Joe Sato Saitama University

1
Relic abundance of dark matter in universal Extra
Dimension models with right-handed neutrinos
Joe Sato (Saitama University)
In collaboration with
Shigeki Matsumoto Masato Senami Masato Yamanaka
Phys.Rev.D76043528,2007
Phys.Lett.B647466-471 and
2
Introduction
What is dark matter ?
Is there beyond the Standard Model ?
http//map.gsfc.nasa.gov
Supersymmetric model
Little Higgs model
Universal Extra Dimension model (UED model)
Appelquist, Cheng, Dobrescu PRD67 (2000)
Contents of todays talk
Solving the problems in UED models
Determination of UED model parameter
3
What is Universal
Extra Dimension (UED) model ?
R
5-dimensions
(time 1 space 4)
1
S
all SM particles propagatespatial extra dimension
4 dimension spacetime
compactified on an S /Z orbifold
1
2
Y
(1)
Y
Y
Y
(2)
(n)
,
, ??,
Standard model particle
KK particle
1/2
2
2
KK particle mass m ( n /R m dm
)
(n)
2
2
SM
2
m corresponding SM particle mass
SM
dm radiative correction
4
Dark matter in UED models
(1)
G
Lightest KK Particle
KK graviton
( LKP )
g
(1)
Next Lightest KK particle
KK photon
( NLKP )
KK parity conservation at each vertex
Lightest KK Particle, i.e., KK graviton is stable
and can be dark matter
(c.f. R-parity and the LSP in SUSY)
5
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 !!
6
Serious problems in UED models
Problem 2
KK parity conservation and kinematics
g
(1)
Possible decay mode
g
g
(1)
(1)
G
Late time decay due to gravitational interaction
high energy SM photon emission
It is forbidden by the observation !
7
Solving the problems by introducing the
right-handed neutrino
To solve the problems
Introducing the right-handed neutrino N
Dirac type with tiny Yukawa coupling
Mass type
Lagrangian y N L F h.c.
n
m
2
1
Mass of the KK right-handed neutrino
n

m

order
(1)
N
R
1/R
8
Solving the problems by introducing the
right-handed neutrino
(1)
G
Lightest KK Particle
KK graviton
g
Next Lightest KK particle
(1)
KK photon
Introducing the right-handed neutrino
(1)
G
Lightest KK Particle
KK graviton
KK right-handedneutrino
Next Lightest KK particle
(1)
N
Next to Next Lightest KK particle
g
(1)
KK photon
9
Serious problems in UED model
and solving the problems
g
(1)
Appearance of the new decay
g
n
(1)
(1)
N
g
(1)
Branching ratio of the decay
Decay rate of dominantphoton emission decay
g
g
(1)
G
G
(1)
( )
-7
5 10


(1)
g
G
( )
n
(1)
Decay rate of new decay mode
N
Neutrino masses are introduced , and problematic
high energy photon emission is highly suppressed
!!
10
KK right-handed neutrino dark matter and relic
abundance calculation of that
m
gt m
gt m
Mass relation
(1)
g
(1)
N
G
(1)
(1)
Possible N decay from the view point of KK
parity conservation
stable, neutral, massive,weakly interaction
(1)
(1)
N
N
G
KK right handed neutrino can be dark matter !
11
KK right-handed neutrino dark matter and relic
abundance calculation of that
Original UED models ( before introducing
right-handed neutrino )
(1)
G
Dark matter
KK graviton
(1)
Produced from g decay only
G
(1)
Our UED models ( after introducing right-handed
neutrino )
(1)
N
Dark matter
KK right-handed neutrino
Produced from g decay and from thermal bath
(1)
(1)
N
Additional contribution to relic abundance
12
KK right-handed neutrino dark matter and relic
abundance calculation of that
W
h (number density) (DM mass)
2

DM

constant
Total DM number density

DM mass ( 1/R )
We must evaluate the DM number density produced
from thermal bath !
13
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
(n)
N
N
N
time
KK Higgs boson
KK gauge boson
KK fermion
space
Fermion mass term ( (yukawa coupling)
(vev) )


14
KK right-handed neutrino dark matter and relic
abundance calculation of that
In the early universe ( T gt 200GeV ), vacuum
expectation value 0
(yukawa coupling) (vev) 0


