# Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → WW/ZZ → 4 fermions

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## Abstract

We perform the renormalization of different types of Two-Higgs-Doublet Models for the calculation of observables at next-to-leading order. In detail, we suggest four different renormalization schemes based on on-shell renormalization conditions as far as possible and on \( \overline{\mathrm{MS}} \) prescriptions for the remaining field-mixing parameters where no distinguished on-shell condition exists and make contact to existing schemes in the literature. In particular, we treat the tadpole diagrams in different ways and discuss issues of gauge independence and perturbative stability in the considered schemes. The renormalization group equations for the \( \overline{\mathrm{MS}} \) parameters are solved in each scheme, so that a consistent renormalization scale variation can be performed. We have implemented all Feynman rules including counterterms and the renormalization conditions into a FeynArts model file, so that amplitudes and squared matrix elements can be generated automatically. As an application we compute the decay of the light, CP-even Higgs boson of the Two-Higgs-Doublet Model into four fermions at next-to-leading order. The comparison of different schemes and the investigation of the renormalization scale dependence allows us to test the perturbative consistency in each of the renormalization schemes, and to get a better estimate of the theoretical uncertainty that arises due to the truncation of the perturbation series.

## Keywords

Beyond Standard Model Higgs Physics## Notes

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## 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]LHC Higgs Cross Section Working Group collaboration, S. Dittmaier et al.,
*Handbook of LHC higgs cross sections: 1. Inclusive observables*, arXiv:1101.0593 [INSPIRE]. - [4]LHC Higgs Cross Section Working Group collaboration, S. Dittmaier et al.,
*Handbook of LHC Higgs cross sections: 2. Differential distributions*, arXiv:1201.3084 [INSPIRE]. - [5]S. Dittmaier and M. Schumacher,
*The Higgs boson in the standard model — From LEP to LHC: expectations, searches and discovery of a candidate*,*Prog. Part. Nucl. Phys.***70**(2013) 1 [arXiv:1211.4828] [INSPIRE].ADSCrossRefGoogle Scholar - [6]LHC Higgs Cross Section Working Group collaboration, J.R. Andersen et al.,
*Handbook of LHC Higgs cross sections: 3. Higgs properties*, arXiv:1307.1347 [INSPIRE]. - [7]LHC Higgs Cross Section Working Group collaboration, D. de Florian et al.,
*Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector*, arXiv:1610.07922 [INSPIRE]. - [8]M. Spira,
*Higgs boson production and decay at hadron colliders*,*Prog. Part. Nucl. Phys.***95**(2017) 98 [arXiv:1612.07651] [INSPIRE].ADSCrossRefGoogle Scholar - [9]T.D. Lee,
*A theory of spontaneous T violation*,*Phys. Rev.***D 8**(1973) 1226 [INSPIRE].ADSGoogle Scholar - [10]J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson,
*The Higgs hunter’s guide*, Westview Press, U.S.A. (1900).Google Scholar - [11]N. Turok and J. Zadrozny,
