masato yamanaka (saitama university) collaborators shigeki matsumoto joe sato masato senami...
TRANSCRIPT
Masato Yamanaka (Saitama University)
collaborators
Shigeki Matsumoto Joe Sato Masato Senami
arXiv:0705.0934 [hep-ph] Phys.Lett.B647:466-471 and
Relic abundance of dark matter in universal extra dimension models
with right-handed neutrinos
(To appear in PRD)
Introduction
What is dark matter ?
http://map.gsfc.nasa.govSupersymmetric modelLittle Higgs model
Is there beyond the Standard Model ?
(1) Construction of problemless UED model
(2) Calculation of dark matter relic abundance
Universal Extra Dimension model (UED model) Appelquist, Cheng, Dobrescu PRD67 (2000)
Contents of today’s talk
What is Universal
5-dimensions
compactified on an S /Z orbifold1 2
all SM particles propagatespatial extra dimension
(time 1 + space 4)
Extra Dimension (UED) model ?
R
4 dimension spacetime
S1
(1)
Standard model particle (2), , ,‥‥ (n)
KK particle
KK particle mass : m = ( n /R + m + m )(n) 222
m : corresponding SM particle mass2SM
1/2SM
2
m : radiative correction
For 1/R < 800 GeV~
For 1/R > 800 GeV~
NLKP : (1)
NLKP : G (1)
LKP : G (1)
LKP : (1)LKP :
&Who is dark matter ?
KK parity
KK parity conservation at each vertexLightest Kaluza-Klein Particle(LKP) is stable and can be dark matter
(c.f. R-parity and the LSP in SUSY)
Dark matter candidate
Possible NLKP decayNLKP LKP + SM particle
NLKP : Next Lightest Kaluza-Klein Particle
Problems in Universal Extra Dimension (UED) model
Allowed
[ Kakizaki, Matsumoto, Senami PRD74(2006) ]
(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
It is forbidden by
the observation !
Excluded
Solving the two problems
Before introducing Dirac neutrino
m G(1)> m(1)
Problematic is always emitted from decay(1)
After introducing Dirac neutrinom G> m> m (1)N (1)
(1)
New decay channels open !!(1)
Introducing the right-handed neutrino N
m N(1)
R1
+ 1/Rm 2
~ orderThe mass of the KK
right-handed neutrino N(1)
Br( )( 1) =
( N )(1) (1)
= 5 × 10500GeV
3
m0.1 eV- 7
2 m1 GeV
1 / R
Presence of neutrino massAbsence of the diffuse photon problem
We have created the realistic UED model
Allowed !!
( G )
Branching ratio of the decay( 1)
( 1)
(1)
(1)
G(1)
N (1)
N (0)
N decay is impossible ! (1)
stable, neutral, massive, weakly interactionKK right handed neutrino can be dark matter !
m N(1)
R1 +
1/Rm2~ order
Change of DM (for 1/R < 800GeV) : G(1)
N (1)
Who is dark matter ??
Br( )( 1) =
( N )(1) (1)
( G DM production process ) ~ 10- 7
< m + mG(1) (0)N
G(1) : Almost produced from decay(1)
N (1) (1)
When dark matter changes from G to N , what happens ?
(1)(1)
: Produced from decay and from thermal bath
Additional contribution to relic abundance
Total DM number density
DM mass ( ~ 1/R )
We must re-evaluate the DM number density !
1 From decoupled decay (1) (1) N(1)
2 From thermal bath (directly)
Thermal bath( 1)N
3 From thermal bath (indirectly)
Thermal bath( n)N
Cascade
decay
( 1)N
( 1)N
Production processes of new dark matter N( 1)
N(n) Production process
In thermal bath, there are many N production processes(n)
N(n)N(n) N(n)
N(n) N(n)
KK Higgs boson
KK gauge bosonKK fermionFermion mass term ( (yukawa coupling) (vev) )~ ・
t
x
N(n) Production process
N(n)N(n) N(n)
t
x
In the early universe ( T > 200GeV ), vacuum expectation value = 0
(yukawa coupling) (vev) = 0 ~ ・
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 ]
2m (T)Any particle mass = 2m (T=0) + m (T)2
m (T) ~ m ・ exp[ ー m / T ]
loop For m > 2Tloop
m (T) ~ T For m < 2Tloop
m loop : mass of particle contributing to the thermal correction
Thermal correction
KK Higgs boson mass
m (T) = m (T=0) + [ a(T) 3+x(T)3y ]
2 2h t2 2 T2
12(n)(n) ・・
x(T) = 2[2RT] + 1
[ ] : Gauss' notation‥‥
a(T) = m=0
∞θ 4T - m R ー 22 2 [ a(T) 3+x(T)3y
]h t2 2・・ T2
12
T : temperature of the universe : quartic coupling of the Higgs bosony : top yukawa coupling
N(n) Production process
In thermal bath, there are many N production processes(n)
N(n)N(n) N(n)
N(n) N(n)
KK Higgs boson
KK gauge bosonKK fermionFermion mass term ( (yukawa coupling) (vev) )~ ・
t
x
Dominant N production process
(n)
UED model withright-handed neutrino
UED model withoutright-handed neutrino
Allowed parameter region changed much !!Excluded
1/R can be less than 500 GeV
In ILC experiment, can be produced !!n=2 KK particle
It is very important for discriminating UED from SUSY at collider experiment
Produced from decay (m = 0)
(1)
Produced from decay + from the thermal bath
(1)
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.
