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 Phys.Rev.D76:043528,2007

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 Solving the problems in UED models Calculation of dark matter relic abundance

What is Universal Extra Dimension (UED) model ? R (time 1 + space 4) 5-dimensions 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

Problems in Universal Extra Dimension (UED) model 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 !!

Problems in Universal Extra Dimension (UED) model 2 (1) G Lightest KK Particle KK graviton g (1) Next Lightest KK particle KK photon 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) Dark matter production Late time decay due to gravitational interaction g g (1) (1) G high energy SM photon emission It is forbidden by the observation !

Solving the 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 Dirac type with tiny Yukawa coupling Mass type (1) G Lightest KK Particle KK graviton KK right-handedneutrino Next Lightest KK particle (1) N Next to Next Lightest KK particle g (1) KK photon

Solving the problems g g (1) N n （1） New decay mode of : （1） g （1） Branching ratio of the decay g g (1) G （1） ( G ) g －7 （1） 5 × 10 = Br( ) = g n (1) (1) ( N ) G Neutrino masses are introduced into UED models, and problematic high energy photon emission is highly suppressed !!

Change of dark matter N (1) decay allowed by KK parity stable, neutral, massive,weakly interaction (1) N N (1) G KK right handed neutrino can be dark matter ! Forbidden by kinematics m + m < m (0) (1) (1) N G N Before introducing the neutrino mass into UED models (1) G Dark matter KK graviton After introducing the neutrino mass into UED models (1) N Dark matter KK right-handed neutrino

(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 (n) N production needs processes including KK Higgs

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) ) ～・

[ Kakizaki, Matsumoto, Senami PRD74(2006) ] Allowed parameter region changed much !! 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 UED models (absence of the neutrino mass, forbidden energetic photon emission) by introducing the right-handed neutrino 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.

Appendix

KK parity 5th dimension momentum conservation Quantization of momentum by compactification 1 P = n/R R : S radius n : 0, 1, 2,…. 5 KK number (= n) conservation at each vertex t KK-parity conservation y (0) (1) y 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 [ 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 ～～

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.

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) ]

< 1 ｰ f > (m) (m) F F L Relic abundance calculation Boltzmann equation S (n) (n) C dg (T) dY T s (m) * m 1 + = sTH 3g (T) dT dT s * 3 d k (n) g (n) G C = 4 g N f n (m) (m) (2p) 3 F = 1 The normal hierarchy g n = 2 The inverted hierarchy = 3 The degenerate hierarchy s, H, g , f : entropy density, Hubble parameter, relativistic degree of freedom, distribution function s * (n) (n) Y = ( number density of N ) ( entropy density )

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) ]

Masato Yamanaka (Saitama University)