*Electroweak baryogenesis in the two doublet model*,*Nucl. Phys.***B 358**(1991) 471 [INSPIRE].ADSCrossRefGoogle Scholar - [12]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].ADSCrossRefGoogle Scholar - [13]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]. - [14]L. Fromme, S.J. Huber and M. Seniuch,
*Baryogenesis in the two-Higgs doublet model*,*JHEP***11**(2006) 038 [hep-ph/0605242] [INSPIRE]. - [15]N.G. Deshpande and E. Ma,
*Pattern of symmetry breaking with two Higgs doublets*,*Phys. Rev.***D 18**(1978) 2574.ADSGoogle Scholar - [16]E.M. Dolle and S. Su,
*The inert dark matter*,*Phys. Rev.***D 80**(2009) 055012 [arXiv:0906.1609] [INSPIRE].ADSGoogle Scholar - [17]J.E. Kim,
*Light pseudoscalars, particle physics and cosmology*,*Phys. Rept.***150**(1987) 1 [INSPIRE].ADSCrossRefGoogle Scholar - [18]R.D. Peccei and H.R. Quinn,
*CP conservation in the presence of instantons*,*Phys. Rev. Lett.***38**(1977) 1440 [INSPIRE].ADSCrossRefGoogle Scholar - [19]H.E. Haber and G.L. Kane,
*The search for supersymmetry: probing physics beyond the standard model*,*Phys. Rept.***117**(1985) 75 [INSPIRE].ADSCrossRefGoogle Scholar - [20]A. Celis, V. Ilisie and A. Pich,
*LHC constraints on two-Higgs doublet models*,*JHEP***07**(2013) 053 [arXiv:1302.4022] [INSPIRE].ADSCrossRefGoogle Scholar - [21]A. Celis, V. Ilisie and A. Pich,
*Towards a general analysis of LHC data within two-Higgs-doublet models*,*JHEP***12**(2013) 095 [arXiv:1310.7941] [INSPIRE].ADSCrossRefGoogle Scholar - [22]S. Chang et al.,
*Two Higgs doublet models for the LHC Higgs boson data at*\( \sqrt{s}=7 \)*and*8*TeV*,*JHEP***09**(2014) 101 [arXiv:1310.3374] [INSPIRE].ADSCrossRefGoogle Scholar - [23]R.V. Harlander, S. Liebler and T. Zirke,
*Higgs Strahlung at the Large Hadron Collider in the 2-Higgs-Doublet Model*,*JHEP***02**(2014) 023 [arXiv:1307.8122] [INSPIRE].ADSCrossRefGoogle Scholar - [24]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].ADSCrossRefzbMATHGoogle Scholar - [25]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 - [26]A. Broggio, E.J. Chun, M. Passera, K.M. Patel and S.K. Vempati,
*Limiting two-Higgs-doublet models*,*JHEP***11**(2014) 058 [arXiv:1409.3199] [INSPIRE].ADSCrossRefGoogle Scholar - [27]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].ADSGoogle Scholar - [28]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]. - [29]D. Goncalves and D. Lopez-Val,
*Pseudoscalar searches with dileptonic tops and jet substructure*,*Phys. Rev.***D 94**(2016) 095005 [arXiv:1607.08614] [INSPIRE].ADSGoogle Scholar - [30]G.C. Dorsch, S.J. Huber, K. Mimasu and J.M. No,
*Hierarchical versus degenerate 2HDM: the LHC run 1 legacy at the onset of run 2*,*Phys. Rev.***D 93**(2016) 115033 [arXiv:1601.04545] [INSPIRE].ADSGoogle Scholar - [31]G. Cacciapaglia, A. Deandrea, S. Gascon-Shotkin, S. Le Corre, M. Lethuillier and J. Tao,
*Search for a lighter Higgs boson in Two Higgs Doublet Models*,*JHEP***12**(2016) 068 [arXiv:1607.08653] [INSPIRE].ADSCrossRefGoogle Scholar - [32]V. Cacchio, D. Chowdhury, O. Eberhardt and C.W. Murphy,
*Next-to-leading order unitarity fits in Two-Higgs-Doublet models with soft*\( {\mathbb{Z}}_2 \)*breaking*,*JHEP***11**(2016) 026 [arXiv:1609.01290] [INSPIRE].CrossRefGoogle Scholar - [33]R. Aggleton et al.,
