1. Universal Extra Dimension models with right-handed neutrinos
Masato Yamanaka (Saitama University)
collaborators
Shigeki Matsumoto Joe Sato Masato Senami
Phys.Lett.B647: and
Phys.Rev.D76:043528,2007

2. Introduction What is dark matter ?
Is there beyond the Standard Model ?
Supersymmetric model
Little Higgs model
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

3. 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

4. What is Universal
Extra Dimension (UED) model ?

5. 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 /Z orbifold R S 1 1 2
4 dimension spacetime
all SM particles propagate spatial extra dimension
Interaction rule same as SM

6. Extra Dimension (UED) model ?
What is Universal
Extra Dimension (UED) model ?
Periodic condition of S manifold 1 Y Y
(1) Y
(2) Y
(n) ,
, ‥‥,
Standard model particle
Kaluza-Klein (KK) particle
1/2
KK particle mass : m = ( n /R + m dm )
(n) 2 2 2 2 SM 2
m : corresponding SM particle mass SM
dm : radiative correction

7. KK parity 5th dimension momentum conservation P = n/R
Quantization of momentum by compactification
P = n/R 1
R : S radius n : 0, 1, 2,…. 5
KK number (= n) conservation at each vertex t
KK-parity conservation y
(0) y
(1)
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) φ φ

8. Dark matter candidate LKP Dark matter candidate Who is dark matter ?
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 ?

9. g g m = m d G G 1/R >> m － degeneration of KK particle massesSM
m = m
(1) G － d g
degeneration of KK particle masses
Origin of mass difference
Radiative correction
Mass difference between the KK graviton and the KK photon g G
(1)
(1)
For 1/R < 800 GeV
LKP :
NLKP : ～ g
(1)
For 1/R > 800 GeV
LKP :
LKP :
NLKP : G
(1) ～
NLKP : Next Lightest Kaluza-Klein Particle

10. Serious problems in UED model and solving the problems

11. Serious problems in UED models
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 !!

12. Serious problems in UED modelsg
Problem 2
Case : LKP NLKP G
(1)
(1)
KK number conservation and kinematics g
(1)
Possible decay mode g g
(1) G
(1)
Late time decay due to gravitational interaction
high energy SM photon emission
It is forbidden by the observation !

13. Serious problems in UED modelsg
(1)
Case : LKP NLKP G
(1)
Same problem due to the late time decay G
(1) g g G
(1)
(1)
Constraining the reheating temperature, we can avoid the problem
[ Feng, Rajaraman, Takayama PRD68(2003) ]

14. 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 = y N L F + h.c. n 1 m 2
Mass of the KK right-handed neutrino m ～ n +
order N
(1) R
1/R

15. Solving the problems by introducing the right-handed neutrino
(1)
Lightest KK Particle
KK graviton g
Next Lightest KK particle
KK photon
(1)
Introducing the right-handed neutrino
Lightest KK Particle
KK graviton G
(1)
KK right-handed neutrino
Next Lightest KK particle N
(1)
Next to Next Lightest KK particle g
KK photon
(1)

16. g n N g g Dominant decay mode from g g g n g n g
Appearance of the new decay
（1） g
(1) n
（1） N g
Many decay mode in our model
（1）
Dominant decay mode from
(1)
Dominant photon emission decay mode from g N
(1) g
（1） g F
(1) N
(1)
（1） W n g n g G
(1)
（1） g
Fermion mass term ( (yukawa coupling) (vev) ) ・ ～

17. Serious problems in UED model and solving the problems
Branching ratio of the decay
（1）
Decay rate of dominant photon emission decay g g G
( )
（1） G
(1) = =
5 × 10 －7 G
Decay rate of new decay mode
( ) g
(1)
(1) n N
Introducing the right-handed neutrino
Neutrino masses are introduced , and problematic high energy photon emission is highly suppressed !!

18. KK right-handed neutrino dark matter and relic abundance calculation of that

19. N G N m + m m > m > m <
KK right-handed neutrino dark matter and relic abundance calculation of that m
> m
> m
Mass relation g
(1)
(1) N G
(1)
(1)
Possible N decay from the view point of KK parity conservation
stable, neutral, massive, weakly interaction N
(1)
(1) G N m N
(1)
m m G
(0)
<
Forbidden by kinematics
KK right handed neutrino can be dark matter !

20. KK right-handed neutrino dark matter and relic abundance calculation of that
Before introducing the neutrino mass into UED models
Dark matter
KK graviton G
(1)
(1) G
: Produced from g decay
(1)
After introducing the neutrino mass into UED models
(1)
Dark matter
KK right-handed neutrino N N
(1)
: Produced from g decay and from thermal bath
(1)
Additional contribution to relic abundance

21. 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 N
(1) = G
(1)
number density from decay (our model)
number density from decay (previous model) g
(1) g
(1)

22. h ～ (number density) × (DM mass)
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 re-evaluate the DM number density !

