1. Bounds on the parameter space in the 3-loop neutrino mass model from triviality and vacuum stability K. Yagyu (Univ. of Toyama) D1 Collaborators M. Aoki (Tohoku Univ.) and S. Kanemura (Univ. of Toyama) Paper in preparation February 18., 2010, KEK-PH 2010, @KEK

2. Contents Introduction A TeV scale model which would explain neutrino masses at the 3-loop level, dark matter and baryon asymmetry of the Universe. Triviality and vacuum stability bounds Summary

3. Introduction Problems which cannot be explained in the SM PDG Tiny neutrino masses Dark matter Baryon asymmetry of the Universe ⊿ m solar 2 ~ 8×10 -5 [eV 2 ] ⊿ m atom 2 ~ 2×10 -3 [eV 2 ] Ω DM h 2 =0.106±0.008 Baryon 4% Dark matter 23% Dark energy 73% n B /n γ =(4.7-6.5)×10 -10 (95% C.L.) Need to go beyond the SM In this talk we discuss a model which would simultaneously explain 3 problems in the TeV scale physics. One of the possibility is the Aoki-Kanemura-Seto (AKS) model.

4. The Aoki-Kanemura-Seto model Aoki, Kanemura, Seto, PRL 102 (2009), Aoki, Kanemura, Seto, PRD 80 (2009) O (1) SMExtended Higgs sector TeV-RHν Z 2 -odd ++ SU(3) c ×SU(2) L ×U(1) Y ×Z 2 ×Z 2 ～ Z 2 (softly broken) : To forbid FCNC at the tree-level Z 2 (exact) :To forbid m ν under the 2-loop level Guarantee of DM stability ～ Symmetry Particle Φ 1, Φ 2 → h, H, A, H ± η, S ±, N R CP-even CP-odd Charged Z 2 -even Z 2 -odd SM-like Higgs ・ Tiny neutrino mass →It is naturally generated at the 3-loop level. ・ Dark matter →The lightest Z 2 -odd scalar is the candidate : η u d Φ２Φ２ e Φ１Φ１ ・ A light H + [O(100)GeV] → Type-X two Higgs doublet model (2HDMX) Aoki, Kanemura, Tsumura, Yagyu, PRD 80 (2009) ・ Baryogenesis →Electroweak baryogenesis ★ Strong 1 st order phase transition ★ The source of CP-violation in addition to the Kobayashi-Maskawa matrix Cohen, Kaplan, Nelson, hep-ph/9302210 Fromme, Huber, Seniuch, JHEP11 (2006)

5. Lagrangian Z 2 -even (2HDM) Z 2 -odd Interaction V= RH neutrinos LY=LY= Type-X Yukawa

6. Prediction of the AKS model 400GeV 100GeV Z 2 -evenZ 2 -odd NRNR η S+S+ H H + A 1TeV 50GeV h Testable at the collider experiments ! Mass Spectrum Current experimental data Neutrino data, DM abundance, Strong 1st OPT, LEP bound, b→sγ, B→τν, g-2, τ leptonic decay, LFV (μ→eγ) Prediction Physics of DM [Seto-san’s talk] -Direct detection (XMASS, CDMS II) - h→ηη [Invisible decay] (h: SM-like Higgs boson) Large deviation in the hhh [Harada-san’s talk] Type-X 2HDM -Light charged Higgs [O(100)GeV is available] -Unique decay property H, A→ττ The Majorana nature [Kanemura-san’s talk] Lepton flavor violation Aoki, Kanemura, Seto, arXiv:0912.5536 [hep-ph] Aoki, Kanemura, arXiv:1001.0092 [hep-ph] -BR(μ→eγ) >> BR(τ →eγ) >> BR(τ→μγ) Aoki, Kanemura, Tsumura, Yagyu, PRD 80 (2009) Kanemura, Okada, Senaha, PLB 606 (2005) Rich physics are predicted!

7. Theoretical consistency of the model ・ Some of the coupling constants are O(1), since neutrino masses are generated at the 3-loop level. ・ There are a lot of additional scalar bosons (H, A, H ±, S ±, η). The AKS model is an effective theory whose cutoff scale should be from multi-TeV to 10TeV, since we do not prefer to unnatural fine-tuning of correction of scalar boson masses. We have to examine whether the model has allowed parameter regions which satisfy the conditions of vacuum stability and triviality even when the cutoff scale is 10TeV. In particular in this model It is non-trivial about the consistency of the model.

8. Vacuum stability and triviality bounds Vacuum stability bound Triviality bound We require that scalar potentials do not have a negative coefficient in any direction even when order parameters take large value: V (rv 1, rv 2, …, rv n ) > 0 r→∞ lim We require that all of the coupling constants which vary according to the RGEs do not become strong coupling up to the cutoff scale. Bosonic loop contributes positive, fermionic loop contributes negative for scalar couplings. RGE The condition of the reliable perturbative calculation. ff f f

9. Vacuum stability conditions in the AKS model Kanemura, Kasai, Lin, Okada, Tseng, Yuan PRD 64 (2000) for Zee model Deshpande, Ma, PRD 18 (1978) for 2HDM If all of these inequality are satisfied then vacuum stability is conserved.