*Review of LHC experimental results on low mass bosons in multi Higgs models*,*JHEP***02**(2017) 035 [arXiv:1609.06089] [INSPIRE].ADSCrossRefGoogle Scholar - [34]L. Wang, F. Zhang and X.-F. Han,
*Two-Higgs-doublet model of type-II confronted with the LHC run-I and run-II data*,*Phys. Rev.***D 95**(2017) 115014 [arXiv:1701.02678] [INSPIRE].ADSGoogle Scholar - [35]R. Santos and A. Barroso,
*On the renormalization of two Higgs doublet models*,*Phys. Rev.***D 56**(1997) 5366 [hep-ph/9701257] [INSPIRE]. - [36]S. Kanemura, Y. Okada, E. Senaha and C.P. Yuan,
*Higgs coupling constants as a probe of new physics*,*Phys. Rev.***D 70**(2004) 115002 [hep-ph/0408364] [INSPIRE]. - [37]D. Lopez-Val and J. Solà,
*Neutral Higgs-pair production at linear colliders within the general 2HDM: quantum effects and triple Higgs boson self-interactions*,*Phys. Rev.***D 81**(2010) 033003 [arXiv:0908.2898] [INSPIRE].ADSGoogle Scholar - [38]C. Degrande,
*Automatic evaluation of UV and R2 terms for beyond the standard model lagrangians: a proof-of-principle*,*Comput. Phys. Commun.***197**(2015) 239 [arXiv:1406.3030] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar - [39]M. Krause, R. Lorenz, M. Muhlleitner, R. Santos and H. Ziesche,
*Gauge-independent renormalization of the 2-Higgs-Doublet model*,*JHEP***09**(2016) 143 [arXiv:1605.04853] [INSPIRE].ADSCrossRefGoogle Scholar - [40]A. Denner, L. Jenniches, J.-N. Lang and C. Sturm,
*Gauge-independent*\( \overline{M\ S} \)*renormalization in the 2HDM*,*JHEP***09**(2016) 115 [arXiv:1607.07352] [INSPIRE].ADSCrossRefGoogle Scholar - [41]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 - [42]A. Denner, G. Weiglein and S. Dittmaier,
*Gauge invariance of green functions: background field method versus pinch technique*,*Phys. Lett.***B 333**(1994) 420 [hep-ph/9406204] [INSPIRE]. - [43]A. Denner, G. Weiglein and S. Dittmaier,
*Application of the background field method to the electroweak standard model*,*Nucl. Phys.***B 440**(1995) 95 [hep-ph/9410338] [INSPIRE]. - [44]T. Hahn,
*Generating Feynman diagrams and amplitudes with FeynArts 3*,*Comput. Phys. Commun.***140**(2001) 418 [hep-ph/0012260] [INSPIRE]. - [45]S. Kanemura, M. Kikuchi and K. Yagyu,
*Radiative corrections to the Yukawa coupling constants in two Higgs doublet models*,*Phys. Lett.***B 731**(2014) 27 [arXiv:1401.0515] [INSPIRE].ADSCrossRefGoogle Scholar - [46]S. Kanemura, M. Kikuchi and K. Yagyu,
*Fingerprinting the extended Higgs sector using one-loop corrected Higgs boson couplings and future precision measurements*,*Nucl. Phys.***B 896**(2015) 80 [arXiv:1502.07716] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [47]R. Harlander et al.,
*Interim recommendations for the evaluation of Higgs production cross sections and branching ratios at the LHC in the Two-Higgs-Doublet Model*, arXiv:1312.5571 [INSPIRE]. - [48]A. Denner,
*Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200*,*Fortsch. Phys.***41**(1993) 307 [arXiv:0709.1075] [INSPIRE].ADSGoogle Scholar - [49]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 - [50]G.C. Branco et al.,
*Theory and phenomenology of two-Higgs-doublet models*,*Phys. Rept.***516**(2012) 1 [arXiv:1106.0034] [INSPIRE].ADSCrossRefGoogle Scholar - [51]M. Böhm, H. Spiesberger and W. Hollik,
