Masato Yamanaka (Saitama University) Solving cosmological problems in Universal Extra Dimension models by introducing Dirac neutrino Masato Yamanaka (Saitama University) collaborators Hello, I am Masato Yamanaka Today, I would like to talk about this work. This work's collaborators are Matsumoto san, Joe san, and Senami san. Shigeki Matsumoto Joe Sato Masato Senami hep-ph/0607331

Introduction CMB, rotating curve, and so on There is a dark matter in our universe ! http://map.gsfc.nasa.gov candidate:Weakly Interacting Massive Particles(WIMPs) Universal Extra Dimension model provides a good candidate for WIMPs However this model has two shortcomings From many observation, we know that there is a dark matter in this universe. Weakly Interacting Massive Particles, called WIMPs, are considered as a dark matter candidate. Universal Extra Dimension model provides a good candidate for WIMPs. However this model has two shortcomings. In this work, we solved these two problems by introducing right-handed neutrino. Introducing right-handed neutrino These two problems can be solved simultaneously !

Today’s story What is Universal Extra Dimension model ? Radiative correction Cosmological problems Solving cosmological problems by introducing Dirac neutrino This talk is organized as this. I would like to talk about What is Universal Extra Dimension model, Radiative correction, Cosmological problems, Solving cosmological problems by introducing Dirac neutrino, and finally Summary and discussion. Summary and discussion

Extra Dimension (UED) model ? 1 What is Universal Extra Dimension (UED) model ? 1 Universal Extra Dimension Appelquist, Cheng, Dobrescu PRD67 (2000) characteristics of UED model 5-dimensions (time 1 + space 4) compactified on an S /Z orbifold 1 2 all SM particles propagate spatial extra dimension and has the excitation mode called KK particle UED model is one of the extra dimension models. This model has five dimensions. 5th dimension is compactified on an S^1 manifold, S^1 is a circle of radius R. In addition to S^1 compactification, the extra dimension is compactified on an S^1/Z_2 orbifold in order to produce the standard model chiral fermions. Typical scale for UED model is order one hundred GeV. In this model, all particle in the standard model can propagate in extra dimensions, and has the excitation mode called KK particle. typical scale : 1/R = order[100 GeV] R : compactification scale (S radius) 1

Extra Dimension (UED) model ? 2 What is Universal Extra Dimension (UED) model ? 2 5th dimension momentum conservation compactification ＆ orbifolding KK parity conservation at each vertex Lightest Kaluza-Klein Particle(LKP) is stable (c.f. R-parity and the LSP in SUSY) As a result of S^1/Z_2 orbifolding, the momentum conservation along the 5th dimension is reduced to KK parity conservation. Under this parity, the Lightest Kaluza-Klein Particle, called LKP, is stabilized. It is similar to the relation between the R-parity in SUSY model and the Lightest Supersymmetric Particle. If the LKP is neutral and massive, it can be the dark matter candidate. If LKP is neutral and massive, LKP can be the dark matter candidate

radiative correction 1 [ Cheng, Matchev, Schmaltz PRD66 (2002) ] Radiative corrections are crucial for determining the LKP in extra dimension models Why ? 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 In UED model, it is important to consider the radiative correction for determining the LKP. At tree level, the KK particle mass is determined by the compactification scale 1/R and the corresponding standard model particle mass. Since the compactification scale is much larger than the standard model particle mass, all KK particle masses are highly degenerated around n/R. Therefore mass differences among KK particles dominantly come from radiative corrections. SM Mass differences among KK particles dominantly come from radiative corrections

radiative correction 2 g KK B boson B Dark matter candidate Important thing : The masses of gauge singlet particles ( U(1) gauge boson B, N , etc ) still remain ～1/R R The candidate for the neutral LKP KK B boson B (1) Dark matter candidate (1) KK graviton G For determining the LKP, this is important thing : the masses of gauge singlet particles still remain about 1/R. In some of the LKP candidates, the KK B boson and the KK graviton are neutral particles. Thus these particles can be dark matter candidate. Here I remark on mass of the KK B boson. In UED model, the neutral gauge boson mixing angle is different from the standard model Weinberg angle. Because the compactification scale is much larger than electro-weak scale. So Weinberg angle in UED model is almost 0, and the photon eigenstate becomes approximately pure B boson state. Therefore we can regard the KK B boson as the KK photon. sin q 2 ～ ～ 0 due to 1/R >> (EW scale) in the W mass matrix g B (1) ～ (1) ～

g g g g G ? m = d m m Dark matter candidate G G G Which is the LKP, or (1) G ? (1) Which is the LKP, or m = d m m g (1) － (1) G Dark matter candidate LKP : G (1) g g For 1/R < 800 GeV LKP : G (1) (1) NLKP : The relation between the KK photon mass and the KK graviton mass is shown in this figure. As shown in this figure, for 1/R is smaller than 800 GeV, the LKP is the KK graviton and the NLKP is the KK photon, while for 1/R is larger than 800 GeV, the LKP is the KK photon and the NLKP is the KK graviton. In both region, the LKP is the dark matter candidate. ～ g (1) (1) For 1/R > 800 GeV LKP : LKP : NLKP : G ～ NLKP : Next Lightest Kaluza-Klein Particle