10. Triviality bound in the AKS model We analyze scale dependence of coupling constants by using RGEs at the 1-loop level then search the allowed parameter regions as a function of cutoff scale. We take into account the threshold effect as follows: |λ(μ)|, |σ (μ)|,|ρ(μ)|, |κ(μ)|, |ξ(μ)| | μ<Λ < 8π mSmS mNRmNR Λ μ 2HDM +η 2HDM +η+S Full Scalar couplings ： Yukawa couplings ： y t 2 (μ), y b 2 (μ), y τ 2 (μ), h 2 (μ) | μ<Λ < 4π Kanemura, Kasai, Lin, Okada, Tseng, Yuan PRD 64 (2000)

11. RGEs in the AKS model Scalar couplingsYukawa couplings

12. Cut off scale from triviality bound sin(β-α)=1: SM-like limit tanβ=25 κ=1.2 ξ=3.0 [ξ|S| 2 η 2 ] M R =3TeV m h =120GeV M=m H+ =m H =100GeV μ S =200GeV μ η =30GeV

13. Allowed regions from Vacuum Stability V<0 sin(β-α)=1: SM-like limit tanβ=25 κ=1.2 ξ=3.0 [ξ|S| 2 η 2 ] M R =3TeV m h =120GeV M=m H+ =m H =100GeV μ S =200GeV μ η =30GeV

14. Allowed regions from Vacuum Stability and 1 st -OPT V<0 1 st OPT sin(β-α)=1: SM-like limit tanβ=25 κ=1.2 ξ=3.0 [ξ|S| 2 η 2 ] M R =3TeV m h =120GeV M=m H+ =m H =100GeV μ S =200GeV μ η =30GeV

15. Allowed regions from vacuum stability, 1 st -OPT, DM abundance and neutrino mass There are allowed regions even when Λ is around 10TeV which satisfy the condition from vacuum stability and triviality bounds not be inconsistent with current experimental bounds. V<0 1 st OPT m ν, Ωh DM 2 sin(β-α)=1: SM-like limit tanβ=25 κ=1.2 ξ=3.0 [ξ|S| 2 η 2 ] M R =3TeV m h =120GeV M=m H+ =m H =100GeV μ S =200GeV μ η =30GeV

16. Allowed regions from vacuum stability, 1 st -OPT, DM abundance and neutrino mass There are allowed regions even when Λ is around 10TeV which satisfy the condition from vacuum stability and triviality not be inconsistent with experimental bounds. V<0 1 st OPT m ν, Ωh DM 2 sin(β-α)=1: SM-like limit tanβ=25 κ=1.2 ξ=4.0 [ξ|S| 2 η 2 ] M R =3TeV m h =120GeV M=m H+ =m H =100GeV μ S =200GeV μ η =30GeV

17. Allowed regions from vacuum stability, 1 st -OPT, DM abundance and neutrino mass There are allowed regions even when Λ is around 10TeV which satisfy the condition from vacuum stability and triviality not be inconsistent with experimental bounds. V<0 1 st OPT m ν, Ωh DM 2 sin(β-α)=1: SM-like limit tanβ=25 κ=1.2 ξ=5.0 [ξ|S| 2 η 2 ] M R =3TeV m h =120GeV M=m H+ =m H =100GeV μ S =200GeV μ η =30GeV

18. Summary The Aoki-Kanemura-Seto model would explain not only neutrino masses but also dark matter and the baryon asymmetry of the Universe. Since this model has O(1) couplings and contains a lot of additional scalar bosons, it is non-trivial whether the model is stable up to the cutoff scale. In the parameter regions which can explain neutrino data, DM abundance, 1 st OPT and LFV, we confirmed that perturbative calculation is reliable up to around 10TeV and satisfy the condition of vacuum stability. Therefore this model is consistent as the effective theory whose cutoff scale is from multi-TeV to 10TeV.

19. Generation Mechanism of Neutrino Masses Generally Majorana masses of neutrino are written by dim-5 operators. Seesaw mechanism (tree-level) m ν ＝ m D 2 /M M=10 10-15 GeV Merit ： Simple Demerit ： It is difficult to be tested directly. νLνL νRνR νRνR νLνL M Radiative Seesaw scenario Loop suppression factor: [1/(16π 2 )] N It is testable at collider experiments ! If we demand on m ν ~ O (0.1) eV then small c/M are required. There are two scenarios to explain small c/M. Large M or Small c ij It is possible that the scale of M can be reduced without fine-tuning. M ～ O(1)TeV is possible. νLνL νLνL

20. Radiative Seesaw Models ZeeMaBabu KNTAKS m ν DM Baryogenesis 1-loop level 2-loop level 3-loop level The Aoki-Kanemura-Seto (AKS) model would be able to solve the 3 problems simultaneously at the TeV-scale physics. PLB 93 (1980) PRD 73 (2006) PRL 102 (2009) PLB 203 (1988) PRD 67 (2003) Zee Ma Babu Krauss-Nasri-Trodden Aoki-Kanemura-Seto

22. LFV (μ → eγ)

23. Mass and coupling relations

24. Neutrino mass The magnitude of F is prefer to greater than 1 to fit the neutrino data. → The mass of S is less than 400GeV.