*On the one loop renormalization of the electroweak standard model and its application to leptonic processes*,*Fortsch. Phys.***34**(1986) 687 [INSPIRE].ADSGoogle Scholar - [52]Y.L. Wu and L. Wolfenstein,
*Sources of CP-violation in the two Higgs doublet model*,*Phys. Rev. Lett.***73**(1994) 1762 [hep-ph/9409421] [INSPIRE]. - [53]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]. - [54]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]. - [55]J.F. Gunion and H.E. Haber,
*Conditions for CP-violation in the general two-Higgs-doublet model*,*Phys. Rev.***D 72**(2005) 095002 [hep-ph/0506227] [INSPIRE]. - [56]S.L. Glashow and S. Weinberg,
*Natural conservation laws for neutral currents*,*Phys. Rev.***D 15**(1977) 1958 [INSPIRE].ADSGoogle Scholar - [57]
- [58]M. Aoki, S. Kanemura, K. Tsumura and K. Yagyu,
*Models of Yukawa interaction in the two Higgs doublet model and their collider phenomenology*,*Phys. Rev.***D 80**(2009) 015017 [arXiv:0902.4665] [INSPIRE].ADSGoogle Scholar - [59]A. Dabelstein,
*The One loop renormalization of the MSSM Higgs sector and its application to the neutral scalar Higgs masses*,*Z. Phys.***C 67**(1995) 495 [hep-ph/9409375] [INSPIRE]. - [60]L. Altenkamp,
*Precise predictions within the two-Higgs-doublet model*, Ph.D. thesis, University of Freiburg, Freiburg, Germany (2017).Google Scholar - [61]A. Denner, E. Kraus and M. Roth,
*Physical renormalization condition for the quark mixing matrix*,*Phys. Rev.***D 70**(2004) 033002 [hep-ph/0402130] [INSPIRE]. - [62]B.A. Kniehl and A. Sirlin,
*A novel formulation of Cabibbo-Kobayashi-Maskawa matrix renormalization*,*Phys. Lett.***B 673**(2009) 208 [arXiv:0901.0114] [INSPIRE].ADSCrossRefGoogle Scholar - [63]C. Becchi, A. Rouet and R. Stora,
*Renormalization of gauge theories*,*Annals Phys.***98**(1976) 287 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [64]A. Freitas and D. Stöckinger,
*Gauge dependence and renormalization of*tan*β in the MSSM*,*Phys. Rev.***D 66**(2002) 095014 [hep-ph/0205281] [INSPIRE]. - [65]M. Sperling, D. Stöckinger and A. Voigt,
*Renormalization of vacuum expectation values in spontaneously broken gauge theories*,*JHEP***07**(2013) 132 [arXiv:1305.1548] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar - [66]G. Degrassi and A. Sirlin,
*Gauge dependence of basic electroweak corrections of the standard model*,*Nucl. Phys.***B 383**(1992) 73 [INSPIRE].ADSCrossRefGoogle Scholar - [67]J. Fleischer and F. Jegerlehner,
*Radiative corrections to Higgs decays in the extended Weinberg-Salam model*,*Phys. Rev.***D 23**(1980) 79.Google Scholar - [68]S. Actis, A. Ferroglia, M. Passera and G. Passarino,
*Two-loop renormalization in the standard model. Part I: prolegomena*,*Nucl. Phys.***B 777**(2007) 1 [hep-ph/0612122] [INSPIRE]. - [69]M. Frank et al.,
*The Higgs boson masses and mixings of the complex MSSM in the Feynman-Diagrammatic approach*,*JHEP***02**(2007) 047 [hep-ph/0611326] [INSPIRE]. - [70]N. Baro, F. Boudjema and A. Semenov,
*Automatised full one-loop renormalisation of the MSSM. I. The Higgs sector, the issue of*tan*β and gauge invariance*,*Phys. Rev.***D 78**(2008) 115003 [arXiv:0807.4668] [INSPIRE]. - [71]H.E. Haber,
*Challenges for nonminimal Higgs searches at future colliders*, in the proceedings of*Perspectives for electroweak interactions in e*^{+}*e*^{−}*collisions*, February 5-8, Tegernsee, Germany (1995), hep-ph/9505240 [INSPIRE]. - [72]H.E. Haber and O. Stal,
