Universal Extra Dimension models
with right-handed neutrinos
Masato Yamanaka (Saitama University)
collaborators
Shigeki Matsumoto Joe Sato Masato Senami
Phys.Lett.B647:466-471
and
Phys.Rev.D76:043528,2007
Introduction
What is dark matter ?
Is there beyond the Standard Model ?
Supersymmetric model
Little Higgs model
http://map.gsfc.nasa.gov
Universal Extra Dimension model (UED model)
Appelquist, Cheng, Dobrescu PRD67 (2000)
Contents of today’s talk
Solving the problems in UED models
Determination of UED model parameter
Outline
1. What is Universal Extra Dimension model ?
2. Serious problems in UED model
and solving the problems
3. KK right-handed neutrino dark matter and
relic abundance calculation of that
4. Numerical result
5. Summary
What is Universal
Extra Dimension (UED) model ?
What is Universal
Extra Dimension (UED) model ?
Feature of UED models
5-dimensions (time 1 + space 4)
Extra dimension is compactified
on an S 1 /Z 2 orbifold
R
S1
4 dimension spacetime
all SM particles propagate spatial extra dimension
Interaction rule same as SM
What is Universal
Extra Dimension (UED) model ?
Periodic condition of S 1 manifold
Y
Standard model particle
Y
, Y , ‥‥, Y
(1)
(2)
(n)
Kaluza-Klein (KK) particle
1/2
KK particle mass : m (n)= ( n2/R 2 + m 2SM + dm 2)
m2SM : corresponding SM particle mass
dm : radiative correction
KK parity
5th dimension momentum conservation
Quantization of momentum by compactification
P 5 = n/R
R : S1 radius
n : 0, 1, 2,….
KK number (= n) conservation at each vertex
t
KK-parity conservation
n = 0,2,4,…
n = 1,3,5,…
＋1
－1
At each vertex the product of
the KK parity is conserved
y (3)
y (1)

(2)
y (1)
y (0)

(0)
Dark matter candidate
KK parity conservation
Stabilization of Lightest Kaluza-Klein Particle (LKP) !
(c.f. R-parity and the LSP in SUSY)
If it is neutral, massive, and weak interaction
LKP
Dark matter candidate
Who is dark matter ?
1/R >> m SM
d m = mg (1) － mG(1)
degeneration of
KK particle masses
Origin of
mass difference
Radiative correction
Mass difference between the KK graviton and the KK photon
For 1/R ～
< 800 GeV
LKP : G(1)
For 1/R ～
> 800 GeV
(1)
LKP : g
NLKP :
g (1)
NLKP : G(1)
NLKP : Next Lightest Kaluza-Klein Particle
Serious problems in UED model
and solving the problems
Serious problems in UED models
Problem 1
UED models had been constructed as
minimal extension of the standard model
Neutrinos are regarded as massless
We must introduce the neutrino
mass into the UED models !!
Serious problems in UED models
Problem 2
Case : LKP G(1)
NLKP
g (1)
KK number conservation and kinematics
Possible g (1) decay mode
g (1)
G(1) g
Late time decay due to gravitational interaction
high energy SM photon emission
It is forbidden by the observation !
Serious problems in UED models
Case : LKP
g (1)
NLKP G(1)
Same problem due to the late time G(1) decay
G(1)
g (1) g
Constraining the reheating temperature,
we can avoid the problem
[ Feng, Rajaraman, Takayama PRD68(2003) ]
Solving the problems
by introducing the right-handed neutrino
To solve the problems
Introducing the right-handed neutrino N
Mass type
Dirac type with tiny Yukawa coupling
Lagrangian = yn N L F + h.c.
Mass of the KK
right-handed neutrino
2
m
n
mN(1) ～ 1 + order
R
1/R
Solving the problems
by introducing the right-handed neutrino
Lightest KK Particle
Next Lightest KK particle
(1)
KK graviton G
KK photon
g (1)
Introducing the right-handed neutrino
Lightest KK Particle
KK graviton G(1)
Next Lightest KK particle
KK right-handed
neutrino N(1)
Next to Next
Lightest KK particle
KK photon
g (1)
Appearance of the new
g
（1）
g （1） decay
N n
(1)
Many g （1）decay mode in our model
g
（1）
(1)
N
n
g
（1）
G(1)
g
Dominant decay
mode(1)
(1)
（1）
N
(1) F
gfrom
g
W
g
n
Dominant photon emission
Fermionfrom
mass term
decay mode
g (1)
(～ (yukawa coupling)・ (vev) )
Serious problems in UED model
and solving the problems
Branching ratio of the g （1）decay
Decay rate of dominant
photon emission decay
Decay rate of
new decay mode
（1）
g
(
G
=
(1)
g
G(
G (1) g )
－7
5
×
10
=
N(1) n )
Introducing the right-handed neutrino
Neutrino masses are introduced , and problematic
high energy photon emission is highly suppressed !!
