Solving cosmological problems in Universal Extra Dimension models by introducing Dirac neutrino

1. Solving cosmological problems in Universal Extra Dimension models by introducing Dirac neutrino Masato Yamanaka (Saitama University) collaborators Shigeki Matsumoto Joe Sato Masato Senami

2. 0. Outline UED model merit Dark matter candidate Cosmological problems demerit for small 1/R Neutrino mass We discuss a solution to the problems by introducing Dirac neutrino

3. 1. Introduction CMB, rotating curve, structure formation, and so on There is a dark matter in our universe ! http://map.gsfc.nasa.gov candidate weakly interacting massive particles Lightest Kaluza-Klein Particle (LKP)

4. 2. Model minimal Universal Extra Dimension (mUED) 5-dimensions 1 compactified on an S /Z orbifold 2 Each SM particle has the excitation mode called KK mode Momentum along the extra dimensionis quantized : p = n/R ( n : integer) 5

5. 3. LKP and dark matter Momentum conservation in the extra dimension Conservation of KK number in each vertex LKP is stable and can be dark matter candidate ! Including radiative correction KK graviton or KK hyper charge boson (1) (1) B G

6. 4. Problems in UED model 1 Cosmological problem Photons emitted from the KK graviton decay might affect CMB and BBN To avoid the problems Excluded parameter region in which the KK graviton is the LKP has been excluded Allowed

7. 5. Problems in UED model 2 Neutrino mass In the UED model, the SM neutrino is regarded as massless particle But, from measurements, we know that neutrino is massive and there is a lepton flavor mixing We have to introduce neutrino mass to the UED model

8. 6. Introduction of the right handed neutrino The neutrino mass must be introduced as a Dirac type mass

9. 7. Masses of the KK modes m If radiative correction to is negative, B (1) m m m < < B (1) G (1) N (1) This case is not problematic, because we can avoid the cosmological problems If radiative correction to is positive, m B (1) m m m < < G (1) N (1) B (1) In this case we could not avoid the problems, and hence this parameter region has been excluded Our purpose in this work is the expansion of the allowed compactification parameter region

10. 8. Solving the problems If the following circumstances are satisfied, the problems are solved simply ! N (1) γ B (1) B (1) ν dominant decay mode B decay processes emitting the photon directly (1) N : KK right handed neutrino (1)

11. 9. Analysis and confirmation 1 ν （1） Decay rate for B （1） N 2 α´ m (δm) 2 ν Decay rate = m 8 3 B （1） 500GeV 3 2 2 m δ m 2×10 [sec ] －9 ν = －1 m 10 eV －2 1GeV B （1） δ m m m － = B （1） N （1）

12. 10. Analysis and confirmation 2 What is the dominant decay mode emitting the photon directly ? （1） B B (1) h (1) N (1) γ B (1) l W l γ G (1) ν

13. 11. Analysis and confirmation 3 γ （1） （1） Decay rate for B G m 7 cosθ 2 W （1） B Decay rate = 2 m 4 144πM Plank(4D) G （1） 3 m m m 2 2 4 × 1－ 1 + 3 （1） + 6 （1） G G G （1） m m m 2 2 4 B B B （1） （1） （1） 3 δ m ´ －15 10 [sec ] －1 = 1GeV M : 4-dimensional Plank scale Plank(4D) δ m : mass difference between m and m ´ G (1) B (1)

14. 12. Analysis and confirmation 4 γ ν （1） （1） Decay rate for B N m 1 2 Decay rate = ν m m 4 2048 (2π) 7 （1） B W 4 ×g g sin θ×(loop factor)×(δ) 6 2 m 2 ´ W －22 1.6×10 [sec ] －1 = 4 2 m 500GeV δ m ν m 10 eV －2 1GeV B （1） loop factor : factor from loop integral 10 －2

15. 13. KK right handed neutrino and thermal history Thermal bath （1） N （1） B （1） G （1） B decouple decay time now stable, neutral, massive, weakly interaction KK right handed neutrino can be dark matter !

16. 14. Summary and discussion According to 5-dimensional algebraic structure, we have introduced the Dirac type neutrino into the UED model We have calculated the decay rate of the relevant processes : γ, and （1） （1） ν, B G （1） B （1） N γ ν （1） （1） B N We have found that the cosmological problems are solved, because the KK hyper charge boson decays mainly into the KK right handed neutrino

17. About compactification 1 S 1 Simplest compact manifold ψ(x , y) = ψ(x , y+2πR) μ μ R : compactfication scale Z Reflection symmetry under y y － 2

18. About compactification 2 / S 1 compactification produces Z 2 chiral theory corresponding to the SM

19. Cosmological problems 1 Gravitational coupling is extremely weak If the KK graviton is the LKP In the early universe, the decoupled NLKP decays into the LKP graviton after a long time The decay products might destroys the CMB spectrum and the successful BBN prediction !

20. Cosmological problems 2 Even if the KK graviton is the NLKP, similarly problems can occur due to the NLKP late time decay In this case, the problems can be avoided by constraining the reheating temperature

21. Radiative correction 1 The mass of the KK particle m = (n) (n/R) + m 2 2 n/R = SM Mass difference for each KK mode is small To identify the LKP, and to determine decay channels, it is important to calculate radiative correction to the KK particle mass

22. Radiative correction 2 Mass matrix of the U(1) and SU(2) gauge boson g g v /4 2 2 1/R + δ 2 m 2 + g v /4 2 ´ ´ (1) B g g v /4 2 + g v /4 2 1/R + δ 2 m 2 2 ´ (1) W g 2 2 39 (3) 1 g ζ ´ ´ δ 2 2 2 m － ln(Λ R ) (1) = － B 2 16π R 4 2 6 16π R 2 2 ζ 2 g g 5 (3) 2 15 δ 2 2 2 m － ln(Λ R ) = － (1) W 16π R 4 2 16π R 2 2 2 2 Λ : cut off scale R : compactification scale

23. Radiative correction 3 Mass of the KK right handed neutrino 2 m 2 1 2 ν m = m + 2 2 + ν (1) N R 2 × 1/R Mass of the KK graviton 1 2 2 m = (1) R G Note : we ignore graviton loops, since gravitational interaction is too weak

24. Dirac type mass algebraic structure of the 5-dimensional space-time SO(1,4) spinor fields in the UED model are represented by 4-compornent field Dirac type mass Majorana type mass