Renormalization in the Higgs triplet model

1. Renormalization in the Higgs triplet model Mariko Kikuchi (Univ. of Toyama) Collaborators: Mayumi Aoki, Shinya Kanemura, Kei Yagyu M. Aoki, S. Kanemura, M. Kikuchi, K. Yagyu,PLB 714, 279(2012) Workshop on Multi-Higgs Models , 31. August, 2012, Lisbon

2. Contents We focus on the Higgs triplet model. The motivation is neutrino masses. Higgs Triplet Model(HTM) Renormalization in the EW parameters One loop calculations in the Higgs potential • Type II seesaw scenario • EW ρ parameter, Mass Formula mW2, ρ, Γ(h→gg) hWW coupling Corrections to Mass formula hhh coupling Corrections to

3. Neutrino Mass Higgs triplet model (HTM) Type II seesaw model Cheng, Li (PRD, 1980) Mohapatra, Senjanovic (PRD, 1981) Mass eigenstates H±±, H±, A, H, h Breaking L# two units ⇒ Majorana massesare produced. × If μ is small, masses of triplet fields can be at the TeV scale. It is possible to test at the collider experiment.⇒MΔ～ O(100)GeV～ 1TeV!!!

4. Neutrino Mass Higgs triplet model (HTM) Type II seesaw model Cheng, Li (PRD, 1980) Mohapatra, Senjanovic (PRD, 1981) Mass eigenstates H±±, H±, A, H, h Breaking L# two units ⇒ Majorana massesare produced. × • ～ O(1) μ～ O(0.1-1)eV If μ is small, masses of triplet fields can be at the TeV scale. It is possible to test at the collider experiment.⇒MΔ～ O(100)GeV～ 1TeV !!!

5. Model • Mass eigenstatesH±±, H±, A, H, h • Mass hierarchy • Mass spectrum Mass difference arises due to λ5

6. Mass Relation • Constraint from ρ parameter i = φ, Δ HTM （experiment） vφ：　VEV of φ vΔ：　VEV of Δ vΔ2vφ2　⇒　mixing between φ and Δis small. (αis small.) • Mass formula mH++2－ mH+2≃ mH+2－ mA2≃ － This mass formula is useful to distinguish the model from the other models. For future precision measurement, we have to obtain the formula with radiative corrections.

7. Phenomenology If Δm≠0, decay processes of triplet-like scalar fields are different from the case with Δm=0. • Ex)) the decay process of H++ Δm≠ 0 Δm= 0 (Δm=30GeV) the cascade decay of H++dominates. H++→　H+W+→　H0W+W+→　bb W+W+ H++→ l+l+⇒ mH++＞400GeV LHCdata In the case (Δm　≠ 0), mH++＞400GeV • Mass identification Aoki, Kanemura, Yagyu (PRD85, 055007) 2012 All masses of triplet-like Higgs bosons may be measured at LHC by evaluating the transverse mass distribution.

8. Renormalization for EW parameter Model with ρ=1 at tree (SM, THDM, …) 3 inputs: GF, α, mZ2 + - Quadraticmass effects appear! Parameters in Gauge Sector: v, vΔ, g, g’ HTM: ρ≠1 at tree 4 inputs: GF, α, mZ2, sin2θW Renormalization Condition for sin2θW Blank, Hollik (NP,1998) Kanemura, Yagyu (PRD, 2012) Quadraticmass effectsare absorbed by the renormalization of sin2θW.

9. Kanemura, Yagyu (PRD,2012) Aoki, Kanemura, Kikuchi, Yagyu (in preparation) mh=125GeV mlightest=150 GeV α = 0

10. EW parameters • Input parameters PDG(2010) • Tree level relations

11. Kanemura, Yagyu (PRD,2012) mW2, ρ Aoki, Kanemura, Kikuchi, Yagyu (in preparation) mh=125GeV mlightest=150GeV, α = 0 Case I is favored !!!!! Case II is constrained !!!