KK right-handed neutrino dark matter
and relic abundance calculation of that
KK right-handed neutrino dark matter
and relic abundance calculation of that
Mass relation
mg (1) > mN(1) > mG(1)
Possible N (1) decay from the view
point of KK parity conservation
N
(1)
(1)
G N
Forbidden by kinematics
mN(1) < mG(1) + mN(0)
stable, neutral, massive,
weakly interaction
KK right handed neutrino
can be dark matter !
KK right-handed neutrino dark matter
and relic abundance calculation of that
Before introducing the neutrino mass into UED models
(1)
Dark matter
KK graviton G
(1)
G : Produced from g (1) decay
After introducing the neutrino mass into UED models
Dark matter
N
(1)
(1)
KK right-handed neutrino N
: Produced from g (1) decay and from thermal bath
Additional contribution to relic abundance
KK right-handed neutrino dark matter
and relic abundance calculation of that
KK right-handed neutrino
production from thermal bath
KK photon decay into KK
right-handed neutrino
(or KK graviton)
KK photon decouple from thermal bath
Relic number density of
KK photon at this time
N(1) number density from
g (1) decay (our model)
=
time
constant
G(1)number density from
g (1) decay (previous model)
KK right-handed neutrino dark matter
and relic abundance calculation of that
W DM h2
～ (number density) × (DM mass)
～ constant
Total DM number density
DM mass ( ～ 1/R )
We must re-evaluate the DM number density !
KK right-handed neutrino dark matter
and relic abundance calculation of that
N(n)production processes in thermal bath
N(n)
(n)
N
(n)
N
KK Higgs boson
KK gauge boson
KK fermion
Fermion mass term
(～ (yukawa coupling) ・ (vev) )
N(n)
(n)
N
t
x
KK right-handed neutrino dark matter
and relic abundance calculation of that
In the early universe ( T > 200GeV ),
vacuum expectation value = 0
～ (yukawa coupling) ・ (vev) = 0
(n)
N
(n)
N
(n)
N
t
x
(n)
N must be produced through the coupling with KK Higgs
KK right-handed neutrino dark matter
and relic abundance calculation of that
The mass of a particle receives a correction by thermal
effects, when the particle is immersed in the thermal bath.
[ P. Arnold and O. Espinosa (1993) , H. A. Weldon (1990) , etc ]
Any particle mass
m2(T) = m2(T=0) + dm 2 (T)
dm (T) ～ m・exp[ ｰ mloop / T ]
dm (T) ～ T
For mloop > 2T
For mloop < 2T
m loop : mass of particle contributing to the thermal correction
KK right-handed neutrino dark matter
and relic abundance calculation of that
N(n)must be produced through the coupling with KK Higgs
KK Higgs boson mass
2
(n)
F (T)
m
=m
2
(n)
F (T=0)
2
T
+ [ a(T)・ 3l +x(T)・ 3yt ]
12
2
h
2
T : temperature of the universe
l : quartic coupling of the Higgs boson
y : top yukawa coupling
a(T)[ x(T) ] : Higgs [top quark] particle number
contributing to thermal correction loop
KK right-handed neutrino dark matter
and relic abundance calculation(n)of that
Dominant N
production process
(n)
N production processes in thermal bath
N(n)
N(n)
N(n)
KK Higgs boson
KK gauge boson
KK fermion
Fermion mass term
(～ (yukawa coupling) ・ (vev) )
N(n)
(n)
N
t
x
Numerical result
Produced from g (1)
decay + from
the thermal bath
Produced from g(1)
decay (mn = 0)
Neutrino mass dependence of the DM relic abundance
In ILC experiment, n=2 KK particle can be produced !!
It is very important for discriminating
UED from SUSY at collider experiment
[ Kakizaki, Matsumoto, Senami PRD74(2006) ]
Excluded
UED model without
right-handed neutrino
UED model with
right-handed neutrino
Allowed parameter
region changed much !!
Summary
Summary
We have solved two problems in UED models (absence of the
neutrino mass, forbidden energetic photon emission) by
introducing the right-handed neutrino
We have shown that after introducing neutrino masses, the dark
matter is the KK right-handed neutrino, and we have calculated the
relic abundance of the KK right-handed neutrino dark matter
In the UED model with right-handed neutrinos, the compactification
scale of the extra dimension 1/R can be less than 500 GeV
This fact has importance on the collider physics, in particular on
future linear colliders, because first KK particles can be produced
in a pair even if the center of mass energy is around 1 TeV.
Appendix
What is Universal
Extra Dimension (UED) model ?
Extra dimension model
Candidate for the theory beyond the standard model
Hierarchy problem
Large extra dimensions [ Arkani-hamed, Dimopoulos, Dvali PLB429(1998) ]
Warped extra dimensions [ Randall, Sundrum PRL83(1999) ]
Existence of dark matter
LKP dark matter due to KK parity [ Servant, Tait NPB650(2003) ]
etc.
What is Universal
Extra Dimension (UED) model ?
