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
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
IntroductionProblems which cannot be explained in the SM
PDG
PDG
Tiny neutrino masses
Dark matter
Baryon asymmetry of the Universe
⊿msolar2 ~ 8×10-5 [eV2]
⊿matom2 ~ 2×10-3 [eV2]
ΩDMh2=0.106±0.008
Baryon 4%
Dark matter 23%
Dark energy 73%
nB/nγ=(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.
The Aoki-Kanemura-Seto modelAoki, Kanemura, Seto, PRL 102 (2009), Aoki, Kanemura, Seto, PRD 80 (2009)
O (1)
SM Extended Higgs sector TeV-RHνZ2-odd
+ +
SU(3)c×SU(2)L×U(1)Y×Z2×Z2～
Z2 (softly broken) :
To forbid FCNC at the tree-level
Z2 (exact) :To forbid mν under the 2-loop level
Guarantee of DM stability～
Symmetry
ParticleΦ1, Φ2 → h, H, A, H±
η, S±, NR
CP-even CP-odd ChargedZ2-even
Z2-oddSM-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
ud
Φ ２
eΦ
１・ A light H+ [O(100)GeV] → Type-X two Higgs doublet model (2HDMX) Aoki, Kanemura, Tsumura, Yagyu, PRD 80 (2009)
・ Baryogenesis → Electroweak baryogenesis ★ Strong 1st 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)
Lagrangian
Z2-even (2HDM)
Z2-odd
Interaction
V=
RH neutrinos
LY= Type-X Yukawa
Prediction of the AKS model
400GeV
100GeV
Z2-even Z2-odd
NR
η
S+
H H+
A
1TeV
50GeV
h
Testable at the collider experiments !
Mass SpectrumCurrent experimental data
Neutrino data , DM abundance, Strong 1st OPT,LEP bound, b→sγ, B→τν, g-2, τ leptonic decay, LFV (μ→eγ)
PredictionPhysics 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!
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.
Vacuum stability and triviality boundsVacuum 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 (rv1, rv2, …, rvn) > 0r→∞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.
f f
f
f
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.
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
mS mNRΛ
μ
2HDM+η
2HDM+η+S Full
Scalar couplings ：Yukawa couplings ： yt 2(μ), yb
2(μ), yτ2(μ), h2(μ) | μ<Λ < 4π
Kanemura, Kasai, Lin, Okada, Tseng, Yuan PRD 64 (2000)
RGEs in the AKS modelScalar couplings Yukawa couplings
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
Allowed regions from Vacuum Stability
V<0 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
Allowed regions from Vacuum Stability and 1st-OPT
V<0
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
Allowed regions from vacuum stability, 1st-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
1st OPT mν, ΩhDM2
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
Allowed regions from vacuum stability, 1st-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
1st OPT mν, ΩhDM2
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
Allowed regions from vacuum stability, 1st-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
1st OPT mν, ΩhDM2
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
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.
Generation Mechanism of Neutrino Masses
Generally Majorana masses of neutrino are written by dim-5 operators.
Seesaw mechanism (tree-level)
mν ＝ mD2/M
M=1010-15 GeV
Merit ： Simple
Demerit ： It is difficult to be tested directly.
νL νR νRνL
M
Radiative Seesaw scenario Loop suppression factor: [1/(16π2)]N
It is testable at collider experiments !
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 M or Small cij
It is possible that the scale of M
can be reduced without fine-tuning.
M ～ O(1)TeV is possible. νL νL
<Φ> <Φ><Φ><Φ>
Radiative Seesaw Models
Zee Ma Babu KNT AKS
mν 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)
ZeeMa
Babu
Krauss-Nasri-Trodden
Aoki-Kanemura-Seto
LFV (μ → eγ)
Mass and coupling relations
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.