*New LHC benchmarks for the*\( \mathcal{C}\mathcal{P} \)*-conserving two-Higgs-doublet model*,*Eur. Phys. J.***C 75**(2015) 491 [arXiv:1507.04281] [INSPIRE].ADSCrossRefGoogle Scholar - [73]S. Heinemeyer, H. Rzehak and C. Schappacher,
*Proposals for bottom quark/squark renormalization in the complex MSSM*,*Phys. Rev.***D 82**(2010) 075010 [arXiv:1007.0689] [INSPIRE].ADSGoogle Scholar - [74]A. Chatterjee, M. Drees, S. Kulkarni and Q. Xu,
*On the on-shell renormalization of the chargino and neutralino masses in the MSSM*,*Phys. Rev.***D 85**(2012) 075013 [arXiv:1107.5218] [INSPIRE].ADSGoogle Scholar - [75]G. Cvetič, S.S. Hwang and C.S. Kim,
*One loop renormalization group equations of the general framework with two Higgs doublets*,*Int. J. Mod. Phys.***A 14**(1999) 769 [hep-ph/9706323] [INSPIRE]. - [76]J. Bijnens, J. Lu and J. Rathsman,
*Constraining general two Higgs doublet models by the evolution of Yukawa couplings*,*JHEP***05**(2012) 118 [arXiv:1111.5760] [INSPIRE].ADSCrossRefGoogle Scholar - [77]N. Chakrabarty, U.K. Dey and B. Mukhopadhyaya,
*High-scale validity of a two-Higgs doublet scenario: a study including LHC data*,*JHEP***12**(2014) 166 [arXiv:1407.2145] [INSPIRE].ADSCrossRefGoogle Scholar - [78]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 [arXiv:1505.04001] [INSPIRE].ADSGoogle Scholar - [79]N.D. Christensen and C. Duhr,
*FeynRules — Feynman rules made easy*,*Comput. Phys. Commun.***180**(2009) 1614 [arXiv:0806.4194] [INSPIRE].ADSCrossRefGoogle Scholar - [80]T. Hahn and M. Pérez-Victoria,
*Automatized one loop calculations in four-dimensions and D-dimensions*,*Comput. Phys. Commun.***118**(1999) 153 [hep-ph/9807565] [INSPIRE]. - [81]A. Bredenstein, A. Denner, S. Dittmaier and M.M. Weber,
*Precise predictions for the Higgs-boson decay H*→*W W/ZZ*→ 4*leptons*,*Phys. Rev.***D 74**(2006) 013004 [hep-ph/0604011] [INSPIRE]. - [82]A. Bredenstein, A. Denner, S. Dittmaier and M.M. Weber,
*Precision calculations for the Higgs decays H*→*ZZ/W W*→ 4*leptons*,*Nucl. Phys. Proc. Suppl.***160**(2006) 131 [hep-ph/0607060] [INSPIRE]. - [83]A. Bredenstein, A. Denner, S. Dittmaier and M.M. Weber,
*Radiative corrections to the semileptonic and hadronic Higgs-boson decays H*→*W W/ZZ*→ 4*fermions*,*JHEP***02**(2007) 080 [hep-ph/0611234] [INSPIRE]. - [84]A. Denner, S. Dittmaier, M. Roth and L.H. Wieders,
*Electroweak corrections to charged-current e*^{+}*e*^{−}→ 4*fermion processes: Technical details and further results*,*Nucl. Phys.***B 724**(2005) 247 [*Erratum ibid.***B 854**(2012) 504] [hep-ph/0505042] [INSPIRE]. - [85]A. Denner, S. Dittmaier and L. Hofer,
*Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations*,*Comput. Phys. Commun.***212**(2017) 220 [arXiv:1604.06792] [INSPIRE].ADSCrossRefGoogle Scholar - [86]S. Dittmaier and M. Krämer, 1,
*Electroweak radiative corrections to W boson production at hadron colliders*,*Phys. Rev.***D 65**(2002) 073007 [hep-ph/0109062] [INSPIRE]. - [87]D. Lopez-Val and J. Solà, Δ
*r in the Two-Higgs-Doublet Model at full one loop level — And beyond*,*Eur. Phys. J.***C 73**(2013) 2393 [arXiv:1211.0311] [INSPIRE].ADSCrossRefGoogle Scholar