Masato Yamanaka (Saitama University)

1
Relic abundance of dark matter in universal extra
dimension models with right-handed neutrinos
Masato Yamanaka (Saitama University)
collaborators
Shigeki Matsumoto Joe Sato Masato Senami
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
Calculation of dark matter relic abundance
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
Problems in Universal
Extra Dimension (UED) model 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 !!
5
Problems in Universal
Extra Dimension (UED) model 2
(1)
G
Lightest KK Particle
KK graviton
g
(1)
Next Lightest KK particle
KK photon
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)
Dark matter production
Late time decay due to gravitational interaction
g
g
(1)
(1)
G
high energy SM photon emission
It is forbidden by the observation !
6
Solving the problems
Introducing the right-handed neutrino N
m
2
1
n
The mass of the KK right-handed neutrino N

m

order
(1)
N
(1)
R
1/R
Dirac type with tiny Yukawa coupling
Mass type
(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
7
Solving the problems
g
g
(1)
n
N
New decay mode of
(1)
(1)
g
(1)
Branching ratio of the decay
g
g
(1)
G
(1)
( G )
g
-7
(1)
5 10
Br( )


g
(1)
(1)
n
( N )
G
Neutrino masses are introduced into UED models,
and problematic high energy photon emission is
highly suppressed !!
8
Change of dark matter
N
(1)
decay allowed by KK parity
stable, neutral, massive,weakly interaction
(1)
N
N
(1)
G
KK right handed neutrino can be dark matter !
Forbidden by kinematics
m m
lt
m
(0)
(1)
(1)
N
G
N
Before introducing the neutrino mass into UED
models
(1)
G
Dark matter
KK graviton
After introducing the neutrino mass into UED
models
(1)
N
Dark matter
KK right-handed neutrino
9
(1)
(1)
When dark matter changes from G to N , what
happens ?
(1)
Almost produced from g decay
G
(1)
Produced from g decay and from thermal bath
(1)
(1)
N
Additional contribution to relic abundance
Total DM number density
DM mass ( 1/R )
We must re-evaluate the DM number density !
10
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)
11
N
(n)
Production process
(n)
In thermal bath, there are many N production
processes
(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) )


12
N
(n)
Production process
In the early universe ( T gt 200GeV ), vacuum
expectation value 0
(yukawa coupling) (vev) 0


(n)
N
(n)
N
t
x
(n)
N production needs processes including KK Higgs
13
Thermal correction
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
14
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
15
N
(n)
Production process
(n)
In thermal bath, there are many N production
processes
(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) )


16
Kakizaki, Matsumoto, Senami PRD74(2006)
Allowed parameter region changed much !!
UED model withoutright-handed neutrino
UED model withright-handed neutrino
17
Produced from g decay from the
thermal bath
(1)
Produced from g decay (m 0)
(1)
n
1/R can be less than 500 GeV
In ILC experiment,
can be produced !!
n2 KK particle
It is very important for discriminating UED from
SUSY at collider experiment
18
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.
19
Appendix
20
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
21
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
22
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


23
Solving cosmological problemsby introducing
Dirac neutrino
g
We investigated some decay mode
(1)
g
(1)
h
(1)
N
N
(1)
(1)
g
g
(1)
l
W
l
n
g
n
g
g
g
etc.
24
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)
25
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)
26
Thermal correction
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)
27
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
)
28
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)