1. 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)

2. Introduction What is dark matter ? http://map.gsfc.nasa.gov Supersymmetric model Little 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

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. 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 vertex Lightest 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 decay NLKP LKP + SM particle NLKP : Next Lightest Kaluza-Klein Particle

5. 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

6. Solving the two problems Before introducing Dirac neutrino m G (1) > m (1) Problematic is always emitted from decay (1) After introducing Dirac neutrino m G > m (1) N    New  decay channels open !! (1) Introducing the right-handed neutrino N m N (1) R 1 + 1/R m 2 ～ order The mass of the KK right-handed neutrino N (1)

7. Br( ) （1）（1） = ( N ) (1) =5 × 10 500GeV 3 m 0.1 eV －7－7 2 m 1 GeV 1 / R      Presence of neutrino mass Absence of the diffuse photon problem We have created the realistic UED model Allowed !! ( G ) Branching ratio of the decay （1）（1）  （1）（1）  (1) 

8. G N N (0) N decay is impossible ! (1) stable, neutral, massive, weakly interaction KK right handed neutrino can be dark matter ! m N (1) R 1 + 1/R m 2 ～ order Change of DM (for 1/R < 800GeV) : G (1) N Who is dark matter ?? Br( ) （1）（1） = ( N ) (1)     ( G DM production process ) ～ 10 －7－7 < m + m G (1) (0) N

9. G (1) : Almost produced from  decay (1) N When dark matter changes from G to N, what happens ? (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 !

10. 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）

11. N (n) Production process In thermal bath, there are many N production processes (n) N N N N N KK Higgs boson KK gauge boson KK fermion Fermion mass term ( (yukawa coupling) (vev) ) ～・ t x

12. N (n) Production process N (n) N N t x In the early universe ( T > 200GeV ), vacuum expectation value = 0 (yukawa coupling) (vev) = 0 ～・

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 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

14. 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

15. N (n) Production process In thermal bath, there are many N production processes (n) N N N N N KK Higgs boson KK gauge boson KK fermion Fermion mass term ( (yukawa coupling) (vev) ) ～・ t x Dominant N production process (n)

16. UED model with right-handed neutrino UED model without right-handed neutrino Allowed parameter region changed much !! Excluded

17. 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)

18. 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.

19. Appendix

20. What is Universal Extra Dimension (UED) model ? Fifth-dimension is compactified on an S 1 R 4 dimension spacetime All SM particles has the excitation mode called Kaluza-Klein (KK) particle  (1) Standard model particle  (2),, ‥‥, (n) KK particle S 1 5-dimension spacetime

21. 5th dimension momentum conservation For S compactification 1 P = n/R 5 R : S radius n : 0, ±1, ±2,…. 1 KK number (= n) conservation at each vertex S 1 / Z 2 orbifolding P = 5 P 5 － 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  (3) (1)  (2) (1) (0) KK parity    

22. 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) ]

23. 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) 

24. = 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    

25. = 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) ]        

26. We expand the thermal correction for UED model Thermal correction 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

27. 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) ]

28. reheating temperature (1/R)  N h 2 1/R = 600 GeV m = 120 GeV h 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

29. Solving cosmological problems by introducing Dirac neutrino We investigated some decay mode (1) N G N h l l W etc.         Dominant decay mode from (1) Dominant photon emission decay mode from (1)  

30. N (n) Production process In thermal bath, there are many N production processes (n) N N N N N N N etc. 1/R > 400GeV ( from precision measurements ) We concentrate on the early universe in T > 200 GeV for relic abundance calculation There is no vacuum expectation value in the era Many processes disappear