Cosmological problems (1) For the case of G LKP Gravitational coupling is extremely weak g (1) g (1) decays into and G　in the recombination era g The emitted distorts the Cosmic Microwave Background ( CMB ) spectrum ! From here I would like to show the cosmological problems. After the universe temperature becomes low enough, annihilation processes of the KK photon is frozen out. This frozen out KK photon decays into the KK graviton and the photon in the recombination era or after the recombination. Then the emitted photon can distort the cosmic microwave background spectrum. This is the cosmological problem. Even if the KK graviton is the NLKP, these problems are replaced with the problems caused by the KK graviton late time decay. However it is known that in this case there is no cosmological problems when the reheating temperature is low enough. Hu, Silk PRL70(1993) , Feng, Rajaraman, Takayama PRL91(2003) (1) Even if G is the NLKP, these problems are replaced with the problems caused by the G late time decay (1) In this case, we can avoid the problems

Cosmological problems ( For the Big-Bang Nucleosynthesis ) decouple G （1） g （1） decay Thermal bath The cause of the problem photon g nuclei early universe destroy ! For the Big-Bang nucleosynthesis, called BBN, there is a similar problem. The emitted photon from the KK photon decay can destroy the synthesized nuclei. As a result, the successful BBN scenario will be inconsistent with the present observation. Both for the CMB and the BBN, the cause of the problems is the emitted photon. Emitted photon destroys nuclei ! Big Bang Nucleosynthesis prediction Present observation Inconsistent !

NO ! Really ? NLKP : G 1/R > 800 GeV Excluded (1) NLKP : G 1/R > 800 GeV Constraining the reheating temperature Excluded Allowed NO ! We can avoid the cosmological problems [ Feng, Rajaraman, Takayama PRD68(2003) ] [ Kakizaki, Matsumoto, Senami PRD74(2006) ] As shown in above figure, allowed region is narrow‥ As a result, allowed compactification scale region which can avoid the cosmological problems is shown in this figure. This shaded region is allowed region. As shown in this figure, allowed region is narrow. But is it really ? If the light (～150 GeV) Higgs is discovered, does the UED model entirely be excluded ? The answer is NO ! In this work, we could extend the allowed parameter region. Really ? If the light (～150 GeV) Higgs is discovered, does the UED model entirely be excluded ?

Solving cosmological problems by introducing Dirac neutrino Key point Careful treatment of the neutrino mass in the UED model In the UED model, the SM neutrino is regarded as massless particle From measurements, we know that neutrino is massive In order to introduce the neutrino mass, we introduce the Dirac type neutrino For solving cosmological problems, the key point is careful treatment of the neutrino mass in the UED model. In the UED model, the SM neutrino is regarded as massless particle. However, from measurements, we know that neutrino is massive. Therefore, In this work, in order to introduce the neutrino mass, we introduce the Dirac type neutrino. Once we introduce right-handed neutrinos into the UED model, KK right-handed neutrino automatically appear in the spectrum. Since right-handed neutrino is the standard model gauge singlet and have only small Yukawa interactions, radiative corrections to their masses are very small. Thus the mass of the KK right-handed neutrino is estimated as this: Mass of the KK right-handed neutrino N (1) m 1 2 m ～ n + order N (1) R 1/R

Solving cosmological problems by introducing Dirac neutrino For excluded region ( 1/R < 800 GeV ) Before introducing Dirac neutrino m > m g (1) (1) G g g Problematic is always emitted from decay (1) After introducing Dirac neutrino Before introducing Dirac neutrino, in the excluded region, the NLKP is the KK photon. So in this case, problematic photon is always emitted from the KK photon late time decay. While after introducing Dirac neutrino, the KK right-handed neutrino is the NLKP. The existence of the KK right-handed neutrino NLKP changes the late time decay of the KK photon. m > m > m g (1) (1) N G (1) g There is no emission !!

