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
Introduction
Problems which cannot be explained in the SM
Tiny neutrino masses
⊿msolar2 ~ 8×10-5 [eV2]
⊿matom2 ~ 2×10-3 [eV2]
Dark matter
ΩDM
h2=0.106±0.008
Baryon 4%
Dark matter
23%
PDG
Dark energy
73%
Baryon asymmetry of the Universe
nB/nγ=(4.7-6.5)×10-10 (95% C.L.)
PDG
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.
Aoki, Kanemura, Seto, PRL 102 (2009), Aoki, Kanemura, Seto, PRD 80 (2009)
The Aoki-Kanemura-Seto model
SM
+ Extended Higgs sector
TeV-RHν
～
SU(3)c×SU(2)L×U(1)Y×Z2×Z2
Symmetry
Φ1, Φ2 → h, H,
Particle
+
A,
H±
Z2-even
CP-even CP-odd Charged
SM-like Higgs
η, S±, NR
Z2-odd
Z2-odd
Z2 (exact) :To forbid mν
under the 2-loop level
Guarantee of DM stability
～
Z2 (softly broken) :
To forbid FCNC at the
tree-level
・ Tiny neutrino mass
→It is naturally generated at the 3-loop level.
O (1)
・ Dark matter
→The lightest Z2-odd scalar is the candidate : η
・ Baryogenesis
Cohen, Kaplan, Nelson, hep-ph/9302210
Fromme, Huber, Seniuch, JHEP11 (2006)
→Electroweak baryogenesis
★ Strong 1st order phase transition
★ The source of CP-violation in addition to the Kobayashi-Maskawa matrix
・A light H+ [O(100)GeV]
→ Type-X two Higgs doublet model (2HDMX)
Aoki, Kanemura, Tsumura, Yagyu, PRD 80 (2009)
Φ２
Φ１
u
d
e
Lagrangian
V=
Z2-even (2HDM)
Z2-odd
Interaction
LY=
Type-X Yukawa
RH neutrinos
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]
NR
1TeV
Aoki, Kanemura, Seto, arXiv:0912.5536 [hep-ph]
-Direct detection (XMASS, CDMS II)
- h→ηη [Invisible decay] (h: SM-like Higgs boson)
400GeV
S+
Large deviation in the hhh [Harada-san’s talk]
Type-X 2HDM
A
Kanemura, Okada, Senaha, PLB 606 (2005)
Aoki, Kanemura, Tsumura, Yagyu, PRD 80 (2009)
-Light charged Higgs [O(100)GeV is available]
-Unique decay property H, A→ττ
The Majorana nature [Kanemura-san’s talk]
100GeV H H+ h
50GeV
η
Aoki, Kanemura, arXiv:1001.0092 [hep-ph]
Lepton flavor violation
-BR(μ→eγ) >> BR(τ →eγ) >> BR(τ→μγ)
Rich physics are predicted!
Testable at the collider experiments !
Theoretical consistency of the model
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.
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.
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.
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:
lim V (rv1, rv2, …, rvn) > 0
r→∞
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.
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 conse
Triviality bound in the AKS model
Scalar couplings：
Yukawa couplings：
|λ(μ)|, |σ (μ)|,|ρ(μ)|, |κ(μ)|, |ξ(μ)| |μ<Λ < 8π
yt 2(μ), yb2(μ), yτ2(μ), h2(μ) | μ<Λ
< 4π
Kanemura, Kasai, Lin, Okada, Tseng, Yuan PRD 64 (2000)
• 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:
2HDM
+η
2HDM
+η+S
mS
Full
mN
R
Λ
μ
RGEs in the AKS model
Scalar 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
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
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.
Allowed regions from vacuum stability, 1st-OPT,
DM abundance and neutrino mass
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
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.
Allowed regions from vacuum stability, 1st-OPT,
DM abundance and neutrino mass
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
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.
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.
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
Seesaw mechanism (tree-level)
<Φ>
<Φ>
M
νL
νR
Radiative Seesaw scenario
Loop suppression factor: [1/(16π2)]N
mν＝ mD2/M
M=1010-15 GeV
νR
Small cij
νL
<Φ>
It is possible that the scale of M
can be reduced without fine-tuning.
M～O(1)TeV is possible.
Merit：Simple
Demerit：It is difficult to be tested directly.
<Φ>
νL
νL
It is testable at collider experiments !
Radiative Seesaw Models
Zee
Ma
mν
Zee
Ma
PLB 93 (1980)
PRD 73 (2006)
PLB 203 (1988)
Babu
Krauss-Nasri-Trodden
PRD 67 (2003)
Aoki-Kanemura-Seto
KNT
Babu
DM
AKS
Baryogenesis
1-loop level
2-loop level
3-loop level
PRL 102 (2009)
The Aoki-Kanemura-Seto (AKS) model would be able to solve
the 3 problems simultaneously at the TeV-scale physics.
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.