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Renormalization of the Higgs Triplet Model

Renormalization of the Higgs Triplet Model. Collaborators M. Aoki （ Kanazawa Univ. ） , S. Kanemura （ Univ. of Toyama ） , K. Yagyu （ National Central University ）. Mariko Kikuchi （ Univ. of Toyama ）. Aoki, Kanemura , Kikuchi, Yagyu arXiv:1204.1951 [ hep-ph ]. 2012. 06. 09.

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Renormalization of the Higgs Triplet Model

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  1. Renormalization of the Higgs Triplet Model Collaborators M. Aoki（Kanazawa Univ.）, S. Kanemura（Univ. of Toyama）, K. Yagyu（ National Central University） Mariko Kikuchi（Univ. of Toyama） Aoki, Kanemura, Kikuchi, Yagyu arXiv:1204.1951 [hep-ph] 2012. 06. 09

  2. Higgs sector is unknown. • The Higgs sector of the SM(minimal) is just assumption. • There are many possibilities for the Higgs sector. • Several phenomena which can not be explained in the SM • Tiny neutrino masses • Existence of dark matter • Baryon asymmetry of the Universe →　New physics beyond the SM is required !!! MSSM • New physics 　⇔　the Higgs sector? • Some new physics models contain each characteristic extended Higgs sector. New physics model (DM) THDs (Φ1＋Φ2) Determination of the Higgs sector New physics Φ1＋Φ2(inart) Introduction Our studying is determining the Higgs sector by the result of the accelerator experiment.

  3. １．We constructed the renormalization scheme for the one-loop calculation of the observables in HTM with Y=1. ρ≠1 at the tree level, renormalization of mixing angles, lepton number breaking ２．We calculate the radiative correction to the characteristic mass formula at the tree level . Mass formula () is given a large contribution of radiative corrections. ３．We calculate radiative corrections to hhh coupling. It can devite from the SM prediction due to the non-decoupling property. • Type II seesaw scenario is a mechanism which generates tiny neutrino masses. • The Higgs sector of the Type II seesaw model is Φ＋Δ. • We focus on the HTM this time. SM-like Triplet-like Type II seesaw model = Higgs triplet model The precision measurement expected in the future Theoretical calculations with radiative corrections = ID of a model × Contents

  4. There is a dimension-five operator relevant for neutrino masses. • Neutrinos cannot have masses in the SM. (Dirac mass, Majoranamass ) The Higgs boson obtains the vacuum expectation values(VEV). • There are many mechanisms which predict this operator . TypeⅡseesaw Type Ⅰ seesaw Radiative seesaw（Zeemodel） × Neutrino mass（Seesaw mechanism） Right hand neutrinos A complex triplet scalar field ・A charged singlet scalar field ・Perturbative effect

  5. × Majorana type neutrino masses are produced because μ term breaks L# two units. must be very large (GeV) in an ordinary way, with O(1) couplings, in order to give tiny neutrino masses. But… TypeⅡseesaw mechanism

  6. × Majorana type neutrino masses are produced because μ term breaks L# two units. must be very large (GeV) in an ordinary way, in order to give tiny neutrino masses. But… h and μ are small → EW scale In this case this model can be tested by LHC or Linear Colliders. TypeⅡseesaw mechanism Recently, a mechanism which have very small μ was proposed by perturbative effects.Kanemura, Sugiyama （arXiv:1202.5231 (2011))

  7. New Yukawa interaction terms A Higgs potential Lagrangian

  8. Extended Higgs with (Ti, Yi) • Constraint from the experimental result of ρ parameter Constraint from ρ parameter vΔ2<<vφ2 →Mixing between φ and Δ is very small. （an experimental value） vφ　：　VEV of the doublet field vΔ　：　VEV of the triplet field Mass structure • Mass eigenstates SM-like scalar field :h Triplet-like scalar field：H±±, H±, H, A

  9. Mass spectrum Constraint from ρ parameter vΔ2<<vΦ2 We focus on the interesting relation among masses mΦ2－ mΦ’2 Mass structure mH++2－ mH+2≃ mH+2－ mA2

  10. This model has a characteristic mass formula at the tree level. mH++2－ mH+2≃ mH+2－ mA2≃ － This mass formula is useful to distinguish the model from the other models when all mass of the triplet-like Higgs bosons.

  11. Phenomenology of the HTM without the mass difference often has been studied. • Phenomenology of the HTM with the mass difference is very different from it without the mass difference. Han et.al(2008) Aoki, Kanemura, Yagyu(2011) Akeroyd, Sugiyama (2011) The mass difference exists NO the mass difference Case Ⅱ(Δm=30GeV) H++のBR Phenomenology mH++2－ mH+2≃ mH+2－ mA2≃ － • The parameter corresponding to the mass • difference is λ5. • λ5is a free parameter.　→　We take λ5≠0, and consider the case which there is • the mass difference.