(n)
N
(n)
N
t
x
(n)
N must be produced through the coupling with KK
Higgs
15
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
2
2
2
m (T)
m (T0) dm (T)
Any particle mass

mexp ? m / T
dm (T)
For m gt 2T
loop
loop
For m lt 2T
dm (T)
T
loop
m
mass of particle contributing to the thermal
correction
loop
16
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
T
2
2
2
m (T) m (T0) a(T) 3l x(T) 3y
2
2


h
t
12
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
17
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)
(n)
N
N
N
t
KK Higgs boson
KK gauge boson
x
KK fermion
Fermion mass term ( (yukawa coupling)
(vev) )


18
Produced from g decay from the
thermal bath
(1)
Produced from g decay (m 0)
(1)
n
Neutrino mass dependence of the DM relic abundance
In LHC/ILC experiment,
can be produced !!
n2 KK particle
It is very important for discriminating UED from
SUSY at collider experiment
19
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.
20
Appendix
21
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.
22
What is Universal
Extra Dimension (UED) model ?
Motivation
3 families from anomaly cancellation
Dobrescu, Poppitz PRL 68 (2001)
Attractive dynamical electroweak symmetry breaking
Cheng, Dobrescu, Ponton NPB 589 (2000)
Arkani-Hamed, Cheng, Dobrescu, Hall PRD 62
(2000)
Preventing rapid proton decay from
non-renormalizable operators
Appelquist, Dobrescu, Ponton, Yee PRL 87
(2001)
Existence of dark matter
Servant, Tait NPB 650 (2003)
23
What is Universal
Extra Dimension (UED) model ?
1
Periodic condition of S manifold
(1)
(2)
(n)
Y
Y
Y
Y
,
, ??,
Standard model particle
Kaluza-Klein (KK) particle
1/2
2
2
KK particle mass m ( n /R m dm
)
(n)
2
2
SM
2
m corresponding SM particle mass
SM
dm radiative correction
24
What is Universal
Extra Dimension (UED) model ?
5-dimensional kinetic term
1/2
(n)
2
2
Tree level KK particle mass m ( n /R m
)
2
SM
2
m corresponding SM particle mass
SM
Since 1/R gtgt m , all KK particle masses are
highly degenerated around n/R
SM
Mass differences among KK particles dominantly
come from radiative corrections
25
KK parity
5th dimension momentum conservation
Quantization of momentum by compactification
1
P n/R
R S radius n 0, 1, 2,.
5
KK number ( n) conservation at each vertex
t
KK-parity conservation
y
(0)
(1)
y
n 0,2,4,
1
y
(1)
y
(3)
n 1,3,5,
-1
At each vertex the product of the KK parity is
conserved
(2)
(0)
f
f
26
Example of KK parity conservation
(1)
(2)
f
f
y
y
(4)
(4)
(1)
(1)
f
f
y
y
(1)
(0)
(2)
(0)
f
f
(1)
(1)
f
f
y
y
(0)
(0)
27
Dependence of the Weinberg angle
Cheng, Matchev, Schmaltz (2002)

2
sin q
0 due to 1/R gtgt (EW scale) in the

W
mass matrix
g
(1)
(1)
B


28
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 ?
29
1/R gtgt m
SM
degeneration of KK particle masses
Origin of mass difference
Radiative correction
Mass difference between the KK graviton and the
KK photon
g
(1)
(1)
G
NLKP
LKP
For 1/R lt 800 GeV

g
(1)
(1)
G
For 1/R gt 800 GeV
NLKP
LKP
LKP

NLKP Next Lightest Kaluza-Klein Particle
30
Radiative correction
Cheng, Matchev, Schmaltz PRD66 (2002)
1
m
Mass of the KK graviton
(1)
R
G
Mass matrix of the U(1) and SU(2) gauge boson
L cut off scale v vev of the Higgs
field
31
Excluded
Allowed
Allowed region in UED models
Kakizaki, Matsumoto, Senami PRD74(2006)
Because of triviality bound on the Higgs mass
term, larger Higgs mass is disfavored
We investigated
? The excluded region is truly excluded ? ?
In collider experiment, smaller extra dimension
scale is favored
32
Serious problems in UED models
g
(1)
(1)
Case LKP NLKP
G
(1)
G
Same problem due to the late time decay
g
g
(1)
(1)
G
Constraining the reheating temperature, we can
avoid the problem
Feng, Rajaraman, Takayama PRD68(2003)
33
g
(1)
Appearance of the new decay
g
n
(1)
(1)
N
g
(1)
Many decay mode in our model
(1)
N
g
(1)
(1)
F
N
(1)
g
(1)
W
n
g
n
G
(1)
g
(1)
g
Fermion mass term ( (yukawa coupling)
(vev) )