5-dimensional kinetic term
Tree level KK particle mass : m (n)= ( n 2/R 2+ m 2SM) 1/2
m2SM : corresponding SM particle mass
Since 1/R >> mSM, all KK particle masses are
highly degenerated around n/R
Mass differences among KK particles dominantly
come from radiative corrections
Radiative correction
[ Cheng, Matchev, Schmaltz PRD66 (2002) ]
Mass of the KK graviton
1
mG(1) = R
Mass matrix of the U(1) and SU(2) gauge boson
L : cut off scale
v : vev of the Higgs field
Dependence of the
‘‘Weinberg’’ angle
[ Cheng, Matchev,
Schmaltz (2002) ]
sin 2 q W ～
～ 0 due to 1/R >> (EW scale) in the
mass matrix
(1)
g
B(1) ～
～
Serious problems in UED models
decouple
g （1）
G （1）
decay
Thermal bath
g
early universe
（1）
g
G(
High energy
photon
3
dm
（1）g
)～
G
2
M planck
g （1）decays after the recombination
Excluded
Allowed region in UED models
Allowed
[ Kakizaki, Matsumoto, Senami PRD74(2006) ]
Because of triviality bound on
the Higgs mass term, larger
Higgs mass is disfavored
In collider experiment, smaller
extra dimension scale is favored
We investigated :
『 The excluded region
is truly excluded ? 』
Solving cosmological problems
by introducing Dirac neutrino
Decay rate for g （1）
N（1）n
N (1)
g (1)
n
mn
dm
10－2 eV 1 GeV
mn : SM neutrino mass
G = 2×10 [sec ] 500GeV
mg
－9
－1
（1）
d m = mg － mN
（1）
（1）
3
2
2
Solving cosmological problems
by introducing Dirac neutrino
（1）
g
Decay rate for
g
(1)
G g
（1）
g
G(1)
G = 10 [sec－1 ]
－15
d m´ = m g (1)－ mG(1)
d m´
1 GeV
3
[ Feng, Rajaraman,
Takayama PRD68(2003) ]
Total injection photon energy from
g (1)decay
e Br( g (1))Yg (1) < 3 × 10－18 GeV
×
1/R
500GeV
2
0.1 eV
mn
2
dm
1 GeV
2
W DM h2
0.10
e : typical energy of emitted photon
Yg (1) : number density of the KK photon
normalized by that of background photons
The successful BBN and CMB scenarios are not
disturbed unless this value exceeds 10－9 - 10－13GeV
[ Feng, Rajaraman, Takayama (2003) ]
Production processes of new dark matter N（1）
1
2
n
From thermal bath (directly)
N（1）
Thermal bath
3
g (1)
From decoupled g (1) decay
From thermal bath (indirectly)
（n）
Thermal bath
N(1)
N
Cascade
decay
N（1）
N（1）
KK right-handed neutrino dark matter
and relic abundance calculation of that
We expand the thermal correction for UED model
The number of the particles contributing to the thermal mass
is determined by the number of the particle lighter than 2T
Gauge bosons decouple from the thermal bath at once
due to thermal correction
We neglect the thermal correction to fermions
and to the Higgs boson from gauge bosons
Higgs bosons in the loop diagrams receive thermal correction
In order to evaluate the mass correction correctly,
we employ the resummation method
[P. Arnold and O. Espinosa (1993) ]
Thermal correction
KK Higgs boson mass
2
(n)
F (T)
m
=m
2
(n)
F (T=0)
2
T
+ [ a(T)・ 3l +x(T)・ 3yt ]
12
2
h
2
T : temperature of the universe
l : quartic coupling of the Higgs boson
y : top yukawa coupling
∞
2
T
a(T) = S θ 4T 2 － m2 R 2ｰ [ a(T)・ 3l +x(T)・ 3yt ]
12
m=0
x(T) = 2[2RT] + 1
2
h
[‥‥] : Gauss' notation
2
Relic abundance calculation
Boltzmann equation
S
(n)
C(m)
m
(n)
dY
=
dT
(n)
C(m) =
gn
s, H, g
*s
sTH
4 gn

=1
=2
=3
dg *s (T)
T
1+
3g*s (T) dT
d3k g (m) N(n)
(m) fF(m)
G
F
3
<
F
(2p)
1 ｰ fL>
The normal hierarchy
The inverted hierarchy
The degenerate hierarchy
, f : entropy density, Hubble parameter,
relativistic degree of freedom, distribution function
Y(n)= ( number density of N(n) ) ( entropy density )
Result and discussion
N(n) abundance from Higgs decay depend on the yn (mn )
Degenerate case
 mn = 2.0 eV
[ K. Ichikawa, M.Fukugita
and M. Kawasaki (2005) ]
[ M. Fukugita, K. Ichikawa,
M. Kawasaki and O. Lahav
(2006) ]
Dotted line :
N(1
abundance produced
)
directly from thermal bath
Dashed line :
N(1 abundance produced
)
indirectly from higher
mode KK right-handed
neutrino decay
Reheating temperature dependence of relic
density from thermal bath
Determination of relic abundance and 1/R
We can constraint the reheating temperature !!