Masato Yamanaka (Saitama University)

Relic abundance of dark matter in universal extra dimension models with right-handed neutrinos Masato Yamanaka (Saitama University) collaborators Shigeki Matsumoto Joe Sato Masato Senami Phys.Lett.B647:466-471 and arXiv:0705.0934[hep-ph] (To appear in PRD)

Introduction What is dark matter ? Is there beyond the Standard Model ? http://map.gsfc.nasa.gov Supersymmetric model Little Higgs model Universal Extra Dimension model (UED model) Appelquist, Cheng, Dobrescu PRD67 (2000) Contents of today’s talk (1) Construction of problemless UED model (2) Calculation of dark matter relic abundance

What is Universal Extra Dimension (UED) model ? (time 1 + space 4) 5-dimensions R 1 S all SM particles propagatespatial extra dimension 4 dimension spacetime compactified on an S /Z orbifold 1 2 Y Y (1) Y (2) Y (n) , , ‥‥, Standard model particle KK particle 1/2 2 2 KK particle mass : m = ( n /R + m + dm ) (n) 2 2 SM 2 m : corresponding SM particle mass SM dm : radiative correction

KK parity Dark matter candidate & Who is dark matter ? 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) Possible NLKP decay NLKP LKP + SM particle NLKP : Next Lightest Kaluza-Klein Particle g (1) (1) G LKP : NLKP : For 1/R < 800 GeV ～ g (1) (1) G For 1/R > 800 GeV LKP : LKP : NLKP : ～

It is forbidden by the observation ! Problems in Universal Extra Dimension (UED) model (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 Excluded Allowed [ Kakizaki, Matsumoto, Senami PRD74(2006) ]

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

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

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

(1) (1) When dark matter changes from G to N , what happens ? (1) : Almost produced from g decay G (1) : Produced from g decay and from thermal bath (1) (1) N Additional contribution to relic abundance Total DM number density DM mass ( ～ 1/R ) We must re-evaluate the DM number density !

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

N (n) Production process (n) In thermal bath, there are many N production processes (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) ) ～・

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

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

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

(n) Dominant N production process N (n) Production process (n) In thermal bath, there are many N production processes (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) ) ～・

Allowed parameter region changed much !! Excluded UED model withoutright-handed neutrino UED model withright-handed neutrino

Produced from g decay + from the thermal bath (1) Produced from g decay (m = 0) (1) n 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

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.

Appendix

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

KK parity 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 / P = P S 1 orbifolding － Z 5 5 2 KK-parity conservation y (0) (1) y n = 0,2,4,… y ＋1 (1) y (3) n = 1,3,5,… －1 (2) (0) At each vertex the product of the KK parity is conserved φ φ

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

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

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

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

Thermal correction 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 fermionsand 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) ]

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) ]

h W 2 N 1/R = 600 GeV m = 120 GeV h m = 0.66 eV n degenerate case reheating temperature (1/R) (n) N abundance depends on the reheating temperature If we know 1/R and m , we can get the constraint for the reheating temperature n

Dominant decay mode from (1) g (1) Dominant photon emission decay mode from G (1) (1) g Solving cosmological problemsby introducing Dirac neutrino g We investigated some decay mode (1) g (1) h (1) N N (1) (1) g g (1) l W l n g n g g g etc.

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

Masato Yamanaka (Saitama University)