12. mW2, ρ Kanemura, Yagyu (PRD,2012) Aoki, Kanemura, Kikuchi, Yagyu (in preparation) mh=125GeV mlightest=150GeV, α = 0 Δm= -400 GeV Δm = -100 GeV |Δm|＝100～400GeV Unitarity requires |Δm| < 300-400 GeV |Δm|＝mH++ - mH+

13. mW2, ρ Kanemura, Yagyu (PRD,2012) mh=125GeV mlightest=150GeV, α = 0 Aoki, Kanemura, Kikuchi, Yagyu (in preparation) vΔis 3.5-8 GeV

14. EW Data |Δm|～ O(100-400) GeV vΔ　～3.5-8 GeV Unitarity Bound |Δm| < 300-400 GeV mH++～ 100-200GeV

15. Rgg 2 t W H++ H+ Rggdepends on λ4 + + + A. Arhrib, R. Benbrik, M. Chabab, G. Moultaka, L. Rahili(arXiv:1112.5453 ) A. G. Akeroyd, S. Moretti (arXiv: 1206.0535 ) vΔ=5.69GeV mlightest=300GeV ICHEP(2012) Summary Talk If λ4 is minus, Rgg can be larger than 1 !! Unitarity Bound -3≦λ4≦4 (Δm=-100GeV)

16. Renormalization of the Higgs potential ＜Physical Parameters＞ ＜Parameters in the Higgs potential＞ μ , m , M , λ1 , λ2 , λ3 , λ4 , λ5 v , vΔ , mH++ , mH+ , mA , mh , mH , α • Counter-terms δv, δvΔ,δmH++2 , δmH+2, δmA2, δmh2, δmH2 , δα Tadpoles：δTφ,δTΔ , Renormalization of wave functions：δZh , δZH , δZA , δZG0 , δZH+ , δZG+ , δZH++ , δChH , δCAG0 , δCH+G+ • We determine δv, δvΔby EW renormalization. • On-shellrenormalization scheme Field strength Mixing angle

17. Radiative correction to the mass formula In favored parameter sets by EW data : mH++＜mH+＜mH,mA, vΔ＝3.5-8 GeV, Δm＝100～300GeV, mlightest＝100～150GeV 1 mA2(tree) have been an output parameter. New Mass formula with the 1-loop correction ΔR is large (O(10)% as a correction). ⇒ We have to take into account the radiative correction for comparing the precision data.

18. hZZ,hWW hZZ hWW Δm= mH++－mH+ • hZZ receives about -1.8～-2.5% correction. • hWW receives about -0.5～-1.8% correction. • ⇒　We expect to test hZZ and hWW coupling at ILC.

19. hhh • hhh receives a large correction, about 25～100% • ⇒We expect to test hhh coupling at ILC.

20. Summary • The tree level The precision measurement in the future Theoretical calculations with radiative corrections × • ρ≠ 1 mH++2－ mH+2≃ mH+2－ mA2 = ID of a model • 1 loop correction • Renormalization scheme is different from the one of the SM. Input parameters Gf, α, mZ2, + sin2θW • Results of radiative corrections • mW2 and ρ ⇒ Constraint to the parameters region • Rggcan be larger than 1. • ΔRcan be large.　～O(10)% • hZZ, hWW receives O(1)% corrections. • hhh can receive large corrections as non-decoupling effects.～10~30% When we compare with the precision data, we should consider the radiative correction !!!

21. Thank you !! Mariko

22. ΔR in the case II

23. Renormalization for EW parameter Blank, Hollik (NP,1998) Kanemura, Yagyu (PDR, 2012) ρ deviates from unity at the tree level. Parameters in the kinetic term: v, vΔ, g, g’ Physical parameters:Gf, α, mZ2, sin2θW, mW2, v, (vΔ) Input parameters Gf, α, mZ2, sin2θW On-shellrenormalization ρ≠1(HTM) ρ=1(SM, THDM) Δr Δr Quadraticmass effects in Δrare absorbed by renormal of sin2θW. Quadraticmass effects appear!