Phys. Lett.***B 751**(2015) 289 [arXiv:1509.06060] [INSPIRE].ADSCrossRefGoogle Scholar - [33]H.E. Haber, G.L. Kane and T. Sterling,
*The fermion mass scale and possible effects of Higgs bosons on experimental observables*,*Nucl. Phys.***B 161**(1979) 493 [INSPIRE].ADSCrossRefGoogle Scholar - [34]G.C. Branco, M.N. Rebelo and J.I. Silva-Marcos,
*Leptogenesis, Yukawa textures and weak basis invariants*,*Phys. Lett.***B 633**(2006) 345 [hep-ph/0510412] [INSPIRE]. - [35]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]. - [36]A.W. El Kaffas, W. Khater, O.M. Ogreid and P. Osland,
*Consistency of the two Higgs doublet model and CP-violation in top production at the LHC*,*Nucl. Phys.***B 775**(2007) 45 [hep-ph/0605142] [INSPIRE]. - [37]M. Sher,
*Electroweak Higgs potentials and vacuum stability*,*Phys. Rept.***179**(1989) 273 [INSPIRE].ADSCrossRefGoogle Scholar - [38]N.G. Deshpande and E. Ma,
*Pattern of symmetry breaking with two Higgs doublets*,*Phys. Rev.***D 18**(1978) 2574 [INSPIRE].ADSGoogle Scholar - [39]S. Nie and M. Sher,
*Vacuum stability bounds in the two Higgs doublet model*,*Phys. Lett.***B 449**(1999) 89 [hep-ph/9811234] [INSPIRE]. - [40]A.W. El Kaffas, W. Khater, O.M. Ogreid and P. Osland,
*Consistency of the two Higgs doublet model and CP-violation in top production at the LHC*,*Nucl. Phys.***B 775**(2007) 45 [hep-ph/0605142] [INSPIRE]. - [41]I.F. Ginzburg and I.P. Ivanov,
*Tree-level unitarity constraints in the most general*2*HDM*,*Phys. Rev.***D 72**(2005) 115010 [hep-ph/0508020] [INSPIRE]. - [42]D. Eriksson, J. Rathsman and O. Stal, 2
*HDMC: two-Higgs-doublet model calculator physics and manual*,*Comput. Phys. Commun.***181**(2010) 189 [arXiv:0902.0851] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [43]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].ADSCrossRefGoogle Scholar - [44]S. Moretti, 2
*HDM charged Higgs boson searches at the LHC: status and prospects*, PoS(CHARGED2016)014, (2016) [arXiv:1612.02063] [INSPIRE]. - [45]M.E. Peskin and T. Takeuchi,
*A new constraint on a strongly interacting Higgs sector*,*Phys. Rev. Lett.***65**(1990) 964 [INSPIRE].ADSCrossRefGoogle Scholar - [46]M.E. Peskin and T. Takeuchi,
*Estimation of oblique electroweak corrections*,*Phys. Rev.***D 46**(1992) 381 [INSPIRE].ADSGoogle Scholar - [47]H.E. Haber and D. O’Neil,
*Basis-independent methods for the two-Higgs-doublet model III: the CP-conserving limit, custodial symmetry and the oblique parameters S, T, U*,*Phys. Rev.***D 83**(2011) 055017 [arXiv:1011.6188] [INSPIRE].ADSGoogle Scholar - [48]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]. - [49]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].ADSCrossRefzbMATHGoogle Scholar - [50]N. Polonsky and S. Su,
*More corrections to the Higgs mass in supersymmetry*,*Phys. Lett.***B 508**(2001) 103 [hep-ph/0010113] [INSPIRE]. - [51]J. Yan et al.,
*Measurement of the Higgs boson mass and e*^{+}*e*^{−}→*ZH cross section using Z*→*μ*^{+}*μ*^{−}*and Z*→*e*^{+}*e*^{−}*at the ILC*,*Phys. Rev.***D 94**(2016) 113002 [arXiv:1604.07524] [INSPIRE].ADSGoogle Scholar - [52]D. Lopez-Val and J. Solà,
*Neutral Higgs-pair production at one-loop from a generic*2*HDM*, PoS(RADCOR2009)045, (2010) [arXiv:1001.0473] [INSPIRE]. - [53]D. Lopez-Val and J. Solà,
*Higgs boson production at linear colliders from a generic*2*HDM: the role of triple Higgs self-interactions*, in*Helmholtz Alliance Linear Collider Forum: proceedings of the Workshops*, DESY, Hamburg, Germany, (2012), pg. 317 [arXiv:1204.1834] [INSPIRE]. - [54]A. Alloul, N.D. Christensen, C. Degrande, C. Duhr and B. Fuks,
*FeynRules*2*.*0 —*a complete toolbox for tree-level phenomenology*,*Comput. Phys. Commun.***185**(2014) 2250 [arXiv:1310.1921] [INSPIRE]. - [55]C. Degrande,
*Automatic evaluation of UV and R*_{2}*terms for beyond the Standard Model Lagrangians: a proof-of-principle*,*Comput. Phys. Commun.***197**(2015) 239 [arXiv:1406.3030] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar - [56]J. Kublbeck, H. Eck and R. Mertig,
*Computer algebraic generation and calculation of Feynman graphs using FeynArts and FeynCalc*,*Nucl. Phys. Proc. Suppl.***A 29**(1992) 204 [INSPIRE].ADSGoogle Scholar - [57]T. Hahn,
*Generating Feynman diagrams and amplitudes with FeynArts*3,*Comput. Phys. Commun.***140**(2001) 418 [hep-ph/0012260] [INSPIRE]. - [58]T. Hahn and M. Rauch,
*News from FormCalc and LoopTools*,*Nucl. Phys. Proc. Suppl.***157**(2006) 236 [hep-ph/0601248] [INSPIRE]. - [59]
- [60]T. Hahn,
*Concurrent Cuba*,*Comput. Phys. Commun.***207**(2016) 341 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [61]Particle Data Group collaboration, S. Eidelman et al.,
*Review of particle physics*,*Phys. Lett.***B 592**(2004) 1 [INSPIRE]. - [62]D.M. Asner et al.,
*ILC Higgs white paper*, in*Proceedings,*2013*Community Summer Study on the Future of U.S. Particle Physics: Snowmass on the Mississippi (CSS*2013*)*, Minneapolis, MN, U.S.A., 29 July–6 August 2013 [arXiv:1310.0763] [INSPIRE]. - [63]J. Tian,
*Study of Higgs self-coupling at the ILC based on the full detector simulation at*\( \sqrt{s}=500 \)*GeV and*\( \sqrt{s}=1 \)*TeV*, in*Helmholtz Alliance Linear Collider Forum: Proceedings of the Workshops*, DESY, Hamburg, Germany, (2012), pg. 224 [INSPIRE]. - [64]K. Fujii et al.,
*The potential of the ILC for discovering new particles*, arXiv:1702.05333 [INSPIRE].