What is UniversalExtra Dimension (UED) model ?
Fifth-dimension is compactified on an S1R
4 dimension spacetime
All SM particles has the excitation mode called Kaluza-Klein (KK) particle
(1)
Standard model particle (2), , ,‥‥ (n)
KK particle
S1
5-dimension spacetime
5th dimension momentum conservation
For S compactification 1 P = n/R5R : S radius n : 0, ±1, ±2,….1
KK number (= n) conservation at each vertex
S1/ Z 2 orbifolding P = 5 P 5-
KK-parity conservation
n = 0,2,4,… + 1n = 1,3,5,… - 1
At each vertex the product of the KK parity is conserved
(3)
(1)
φ (2)
(1)
(0)
(0)
KK parity
φ
m = R1
G(1)Mass of the KK graviton
Mass matrix of the U(1) and SU(2) gauge boson
: cut off scale v : vev of the Higgs field
Radiative correction[ Cheng, Matchev, Schmaltz PRD66 (2002) ]
Dependence of the ‘‘Weinberg’’ angle
[ Cheng, Matchev, Schmaltz (2002) ]
sin 2W~~ 0 due to 1/R >> (EW scale) in the
mass matrix
~~B(1) (1)
= 2×10 [sec ]- 9 - 1 500GeV
( 1)
m3 m
10 eV- 2
2 m1 GeV
2
m = mN( 1 )m - m : SM neutrino mass( 1 )
Decay rate for ( 1) N( 1
)
Solving cosmological problemsby introducing Dirac neutrino
(1)
N (1)
= 10 [sec ]- 15 - 1
3
1 GeVm´
m = m - m(1) G(1)
Decay rate for ( 1) G( 1
)
(1)
G(1)
Solving cosmological problemsby introducing Dirac neutrino
[ Feng, Rajaraman, Takayama PRD68(2003) ]
We expand the thermal correction for UED model
Thermal correction
We neglect the thermal correction to fermionsand to the Higgs boson from gauge bosons
Gauge bosons decouple from the thermal bath at once due to thermal correction
Higgs bosons in the loop diagrams receive thermal correctionIn order to evaluate the mass correction correctly,
we employ the resummation method[P. Arnold and O. Espinosa (1993) ]
The number of the particles contributing to the thermal mass is determined by the number of the particle lighter than 2T
Result and discussion
N abundance from Higgs decay depend on the y (m )(n)
Degenerate case
m = 2.0 eV
[ K. Ichikawa, M.Fukugita and M. Kawasaki (2005) ]
[ M. Fukugita, K. Ichikawa, M. Kawasaki and O. Lahav (2006) ]
reheating temperature (1/R)
Nh2
1/R = 600 GeV
m = 120 GeVh
m = 0.66 eV
degenerate case
N abundance depends on the reheating temperature(n)
If we know 1/R and m , we can get the constraint for the reheating temperature
Solving cosmological problemsby introducing Dirac neutrino
We investigated some decay mode(1)
(1)N(1)
(1)
G(1)
(1)N(1)h(1)
llW
etc.
Dominant decay mode from (1)
Dominant photon emission decay mode from (1)
N(n) Production process
In thermal bath, there are many N production processes(n)
N(n)N(n) N(n) N(n) N(n)
N(n) N(n)
etc.
1/R > 400GeV ( from precision measurements )
We concentrate on the early universe inT > 200 GeV for relic abundance calculation
There is no vacuum expectation value in the era
Many processes disappear