Solving cosmological problems by introducing Dirac neutrino We investigated some decay mode (1) Dominant decay mode from (1) Dominant photon emission decay mode from g g (1) h (1) (1) N N (1) g g l W l n g g n (1) G In the work, we investigated several decay modes of the KK photon. We found that it is the dominant decay mode from the KK photon, and it is the dominant photon emission decay mode from the KK photon. I will show the calculation results. g g etc.

Solving cosmological problems by introducing Dirac neutrino Decay rate for （1） N （1） n N (1) g (1) n As noted above, the KK photon decays dominantly into the KK right-handed neutrino and the left-handed neutrino at tree level. The decay width is given by this : Where delta m is the mass difference between the KK photon and the KK right-handed neutrino, and the m_ν is the standard model neutrino mass. This value looks like very small, but the decay width of the photon emission decay is more small. 3 2 2 500GeV G －9 m d m －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

Solving cosmological problems by introducing Dirac neutrino Decay rate for （1） G （1） g g (1) G (1) This is the dominant photon emission decay mode from the KK photon. Its decay width is given by this : As noted above, this decay width is much smaller than that of the KK right-handed neutrino emission decay. 3 d m ´ G －15 = 10 [sec ] －1 1 GeV [ Feng, Rajaraman, Takayama PRD68(2003) ] d m ´ = m － m g (1) G (1)

Solving cosmological problems by introducing Dirac neutrino Branching ratio of the decay （1） g g G ( G ) (1) (1) g Br( ) （1） = g G ( N ) (1) (1) n 3 2 0.1 eV 1 / R d m = 5 × 10 －7 500GeV m 1 GeV n The branching ratio of the KK photon decay is given by this: It is clear that the KK photon decay associated with a photon is very suppressed. Finally, to confirm that cosmological problems are solved, we estimated the total injection photon energy from the KK photon decay. decay associated with a photon is very suppressed !! g （1）

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. 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 10 - 10 GeV －9 －13 [ Feng, Rajaraman, Takayama (2003) ]

Summary and discussion

Summary We have introduced the Dirac neutrino into the UED model, and solved cosmological problems by satisfying the necessary condition, i.e. no emission g Allowed Excluded Allowed There is no excluded region in our model ! I would like to summarize this talk. We have introduced the Dirac neutrino into the UED model, and solved cosmological problems. By solving cosmological problems, allowed region figure changes.(言いながらボタン押す) As shown this figure, in our model, there is no excluded region. Smaller value of 1/R has a great advantage for collider experiments. For example, not only first KK particles but also second KK particles can be produced. And our idea is applicable to extended UED model [ Kakizaki, Matsumoto, Senami PRD74(2006) ] Our idea is applicable to extended UED model

Future work 1 m m + R 1/R ～ order N N N decay is impossible ! G 2 Mass of the KK right-handed neutrino m ～ n + order N (1) R 1/R N (0) N (1) (1) N decay is impossible ! G (1) stable, neutral, massive, weakly interaction Finally, I show the our future work. As seen above, the mass of the KK right-handed neutrino is given by this: The right-handed neutrino can not decay into the KK graviton LKP, since it is kinematically forbidden. As a result, the KK right-handed neutrino remains as a non-baryonic cold dark matter in the present universe. We are calculating the dark matter relic abundance in UED model including right-handed neutrino. Thank you very much. KK right handed neutrino can be dark matter ! We are calculating the dark matter relic abundance in UED model including right-handed neutrino

Appendix

Extra Dimension (UED) model ? 1 What is Universal Extra Dimension (UED) model ? 1 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 First, I summarize the Extra Dimension model, and Universal Extra dimension model, called UED model. Extra dimension models are one of the good candidate for the theory beyond the standard model. Because extra dimension models provide new views of various problems. Particularly, in this talk, this is an important point. LKP dark matter due to KK parity [ Servant, Tait NPB650(2003) ] etc.

Extra Dimension (UED) model ? 3 What is Universal Extra Dimension (UED) model ? 3 5th dimension momentum conservation 1 For S compactification P = n/R 5 1 R : S radius n : 0,1,2,…. KK number (= n) conservation at each vertex S 1 / orbifolding P = － P Z 5 5 2 KK-parity conservation y (0) y (1) Here, I show the fact that the Lightest Kaluza-Klein Particle is stable and can be dark matter. 5th dimension momentum is quantized by S^1 compactification, and the momentum conservation along the 5th dimension becomes KK number conservation. Furthermore the KK number conservation is reduced to KK parity conservation due to S^1/Z_2 orbifolding. Under this parity, particles with odd KK number have odd charge, while the others have even ones. Therefore such a process is allowed, while such a process is forbidden. 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