23. N production processes in thermal bath
KK right-handed neutrino dark matter and relic abundance calculation of that
N production processes in thermal bath
(n)
(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) ) ～ ・

24. 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

25. 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 ]
m (T) 2
m (T=0) + dm (T) 2 2
Any particle mass =
dm (T)
～ m・exp[ ｰ m / T ]
For m > 2T
loop
loop
For m < 2T
dm (T)
～ T
loop m
: mass of particle contributing to the thermal correction
loop

26. m (T) = m (T=0) + [ a(T) 3l +x(T) 3y ]
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
m (T) = m (T=0) + [ a(T) 3l +x(T) 3y ] 2 2 2 2 F
(n) F
(n) ・ ・ 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

27. N production processes in thermal bath
KK right-handed neutrino dark matter and relic abundance calculation of that
Dominant N production process
(n)
N production processes in thermal bath
(n) 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) ) ～ ・

28. Numerical result

29. 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 ILC experiment, can be produced !!
n=2 KK particle
It is very important for discriminating UED from SUSY at collider experiment

30. Allowed parameter region changed much !!
[ Kakizaki, Matsumoto, Senami PRD74(2006) ]
Allowed parameter region changed much !!
Excluded
UED model without right-handed neutrino
UED model with right-handed neutrino

31. Summary

32. 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.

33. Appendix

34. Extra Dimension (UED) model ?
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.

35. Extra Dimension (UED) model ?
What is Universal
Extra Dimension (UED) model ?
5-dimensional kinetic term
1/2
Tree level KK particle mass : m = ( n /R + m )
(n) 2 2 2 SM
m : corresponding SM particle mass 2 SM
Since 1/R >> m , all KK particle masses are highly degenerated around n/R SM
Mass differences among KK particles dominantly come from radiative corrections

36. Radiative correction 1 m = R Mass of the KK graviton
[ Cheng, Matchev, Schmaltz PRD66 (2002) ] 1
m =
Mass of the KK graviton
(1) G R
Mass matrix of the U(1) and SU(2) gauge boson
L : cut off scale v : vev of the Higgs field

37. g B Dependence of the ‘‘Weinberg’’ angle ～ sin q ～
[ Cheng, Matchev, Schmaltz (2002) ] ～
sin q 2 ～
0 due to 1/R >> (EW scale) in the W
mass matrix g B
(1) ～
(1) ～

38. G ( ) Serious problems in UED models dm g g g g ～ G M g G
decouple G
（1） g
（1）
decay
Thermal bath g
early universe
High energy photon dm 3
G ( ) g g
（1） G
（1） ～ 2 M
planck g
（1）
decays after the recombination

39. 『 The excluded region is truly 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

40. Solving cosmological problems by introducing Dirac neutrino
Decay rate for
（1） N
（1） n N
(1) g
(1) n 3 2 2
500GeV m d m G －9 －1 =
2×10 [sec ] n m
10 eV －2
1 GeV g
（1） d m m = － m m
: SM neutrino mass g
（1） N
（1） n

41. Solving cosmological problems by introducing Dirac neutrino
Decay rate for
（1） G
（1） g g
(1) G
(1) 3 d m G
－15 =
10 [sec ] －1
1 GeV
[ Feng, Rajaraman, Takayama PRD68(2003) ] d m
= m － m g
(1) G
(1)

42. g g e Br( ) Y < 3 × 10 0.1 eV W d m h × 500GeV m 1 GeV 0.10 e Y
Total injection photon energy from decay
(1) g
－18 e
Br( )
(1) Y
< 3 × 10 g
(1)
GeV 2 2
0.1 eV 2 W d m h 2
1 / R × DM
500GeV m
1 GeV
0.10 n e
: typical energy of emitted photon Y g
(1)
: number density of the KK photon normalized by that of background photons
The total injection photon energy from the KK photon decay is estimated as this:
Where epsilon is the typical energy of emitted photon, and the Y_ganma is the number density of the KK photon normalized by that of background photons.
It is known that the successful BBN and CMB scenarios are not disturbed unless this value exceeds 10^(-9) - 10^(-13) GeV.
This value is clearly much smaller than this constraint value.
Therefore we can say that cosmological problems and the neutrino mass problem are solved simultaneously.
The successful BBN and CMB scenarios are not disturbed unless this value exceeds GeV －9
－13
[ Feng, Rajaraman, Takayama (2003) ]

43. Production processes of new dark matter N
（1） N
(1) 1
From decoupled g decay
(1) g
(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）

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 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) ]

45. S Thermal correction m (T) = m (T=0) + [ a(T) 3l +x(T) 3y ]
KK Higgs boson mass T 2
m (T) = m (T=0) + [ a(T) 3l +x(T) 3y ] 2 2 2 2 F
(n) F
(n) ・ ・ h t 12
T : temperature of the universe
l : quartic coupling of the Higgs boson
y : top yukawa coupling
a(T) = S
m=0 ∞ θ
4T － m R ｰ 2
[ a(T) 3l +x(T) 3y ] h t ・ T 12
x(T) = 2[2RT] + 1
[‥‥] : Gauss' notation

46. S G f < 1 ｰ f > Relic abundance calculation g dY C dg (T) T 1 +
Boltzmann equation S
(n)
(n) dY C
dg (T) T s
(m) * = m
1 + dT
s T H
3g (T) dT s *
(n)
d k 3 g
(n) C
= 4 g G N f
< 1 ｰ f > L n F
(m) F
(m)
(m)
(2p)
(m) 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) Y
(n)
= ( number density of N ) ( entropy density )

47. 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) ]

48. We can constraint the reheating temperature !!
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 !!