  12. The case of Δm2≠0 Cascade decays of triplet fields dominate. Aoki, Kanemura, Yagyu, (Phys.Rev. D85 (2012)) H++→　H+W+→　H0W+W+→　bb W+W+ Phenomenology Production and decay processes of H++ in the Case II All masses of triplet-like Higgs bosons can be measured in LHC by observing the Yacobian peak in the transverse mass distribution.

  13. Kanemura, Yagyu(arXiv:1201.6287 (2011)) • Renormalization of the gauge sector（g,g’,v,vΔ） • In the HTM(Y=1), ρ parameter deviates from unity at the tree level. • Renormalization scheme of the HTM is different from it of the SM. There is more one independently measured parameters of the HTM than them of the SM. • Renormalization of V(φ, Δ) This talk Radiative corrections to the mass formula • Mass spectrum Radiative correction of the HTM • hhh coupling We calculate radiative corrections and evaluate the ratio of them of the HTM to them of the SM.

  14. Kanemura, Yagyu(arXiv:1201.6287 (2011)) • Renormalization of the gauge sector（g,g’,v,vΔ） • In the HTM(Y=1), ρ parameter deviates from unity at the tree level. • Renormalization scheme of the HTM is different from it of the SM. There is more one independently measured parameters of the HTM than them of the SM. • Renormalization of V(φ, Δ) This talk Radiative corrections to the mass formula • Mass spectrum Radiative correction of the HTM • hhh coupling We calculate radiative corrections and evaluate the ratio of them of the HTM to them of the SM.

  15. Parameters of potential（8） μ , m , M , λ1 , λ2 , λ3 , λ4 , λ5 • Physical parameters (8) v , vΔ , mH++ , mH+ , mA , mh , mH , α • Counter-terms (20) δv, δvΔ,δmH++2 , δmH+2 , δmA2, δmh2, δmH2 , δα Tadpole ：δTφ,δTΔ, Renormalization of the Higgs sector Wave function renormalization ： δZh , δZH , δZA , δZG0 , δZH+ , δZG+ , δZH++ , δChH , δCAG0 , δCH+G+

  16. Determining counter-terms • By renormalization conditions of electroweak parameters (GF ,sin2θW , αEM, mZ) δv, δvΔ Kanemura, Yagyu(arXiv:1201.6287), 2011 • The others are determined by renormalization conditions of the Higgs sector. Tadpoles Two point functions Vacuum conditions δTφ,δTΔ Renormalization of the Higgs sector δmH++2 , δmH+2, δmA2, δmh2 , δmH2 On-shell conditions P2=mφ2 Diagonalization at the one-loop level δα , δChH, δCAG0 , δCH+G+, ….. P2=mφ2，mφ’2

  17. mh=125GeV , α=0 Δm = mH++ - mH+ Case Ⅰ Ratio of the mass difference R 1 (mA2)treeis determined by mH++2and mH+2 ΔR The pole mass of A is a predicted value In favored parameter sets by EW precision date: mH++～O(100)GeV,|Δm|～100GeV R is given a large correction as large as O(10)%. Radiative corrections to the mass spectrum Modification of R= 1 by the one-loop correction : ΔR

  18. on-shell renormalization of the hhh coupling α=0,vΔ2 << vφ2 Quartic mass dependence of Δ-like Higgs bosons appears to the hhh coupling.　→　non-decoupling property of the Higgs sector Results for the renormalization of EW parameters suggest mH++～O(100)GeV, |Δm|～100GeV. In this parameter region, Deviation in hhh is predected more than25% ！ One-loop corrected hhhcoupling Case Ⅰ (%) By measuring the hhhcoupling in ILC, the HTM can be tested！ Unitarity is broken

  19. Type II seesaw model (the HTM) has a mechanism which can simply produce tiny neutrino masses . • In the HTM, there is a characteristic mass formula at the tree level from a constraint from ρ parameter. → It’s very useful to test the model. • It is important to calculate the observables at one-loop level to compare them from the precision measurement expected in future. So we have constructed the renormalization of the Higgs sector in the HTM and calculated some observables at the one-loop level. • We find that the radiative correction to the mass formula which depends on triplet like Higgs masses and the mass difference is large. →we may be able to identify the model by precisely measuring the mass spectrum at the LHC and the ILC. • We find that the radiative correction to the hhh coupling is large in the allowed region under the EW precision data. →We may be able to identify the model at the ILC. mH++2－ mH+2≃ mH+2－ mA2 Summary

  20. hhh coupling in the THDM Kanemura, Okada, Senaha, Yuan (2004)

  21. Widths of Δ-like Higgs bosons

  22. Production cross section

  23. ΔR in the case II

  24. hhh coupling in the case II

  25. LHC ILC

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