34
Serious problems in UED models
decouple
(1)
G
g
(1)
decay
Thermal bath
g
early universe
High energy photon
dm
3
G ( )
g
g

(1)
(1)
G
2
M
planck
g
(1)
decays after the recombination
35
Solving cosmological problemsby introducing
Dirac neutrino
g
(1)
n
Decay rate for
(1)
N
N
(1)
g
(1)
n
3
2
2
500GeV
m
m
d
-9
G
-1
n
210 sec

m
10 eV
-2
1 GeV
g
(1)
m
m
d
m
-

m
SM neutrino mass
g
(1)
n
N
(1)
36
Solving cosmological problemsby introducing
Dirac neutrino
g
g
(1)
(1)
Decay rate for
G
g
g
(1)
G
(1)
3
m

d
-15
G
10 sec
-1

1 GeV
Feng, Rajaraman, Takayama PRD68(2003)
m
m - m
d

g
(1)
G
(1)
37
g
(1)
Total injection photon energy from decay
-18
g
(1)
Y
lt 3 10
e
Br( )
GeV
g
(1)
2
2
2
W
0.1 eV
h
2
m
d
1 / R
DM

m
500GeV
1 GeV
0.10
n
e
typical energy of emitted photon
Y
number density of the KK photon normalized by
that of background photons
g
(1)
The successful BBN and CMB scenarios are not
disturbed unless this value exceeds 10 - 10
GeV
-9
-13
Feng, Rajaraman, Takayama (2003)
38
First summary
Two problems in UED models
Absence of neutrino masses
KK graviton problem
Introducing the right-handed neutrinos and
assuming Dirac type mass
g
n
(1)
g
(1)
N
(1)
Appearance of the new decay
Two problems have been solved simultaneously !!
39
Production processes of new dark matter N
(1)
N
(1)
From decoupled g decay
g
(1)
1
(1)
n
2
From thermal bath (directly)
N
(1)
Thermal bath
3
From thermal bath (indirectly)
N
(1)
Cascade decay
N
(n)
Thermal bath
N
(1)
40
KK right-handed neutrino dark matter and relic
abundance calculation of that
KK photon decay into KK right-handed neutrino
(or KK graviton)
KK right-handed neutrino production from thermal
bath
time
KK photon decouple from thermal bath
Relic number density of KK photon at this time
constant
(1)
(1)
G
N

number density from
decay (our model)
number density from decay
(previous model)
(1)
g
(1)
g
41
Thermal correction
KK Higgs boson mass
T
2
2
2
m (T) m (T0) a(T) 3l x(T) 3y
2
2


h
t
12
T temperature of the universe
l quartic coupling of the Higgs boson
y top yukawa coupling
x(T) 22RT 1
?? Gauss' notation
42
Kakizaki, Matsumoto, Senami PRD74(2006)
Allowed parameter region changed much !!
Excluded
UED model withoutright-handed neutrino
UED model withright-handed neutrino
43
Result and discussion
N abundance from Higgs decay depend on the y
(m )
(n)
n
n
Degenerate case
m
2.0 eV
n
K. Ichikawa, M.Fukugita and M. Kawasaki (2005)

M. Fukugita, K. Ichikawa, M. Kawasaki and O.
Lahav (2006)
44
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 fermionsand
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)
45
Relic abundance calculation
Boltzmann equation
S
(n)
(n)
C
dg (T)
dY
T
s
(m)

m
1

s T H
3g (T)
dT
dT
s

3
d k
(n)
g
(n)
G
C
4 g
N
f
n
(m)
(m)
(2p)
3
F
1
The normal hierarchy
g
n
2
The inverted hierarchy
3
The degenerate hierarchy
s, H, g , f entropy density, Hubble
parameter, relativistic
degree of freedom, distribution function
s

(n)
(n)
Y
( number density of N ) ( entropy density
)
46
Dotted line
(1)
N abundance produced directly from thermal bath
Dashed line
(1)
N 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 !!