radiative correction 3 1 m = R d g g v /4 1/R + m + g v /4 g g v /4 Mass of the KK graviton (1) G R Mass matrix of the U(1) and SU(2) gauge boson d g g v /4 2 1/R + 2 m 2 + g v /4 2 2 ´ ´ (1) B g g v /4 2 + g v /4 1/R + 2 d m 2 2 2 ´ (1) W To determine the LKP, first, I consider the mass of the KK graviton. Since all interactions relevant to the KK graviton are suppressed by the Planck scale, radiative corrections to the KK graviton are negligible. Therefore the KK graviton mass is simply given by 1/R. Next, I consider the KK B boson mass. The mass of the KK B boson is obtained by diagonalizing this mass matrix. Where Λ is the cutoff scale of the UED model. z g 2 (3) g 2 39 ´ 1 ´ d m 2 － 2 2 = － ln( R ) L (1) B 2 4 2 6 16π R 2 2 16π R z g 2 (3) g 2 d m 2 5 15 (1) = － ＋ 2 2 ln( R ) L W 2 16π R 4 2 2 16π R 2 2 L : cut off scale v : vev of the Higgs field

g B Dependence of the ‘‘Weinberg’’ angle sin q ～ ～ [ Cheng, Matchev, Schmaltz (2002) ] Here I remark on mass matrix of the KK B boson. For KK particles the neutral gauge boson mixing angle is different from the standard model Weinberg angle. Because the compactification scale is much larger than electro-weak scale. So Weinberg angle in UED model is almost 0, and the photon eigenstate becomes approximately pure B boson state. Therefore we regard the KK B boson as the KK photon. sin q 2 ～ ～ 0 due to 1/R >> (EW scale) in the W mass matrix g B (1) ～ (1) ～

Connection between collider experiment and determination of the neutrino mass type In the case of UED model There will be no evidence of the extra dimension existence for 1/R < 800 GeV In the case of UED model with right-handed neutrino KK particles can be discovered at lower energy (≦ 800 GeV) Here I show the connection between collider experiment and determination of the neutrino mass type. In the case of UED model, at collider experiment there will be no evidence of the extra dimension existence for lower energy scale. Because, as seen above, lower energy scale UED model is forbidden by cosmological implication. However, in the case of UED model with right-handed neutrino, i.e. in the our model, KK particles can be discovered at lower energy. Thus by considering the fact, neutrino mass type can be indirectly determined as Dirac at collider experiment. Neutrino mass type can be indirectly determined as Dirac at collider experiment !!

radiative correction 2 KK B boson B Dark matter candidate KK graviton Important things : Colored KK particles are heavier than other KK particles The masses of U(1) gauge boson and right-handed leptons still remain ～n/R Furthermore we can see the important things. Particularly, for determining the LKP, it is important thing : the masses of U(1) gauge boson and right-handed leptons still remain about 1/R. In some of the LKP candidates, the KK B boson and the KK graviton are neutral particles. Thus these particles can be dark matter candidate. Where the KK B boson is the KK particle of the U(1) gauge boson, and the KK graviton is the KK particle of the graviton. The candidate for the neutral LKP KK B boson B (1) Dark matter candidate (1) KK graviton G

Cosmological problems has been solved by introducing the Dirac type mass neutrino As a result‥‥ Allowed Excluded By solving cosmological problems, allowed region figure changes.(言いながらボタン押す) As seen this figure, in our model, there is no excluded region. Smaller value of 1/R has a great advantage for collider experiments. For example, not only first KK particles but also second KK particles can be produced at the Large Hadron Collider. [ Kakizaki, Matsumoto, Senami PRD74(2006) ]

Extra Dimension (UED) model ? What is Universal Extra Dimension (UED) model ? S : 1 compactification on circle ψ(x , y) = ψ(x , y+2πR) μ μ Z : reflection symmetry under y 　　y － 2 y : extra dimension coordinate S 1 / Z compactification produces 2 chiral theory corresponding to the SM

+ Solving cosmological problems by introducing Dirac neutrino m 1 m + UED model small Dirac mass type neutrino We can extend the allowed region !! N : KK right handed neutrino (1) Once we introduce right-handed neutrinos in the UED model, their KK particles automatically appear in the spectrum. Since these particles are the standard model gauge singlet and have only small Yukawa interactions, radiative corrections to their masses are very small. Thus the mass of the KK right-handed neutrino is estimated as this: Mass of the KK right-handed neutrino m 1 2 m ～ n + order N (1) R 1/R