K. Yagyu (Univ. of Toyama) D1 Collaborators

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. Baryon 4% Dark matter 23% Dark energy 73% 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. Introduction Tiny neutrino masses ⊿msolar2 ~ 8×10-5 [eV2] ⊿matom2 ~ 2×10-3 [eV2] Problems which cannot be explained in the SM PDG Dark matter ΩDMh2=0.106±0.008 Baryon asymmetry of the Universe nB/nγ=(4.7-6.5)×10-10 (95% C.L.) PDG Need to go beyond the SM

4. + + TeV-RHν SM Extended Higgs sector Z2-odd Symmetry Particle O (1) Cohen, Kaplan, Nelson, hep-ph/9302210 Fromme, Huber, Seniuch, JHEP11 (2006) ・ Baryogenesis →Electroweak baryogenesis ★Strong 1st order phase transition ★The source of CP-violation in addition to the Kobayashi-Maskawa matrix Φ２ Φ１ u e ・A light H+ [O(100)GeV] → Type-X two Higgs doublet model (2HDMX) Aoki, Kanemura, Tsumura, Yagyu, PRD 80 (2009) d Aoki, Kanemura, Seto, PRL 102 (2009), Aoki, Kanemura, Seto, PRD 80 (2009) The Aoki-Kanemura-Seto model ～ Z2 (exact):To forbid mν under the 2-loop level Guarantee of DM stability SU(3)c×SU(2)L×U(1)Y×Z2×Z2 Φ1, Φ2 → h, H, A, H± ～ Z2-even Z2 (softly broken): To forbid FCNC at the tree-level CP-even CP-odd Charged η, S±, NR Z2-odd SM-like Higgs ・ Tiny neutrino mass →It is naturally generated at the 3-loop level. ・ Dark matter →The lightest Z2-odd scalar is the candidate : η

5. Lagrangian V= Z2-even (2HDM) Z2-odd Interaction Type-X Yukawa LY= RH neutrinos

6. Prediction of the AKS model Current experimental data Neutrino data , DM abundance, Strong 1st OPT, LEP bound, b→sγ, B→τν, g-2, τ leptonic decay, LFV (μ→eγ) Mass Spectrum Z2-even Z2-odd 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 propertyH, A→ττ The Majorana nature [Kanemura-san’s talk] Lepton flavor violation NR 1TeV Aoki, Kanemura, Seto, arXiv:0912.5536 [hep-ph] 400GeV S+ A Kanemura, Okada, Senaha, PLB 606 (2005) Aoki, Kanemura, Tsumura, Yagyu, PRD 80 (2009) h 100GeV H H+ 50GeV η Aoki, Kanemura, arXiv:1001.0092 [hep-ph] -BR(μ→eγ) >> BR(τ →eγ) >> BR(τ→μγ) Rich physics are predicted! Testable at the collider experiments !

7. 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. Theoretical consistency of the model The AKS model is an effective theory whose cutoff scale should be from multi-TeV to 10TeV, sincewe do not prefer to unnatural fine-tuning of correction of scalar boson masses. In particular in this 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). It is non-trivial about the consistency of the model.

8. lim r→∞ Vacuum stability and triviality bounds Vacuum stability bound We require that scalar potentials do not have a negative coefficient in any direction even when order parameters take large value: V (rv1, rv2, …, rvn) > 0 Triviality bound The condition of the reliable perturbative calculation. We require that all of the coupling constants which vary according to the RGEs do not become strong coupling up to the cutoff scale. f RGE f f f Bosonic loop contributes positive, fermionic loop contributes negative for scalar couplings.

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

10. Triviality bound in the AKS model Scalar couplings： |λ(μ)|, |σ(μ)|,|ρ(μ)|, |κ(μ)|, |ξ(μ)| |μ<Λ < 8π • 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: Yukawa couplings： yt2(μ), yb2(μ), yτ2(μ), h2(μ) | μ<Λ < 4π Kanemura, Kasai, Lin, Okada, Tseng, Yuan PRD 64 (2000) 2HDM +η 2HDM +η+S Full μ mS Λ mNR

11. RGEs in the AKS model Scalar couplings Yukawa 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|2η2] MR=3TeV mh=120GeV M=mH+=mH=100GeV μS=200GeV μη=30GeV

13. Allowed regions from Vacuum Stability sin(β-α)=1:SM-like limit tanβ=25 κ=1.2 ξ=3.0 [ξ|S|2η2] MR=3TeV mh=120GeV M=mH+=mH=100GeV μS=200GeV μη=30GeV V<0

14. 1st OPT Allowed regions from Vacuum Stability and 1st-OPT sin(β-α)=1:SM-like limit tanβ=25 κ=1.2 ξ=3.0 [ξ|S|2η2] MR=3TeV mh=120GeV M=mH+=mH=100GeV μS=200GeV μη=30GeV V<0

15. mν, ΩhDM2 1st OPT Allowed regions from vacuum stability, 1st-OPT, DM abundance and neutrino mass sin(β-α)=1:SM-like limit tanβ=25 κ=1.2 ξ=3.0 [ξ|S|2η2] MR=3TeV mh=120GeV M=mH+=mH=100GeV μS=200GeV μη=30GeV V<0 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.

16. mν, ΩhDM2 1st OPT Allowed regions from vacuum stability, 1st-OPT, DM abundance and neutrino mass sin(β-α)=1:SM-like limit tanβ=25 κ=1.2 ξ=4.0 [ξ|S|2η2] MR=3TeV mh=120GeV M=mH+=mH=100GeV μS=200GeV μη=30GeV V<0 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.

17. mν, ΩhDM2 1st OPT Allowed regions from vacuum stability, 1st-OPT, DM abundance and neutrino mass sin(β-α)=1:SM-like limit tanβ=25 κ=1.2 ξ=5.0 [ξ|S|2η2] MR=3TeV mh=120GeV M=mH+=mH=100GeV μS=200GeV μη=30GeV V<0 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.

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, 1st 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. If we demand on mν ~ O (0.1) eV then small c/M are required. There are two scenarios to explain small c/M. Large MorSmall cij Seesaw mechanism (tree-level) Radiative Seesaw scenario Loop suppression factor: [1/(16π2)]N <Φ> <Φ> mν＝ mD2/M M=1010-15 GeV <Φ> <Φ> M • It is possible that the scale of M • can be reduced without fine-tuning. • M～O(1)TeV is possible. νL νL νR νR νL νL Merit：Simple Demerit：It is difficult to be tested directly. It is testable at collider experiments !

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

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.