1. Masato Yamanaka (Saitama University) collaborators Shigeki Matsumoto Joe Sato Masato Senami Phys.Rev.D76:043528,2007Phys.Lett.B647:466-471 and Universal Extra Dimension models with right-handed neutrinos

2. Introduction What is dark matter ? http://map.gsfc.nasa.gov Supersymmetric model Little Higgs model Is there beyond the Standard 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. What is Universal 5-dimensions compactified on an S /Z orbifold 1 2 all SM particles propagate spatial extra dimension (time 1 + space 4) Extra Dimension (UED) model ? R 4 dimension spacetime S 1  (1) Standard model particle  (2),, ‥‥, (n) KK particle KK particle mass : m = ( n /R + m +  m ) (n) 2 22 m : corresponding SM particle mass 2 SM 1/2 SM 2  m : radiative correction

4. Dark matter in UED models Lightest KK Particle Next Lightest KK particle G (1) KK graviton KK photon (1)  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) ( NLKP ) ( LKP )

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. Problem 2 KK parity conservation and kinematics Possible decay mode (1)   G  high energy SM photon emission It is forbidden by the observation ! Late time decay due to gravitational interaction Serious problems in UED models

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  + h.c. m N (1) R 1 + 1/R m 2 ～ order Mass of the KK right-handed neutrino

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

9. Branching ratio of the decay （1）（1）  = ( ) (1)    ( ) （1）（1）  (1)  = －7－7 5 × 10 Neutrino masses are introduced, and problematic high energy photon emission is highly suppressed !! Decay rate of dominant photon emission decay Decay rate of new decay mode G N Serious problems in UED model and solving the problems （1）（1）  N (1) Appearance of the new decay （1）（1） 

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

11. KK right-handed neutrino dark matter and relic abundance calculation of that Our UED models ( after introducing right-handed neutrino ) Original UED models ( before introducing right-handed neutrino ) Dark matterKK graviton Dark matter KK right-handed neutrino N (1) G G : Produced from  decay only (1) N : Produced from  decay and from thermal bath Additional contribution to relic abundance

12. Total DM number density DM mass ( 1/R ) We must evaluate the DM number density produced from thermal bath ! KK right-handed neutrino dark matter and relic abundance calculation of that  h (number density) × (DM mass) constant 2 DM ～ ～ ～

13. N production processes in thermal bath (n) N N N N N KK Higgs boson KK gauge boson KK fermion Fermion mass term ( (yukawa coupling) (vev) ) ～・ time space KK right-handed neutrino dark matter and relic abundance calculation of that

14. N (n) N N t x In the early universe ( T > 200GeV ), vacuum expectation value = 0 (yukawa coupling) (vev) = 0 ～ ・ N must be produced through the coupling with KK Higgs (n) KK right-handed neutrino dark matter and relic abundance calculation of that

15. 2 m (T) Any particle mass = 2 m (T=0) +  m (T) 2  m (T) ～ m ・ exp[ ｰ m / T ] loop For m > 2T loop  m (T) ～ T～ T For m < 2T loop m : mass of particle contributing to the 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 ] KK right-handed neutrino dark matter and relic abundance calculation of that

16. KK Higgs boson mass m (T) = m (T=0) + [ a(T) 3  +x(T)  3 y ] 22 h t 22 T 2 12  (n)  ・・ T : temperature of the universe : quartic coupling of the Higgs boson y : top yukawa coupling N must be produced through the coupling with KK Higgs (n) a(T)[ x(T) ] : Higgs [top quark] particle number contributing to thermal correction loop KK right-handed neutrino dark matter and relic abundance calculation of that

17. N (n) N N N N KK Higgs boson KK gauge boson KK fermion Fermion mass term ( (yukawa coupling) (vev) ) ～・ t x N production processes in thermal bath (n) KK right-handed neutrino dark matter and relic abundance calculation of that Dominant N production process (n)

18. 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) Neutrino mass dependence of the DM relic abundance

19. Summary 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. We have solved two problems in UED models (absence of the neutrino mass, forbidden energetic photon emission) by introducing the right-handed neutrino

20. Appendix

21. What is Universal Extra Dimension (UED) model ? Hierarchy problem Candidate for the theory beyond the standard model Large extra dimensions [ Arkani-hamed, Dimopoulos, Dvali PLB429(1998) ] Warped extra dimensions [ Randall, Sundrum PRL83(1999) ] Extra dimension model Existence of dark matter etc. LKP dark matter due to KK parity [ Servant, Tait NPB650(2003) ]

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) ] [ Servant, Tait NPB 650 (2003) ] Existence of dark matter

23. What is Universal Extra Dimension (UED) model ? Periodic condition of S manifold 1  (1) Standard model particle  (2),, ‥‥, (n) Kaluza-Klein (KK) particle KK particle mass : m = ( n /R + m +  m ) (n) 2 22 m : corresponding SM particle mass 2 SM 1/2 SM 2  m : radiative correction

24. What is Universal Extra Dimension (UED) model ? 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 5-dimensional kinetic term Tree level KK particle mass : m = ( n /R + m ) (n) 2 22 SM m : corresponding SM particle mass 2 SM 1/2

25. KK parity  (3) (1)  (2) (1) (0)     5th dimension momentum conservation Quantization of momentum by compactification P = n/R 5 R : S radius n : 0, 1, 2,…. 1 KK number (= n) conservation at each vertex KK-parity conservation n = 0,2,4,… ＋1＋1 n = 1,3,5,… －1－1 At each vertex the product of the KK parity is conserved t

26. (4) (1)    (0)  (1)   (0)   (1)  (2)  (0)  (4) (1)   (2)  Example of KK parity conservation

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

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 LKPDark matter candidate Who is dark matter ?

