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

Introduction  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 !!!  New physics ⇔ the Higgs sector ? Some new physics models contain each characteristic extended Higgs sector. Determination of the Higgs sector New physics Our studying is determining the Higgs sector by the result of the accelerator experiment. THDs (Φ 1 ＋ Φ 2 ) MSSM Φ 1 ＋ Φ 2 (inart) New physics model (DM)

Contents SM-like Triplet-like The precision measurement expected in the future × Theoretical calculations with radiative corrections =ID of a model 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. Type II seesaw model = Higgs triplet model

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

Type Ⅱ seesaw mechanism × SU(2) L U(1) Y U(1) L Φ21/20 Δ31-2 Majorana type neutrino masses are produced because μ term breaks L# two units.

Type Ⅱ seesaw mechanism × SU(2) L U(1) Y U(1) L Φ21/20 Δ31-2 Majorana type neutrino masses are produced because μ term breaks L# two units. Recently, a mechanism which have very small μ was proposed by perturbative effects. Kanemura, Sugiyama （ arXiv: (2011))

Lagrangian SU(2) L U(1) Y U(1) L Φ21/20 Δ31-2 New Yukawa interaction terms A Higgs potential

Mass structure  Constraint from the experimental result of ρ parameter Constraint from ρ parameter v Δ 2 <<v φ 2 →Mixing between φ and Δ is very small. （ an experimental value ） SM-like scalar field : h Triplet-like scalar field ： H ±±, H ±, H, A v φ ： VEV of the doublet field v Δ ： VEV of the triplet field  Mass eigenstates Extended Higgs with (T i, Y i )

Mass structure Mass spectrum Constraint from ρ parameter v Δ 2 <<v Φ 2 We focus on the interesting relation among masses m Φ 2 － m Φ’ 2 m H++ 2 － m H+ 2 ≃ m H+ 2 － m A 2

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

Phenomenology 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. Case Ⅱ (Δm=30GeV) NO the mass difference The mass difference exists H ++ の BR Han et.al (2008) Aoki, Kanemura, Yagyu (2011) Akeroyd, Sugiyama (2011) The parameter corresponding to the mass difference is λ 5. λ 5 is a free parameter. → We take λ 5 ≠0, and consider the case which there is the mass difference.

Phenomenology Aoki, Kanemura, Yagyu, (Phys.Rev. D85 (2012)) Production and decay processes of H ++ in the Case II H ++ → H + W + → H 0 W + W + → bb W + W + The case of Δm 2 ≠0 Cascade decays of triplet fields dominate. All masses of triplet-like Higgs bosons can be measured in LHC by observing the Yacobian peak in the transverse mass distribution.

Radiative correction of the HTM Renormalization of the gauge sector （ g,g’,v,v Δ ） 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 Mass spectrum Radiative corrections to the mass formula hhh coupling We calculate radiative corrections and evaluate the ratio of them of the HTM to them of the SM. Kanemura, Yagyu (arXiv: (2011))

Radiative correction of the HTM Renormalization of the gauge sector （ g,g’,v,v Δ ） 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 Mass spectrum Radiative corrections to the mass formula hhh coupling We calculate radiative corrections and evaluate the ratio of them of the HTM to them of the SM. Kanemura, Yagyu (arXiv: (2011))

Renormalization of the Higgs sector Tadpole ： δT φ, δT Δ, δv, δv Δ, δm H++ 2, δm H+ 2, δm A 2, δm h 2, δm H 2, δα Wave function renormalization ： δZ h, δZ H, δZ A, δZ G0, δZ H+, δZ G+, δZ H++, δC hH, δC AG0, δC H+G+  Parameters of potential （ 8 ）  Physical parameters (8)  Counter-terms (20) v, v Δ, m H++, m H+, m A, m h, m H, α μ, m, M, λ 1, λ 2, λ 3, λ 4, λ 5

Renormalization of the Higgs sector δv, δv Δ Vacuum conditions On-shell conditions Diagonalization at the one-loop level By renormalization conditions of electroweak parameters (G F, sin 2 θ W, α EM, m Z ) The others are determined by renormalization conditions of the Higgs sector. Tadpoles Two point functions δT φ, δT Δ δα, δC hH, δC AG0, δC H+G+, ….. δm H++ 2, δm H+ 2, δm A 2, δm h 2, δm H 2  Determining counter-terms Kanemura, Yagyu (arXiv: ), 2011 P 2 =m φ 2 ， m φ’ 2 P 2 =m φ 2

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

One-loop corrected hhh coupling By measuring the hhh coupling in ILC, the HTM can be tested ！ α=0, v Δ 2 << v φ 2 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 m H++ ～ O(100)GeV, |Δm| ～ 100GeV. In this parameter region, Deviation in hhh is predected more than 25% ！ Case Ⅰ (%) Unitarity is broken on-shell renormalization of the hhh coupling

Summary 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. m H++ 2 － m H+ 2 ≃ m H+ 2 － m A 2

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

Widths of Δ-like Higgs bosons

Production cross section

ΔR in the case II

hhh coupling in the case II

LHC ILC