Transcript PowerPoint プレゼンテーション

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.Lett.B647:466-471
and
arXiv:0705.0934 [hep-ph]
(To appear in PRD)
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
(1) Construction of problemless UED model
(2) Calculation of dark matter relic abundance
What is Universal
Extra Dimension (UED) model ?
R
5-dimensions (time 1 + space 4)
S1
all SM particles propagate
4 dimension spacetime
spatial extra dimension
compactified on an S 1/Z 2 orbifold
Y
Y
Standard model particle
KK particle mass :
, Y (2), ‥‥, Y (n)
(1)
KK particle
m (n)= ( n2/R 2 + m 2SM + dm 2) 1/2
m2SM : corresponding SM particle mass
dm : radiative correction
KK parity
&
Who is dark matter ?
KK parity conservation at each vertex
Lightest Kaluza-Klein Particle(LKP) is stable
and can be dark matter
(c.f. R-parity and the LSP in SUSY)
Possible NLKP decay
NLKP
LKP + SM particle
NLKP : Next Lightest Kaluza-Klein Particle
Dark matter candidate
g (1)
For 1/R ～
< 800 GeV
LKP : G(1)
NLKP :
For 1/R ～
> 800 GeV
LKP : g
(1)
NLKP : G(1)
Problems in Universal
Extra Dimension (UED) model
(1) The absence of the neutrino mass
(2) The diffuse photon from the KK photon decay
KK photon (from thermal bath)
Late time decay into KK graviton
and high energy SM photon
Excluded
Allowed
It is forbidden by
the observation !
[ Kakizaki, Matsumoto, Senami PRD74(2006) ]
Solving the two problems
Introducing the right-handed neutrino N
The mass of the KK
(1)
right-handed neutrino N
2
m
n
mN(1) ～ 1 + order
R
1/R
Before introducing Dirac neutrino
mg (1) > mG(1)
Problematic g is always emitted from g (1) decay
After introducing Dirac neutrino
mg (1) > mN(1) > mG(1)
New g(1) decay channels open !!
Branching ratio of the g （1）decay
（1）
g
(
G
（1）
g
Br(
)=
(1)
g
G(
= 5 × 10－7
G g )
(1)
N n )
(1)
1/R
500GeV
3
0.1 eV
mn
2
dm
1 GeV
We have created
the realistic UED model
Presence of neutrino mass
Absence of the diffuse
photon problem
Allowed !!
( G DM production process )
G
Br( g ) =
(1)
(1)
g
N n )
G(
(1)
（1）
～ 10－7
Who is dark matter ??
N (0)
N (1)
G(1)
2
1
m
n
mN(1) ～
order
+
R
1/R
< mG(1) + mN(0)
(1)
N decay is impossible !
stable, neutral, massive, weakly interaction
KK right handed neutrino can be dark matter !
Change of DM (for 1/R < 800GeV) : G(1)
N(1)
(1)
(1)
When dark matter changes from G to N ,
what happens ?
G : Almost produced from g (1) decay
(1) : Produced from g (1) decay and from thermal bath
N
(1)
Additional contribution to relic abundance
Total DM number density
DM mass ( ～ 1/R )
We must re-evaluate the DM number density !
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）
(n)
N Production process
(n)
In thermal bath, there are many N production processes
(n)
(n)
N
N
(n)
N(n)
N(n)
N
KK Higgs boson
KK gauge boson
KK fermion
Fermion mass term
(～ (yukawa coupling) ・ (vev) )
t
x
(n)
N Production process
In the early universe ( T > 200GeV ),
vacuum expectation value = 0
～ (yukawa coupling) ・ (vev) = 0
(n)
N
N(n)
N(n)
t
x
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 ]
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
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
(n)
N Production process
Dominant N(n)
production
process
(n)
In thermal bath, there are many N production processes
(n)
(n)
N
N
(n)
N(n)
N(n)
N
KK Higgs boson
KK gauge boson
KK fermion
Fermion mass term
(～ (yukawa coupling) ・ (vev) )
t
x
Excluded
UED model without
right-handed neutrino
UED model with
right-handed neutrino
Allowed parameter
region changed much !!
Produced from g (1)
decay + from
the thermal bath
Produced from g(1)
decay (mn = 0)
1/R can be less than 500 GeV
In ILC experiment, n=2 KK particle can be produced !!
It is very important for discriminating
UED from SUSY at collider experiment
Summary
We have solved two problems in Universal Extra Dimension (UED)
models (absence of the neutrino mass, forbidden energetic photon
emission), and constructed realistic UED model.
In constructed UED model, we have investigated the relic
abundance of the dark matter
KK right-handed neutrino
In the UED model with right-handed neutrinos, the
compactification scale 1/R can be as large as 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 ?
5-dimension spacetime
R
Fifth-dimension is compactified on an S 1
S1
4 dimension spacetime
All SM particles has the excitation mode
called Kaluza-Klein (KK) particle
Y
Standard model particle
Y ,Y
(1)
, ‥‥, Y
(2)
KK particle
(n)
KK parity
5th dimension momentum conservation
For S1 compactification
R : S1 radius
P 5 = n/R
n : 0, ±1, ±2,….
KK number (= n) conservation at each vertex
P5 = － P5
S 1 / Z 2 orbifolding
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)
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) ～
～
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) ]
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 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) ]
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) ]
1/R = 600 GeV
WN h2
mh = 120 GeV
mn = 0.66 eV
degenerate
case
reheating temperature (1/R)
N(n)abundance depends on the reheating temperature
If we know 1/R and mn , we can get the
constraint for the reheating temperature
Solving cosmological problems
by introducing Dirac neutrino
We investigated some g (1)decay mode
g (1)
N(1)
(1)
gDominant
(1) decay mode
(1)
h
from g
l
W
n
g (1)
g
N
(1)
l
g
n
Dominant photon emission
g (1)
decay mode
from
etc.
G(1)
(n)
N Production process
(n)
In thermal bath, there are many N production processes
N(n)
(n)
N
(n)
N
N(n)
(n)
N
1/R > 400GeV ( from precision measurements )
We concentrate on the early universe in
T > 200 GeV for relic abundance calculation
N(n)
N(n)
There is no vacuum expectation value in the era
etc.
Many processes disappear