29. 1/R >> m SM degeneration of KK particle masses Origin of mass difference Radiative correction For 1/R < 800 GeV ～ For 1/R > 800 GeV ～ NLKP : (1) NLKP : G (1) NLKP : Next Lightest Kaluza-Klein Particle LKP : G (1) LKP : (1) LKP :   m =m (1) m G －   Mass difference between the KK graviton and the KK photon

30. m = R 1 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) ]

31. Allowed [ Kakizaki, Matsumoto, Senami PRD74(2006) ] Excluded Allowed region in UED models Because of triviality bound on the Higgs mass term, larger Higgs mass is disfavored In collider experiment, smaller extra dimension scale is favored We investigated : 『 The excluded region is truly excluded ? 』

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

33. （1）（1）  N (1) Appearance of the new decay （1）（1）  （1）（1）  N (1) N （1）（1）  （1）（1）   W G (1)   Fermion mass term ( (yukawa coupling) (vev) ) ～ ・ （1）（1）  Many decay mode in our model Dominant decay mode from (1) Dominant photon emission decay mode from (1)  

34. Thermal bath （1）（1） decouple G （1）（1） decay early universe   High energy photon  ～ M 2 planck mm 3 （1）（1） G （1）（1）   decays after the recombination  （1）（1） Serious problems in UED models

35. = 2×10 [ sec ] －9－9 －1－1 500GeV （1）（1） m 3 m 10 eV －2－2 2 m 1 GeV 2 m = m N （1）（1） m － m : SM neutrino mass （1）（1） Decay rate for （1）（1） N （1）（1） Solving cosmological problems by introducing Dirac neutrino    (1) N    

36. = 10 [sec ] － 15 －1－1 3 1 GeV m ´ m ´ = m － m (1) G Decay rate for （1）（1） G （1）（1） (1) G Solving cosmological problems by introducing Dirac neutrino [ Feng, Rajaraman, Takayama PRD68(2003) ]        

37. Br( ) (1) Y < 3 × 10 － 18 GeV 500GeV 2 m 0.1 eV 2 m 1 GeV 1 / R 0.10 DM h 2 2 × The successful BBN and CMB scenarios are not disturbed unless this value exceeds 10 - 10 GeV －9－9 － 13 [ Feng, Rajaraman, Takayama (2003) ] : typical energy of emitted photon Y (1) : number density of the KK photon normalized by that of background photons        Total injection photon energy from decay (1) 

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 （1）（1）  N (1) Appearance of the new decay （1）（1）  Two problems have been solved simultaneously !!

39. 1 From decoupled  decay (1) N  2 From thermal bath (directly) Thermal bath （1）（1） N 3 From thermal bath (indirectly) Thermal bath （n）（n） N Cascade decay （1）（1） N （1）（1） N Production processes of new dark matter N （1）（1）

40. KK right-handed neutrino dark matter and relic abundance calculation of that time KK photon decouple from thermal bath Relic number density of KK photon at this time constant KK photon decay into KK right-handed neutrino (or KK graviton) KK right-handed neutrino production from thermal bath N (1) number density from decay (our model) (1)  = G number density from decay (previous model) (1) 

41. Thermal correction KK Higgs boson mass m (T) = m (T=0) + [ a(T) 3  +x(T)  3 y ] 22 h t 22 T 2 12  (n)  ・・ x(T) = 2[2RT] + 1 [ ‥‥ ] : Gauss' notation a(T) =  m=0 ∞ θ 4T － m R ｰ 2 22 [ a(T) 3  +x(T)  3 y ] h t 22 ・・ T 2 12 T : temperature of the universe : quartic coupling of the Higgs boson y : top yukawa coupling

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

43. 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) ]

44. We expand the thermal correction for UED model We neglect the thermal correction to fermions and 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 correction In 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 KK right-handed neutrino dark matter and relic abundance calculation of that

45. Boltzmann equation dT dY (n) = s T Hs T H  m C (m) (n) 1 + dT dg (T) * s 3g (T) s * T C (m) (n) = 4 g (2  ) 3 d k 3   (m)   N (n) f  (m) L s, H, g, f : entropy density, Hubble parameter, relativistic degree of freedom, distribution function * s Relic abundance calculation g = 3 = 2 = 1The normal hierarchy The inverted hierarchy The degenerate hierarchy Y (n) = ( number density of N ) ( entropy density ) (n)

46. Reheating temperature dependence of relic density from thermal bath Dotted line : N abundance produced directly from thermal bath (1) Dashed line : N abundance produced indirectly from higher mode KK right-handed neutrino decay (1) Determination of relic abundance and 1/R We can constraint the reheating temperature !!