Masato Yamanaka (Saitama University)

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 Determination of UED model parameter

Outline 1. What is Universal Extra Dimension model ? 2. Serious problems in UED model and solving the problems 3. KK right-handed neutrino dark matter and relic abundance calculation of that 4. Numerical result 5. Summary

What is Universal Extra Dimension (UED) model ?

What is Universal Extra Dimension (UED) model ? Feature of UED models (time 1 + space 4) 5-dimensions Extra dimension is compactified on an S /Z orbifold R 1 S 1 2 4 dimension spacetime all SM particles propagate spatial extra dimension Interaction rule same as SM

What is Universal Extra Dimension (UED) model ? 1 Periodic condition of S manifold (1) (2) (n) Y Y Y Y , , ‥‥, Standard model particle Kaluza-Klein (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 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

Dark matter candidate KK parity conservation Stabilization of Lightest Kaluza-Klein Particle (LKP) ! (c.f. R-parity and the LSP in SUSY) If it is neutral, massive, and weak interaction LKP Dark matter candidate Who is dark matter ?

m m = d m － (1) (1) g G 1/R >> m SM degeneration of KK particle masses Origin of mass difference Radiative correction Mass difference between the KK graviton and the KK photon g (1) (1) G LKP : NLKP : For 1/R < 800 GeV ～ g (1) (1) G For 1/R > 800 GeV LKP : LKP : NLKP : ～ NLKP : Next Lightest Kaluza-Klein Particle

Serious problems in UED model and solving the problems

Serious problems in UED models Problem 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 !!

Serious problems in UED models g (1) (1) G Problem 2 Case : LKP NLKP KK number conservation and kinematics g (1) Possible decay mode g g (1) (1) G Late time decay due to gravitational interaction high energy SM photon emission It is forbidden by the observation !

Serious problems in UED models g (1) (1) G Case : LKP NLKP (1) G Same problem due to the late time decay g g (1) (1) G Constraining the reheating temperature, we can avoid the problem [ Feng, Rajaraman, Takayama PRD68(2003) ]

Solving the problems by introducing the right-handed neutrino To solve the problems Introducing the right-handed neutrino N Dirac type with tiny Yukawa coupling Mass type Lagrangian = y N L F + h.c. n m 2 1 Mass of the KK right-handed neutrino n ～ m + order (1) N R 1/R

Solving the problems by introducing the right-handed neutrino (1) G Lightest KK Particle KK graviton g Next Lightest KK particle (1) KK photon Introducing the right-handed neutrino (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

g Dominant decay mode from (1) g Dominant photon emission decay mode from (1) g （1） Appearance of the new decay g n (1) （1） N g （1） Many decay mode in our model (1) N g （1） (1) F N (1) g （1） W n g n G (1) g （1） g Fermion mass term ( (yukawa coupling) (vev) ) ・～

Serious problems in UED model and solving the problems g （1） Branching ratio of the decay Decay rate of dominantphoton emission decay g g (1) G G （1） ( ) －7 5 × 10 = = (1) G g ( ) n (1) Decay rate of new decay mode N Introducing the right-handed neutrino Neutrino masses are introduced , and problematic high energy photon emission is highly suppressed !!

KK right-handed neutrino dark matter and relic abundance calculation of that

Forbidden by kinematics m + m < m (0) (1) (1) N G N KK right-handed neutrino dark matter and relic abundance calculation of that m > m > m Mass relation (1) g (1) N (1) G (1) Possible N decay from the view point of KK parity conservation stable, neutral, massive,weakly interaction (1) (1) N N G KK right handed neutrino can be dark matter !

KK right-handed neutrino dark matter and relic abundance calculation of that Before introducing the neutrino mass into UED models (1) G Dark matter KK graviton (1) : Produced from g decay G (1) After introducing the neutrino mass into UED models (1) N Dark matter KK right-handed neutrino : Produced from g decay and from thermal bath (1) (1) N Additional contribution to relic abundance

KK right-handed neutrino dark matter and relic abundance calculation of that KK photon decay into KK right-handed neutrino (or KK graviton) KK right-handed neutrino production from thermal bath time KK photon decouple from thermal bath Relic number density of KK photon at this time constant (1) (1) G N = number density from decay (our model) number density from decay (previous model) g g (1) (1)

KK right-handed neutrino dark matter and relic abundance calculation of that W h～ (number density) × (DM mass) 2 DM ～ constant Total DM number density DM mass ( ～ 1/R ) We must re-evaluate the DM number density !

KK right-handed neutrino dark matter and relic abundance calculation of that (n) Nproduction processes in thermal bath (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 KK right-handed neutrino dark matter and relic abundance calculation of that In the early universe ( T > 200GeV ), vacuum expectation value = 0 (yukawa coupling) (vev) = 0 ～・ (n) N (n) N t x (n) N must be produced through the coupling with KK Higgs

KK right-handed neutrino dark matter and relic abundance calculation of that 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 KK right-handed neutrino dark matter and relic abundance calculation of that (n) N must be produced through the coupling with KK Higgs 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 a(T)[ x(T) ] : Higgs [top quark] particle number contributing to thermal correction loop

(n) Dominant N production process KK right-handed neutrino dark matter and relic abundance calculation of that (n) Nproduction processes in thermal bath (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) ) ～・

Numerical result

Produced from g decay + from the thermal bath (1) Produced from g decay (m = 0) (1) n Neutrino mass dependence of the DM relic abundance In ILC experiment, can be produced !! n=2 KK particle It is very important for discriminating UED from SUSY at collider experiment

[ Kakizaki, Matsumoto, Senami PRD74(2006) ] Allowed parameter region changed much !! Excluded UED model withoutright-handed neutrino UED model withright-handed neutrino

Summary

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

What is Universal Extra Dimension (UED) model ? 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 LKP dark matter due to KK parity [ Servant, Tait NPB650(2003) ] etc.

What is Universal Extra Dimension (UED) model ? 5-dimensional kinetic term 1/2 (n) 2 2 Tree level KK particle mass : m = ( n /R + m ) 2 SM 2 m : corresponding SM particle mass SM Since 1/R >> m , all KK particle masses are highly degenerated around n/R SM Mass differences among KK particles dominantly come from radiative corrections

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 ～～

Serious problems in UED models decouple （1） G g （1） decay Thermal bath g early universe High energy photon dm 3 G ( ) g g ～（1）（1） G 2 M planck g （1） decays after the recombination

Excluded Allowed Allowed region in UED models [ Kakizaki, Matsumoto, Senami PRD74(2006) ] Because of triviality bound on the Higgs mass term, larger Higgs mass is disfavored We investigated : 『 The excluded region is truly excluded ? 』 In collider experiment, smaller extra dimension scale is favored

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)

g (1) Total injection photon energy from decay －18 g e (1) Y < 3 × 10 Br( ) g GeV (1) 2 2 2 W 0.1 eV h 2 m d 1 / R DM × m 500GeV 1 GeV 0.10 n e : typical energy of emitted photon Y g : number density of the KK photon normalized by that of background photons (1) The successful BBN and CMB scenarios are not disturbed unless this value exceeds 10 - 10 GeV －9 －13 [ Feng, Rajaraman, Takayama (2003) ]

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）

KK right-handed neutrino dark matter and relic abundance calculation of that 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) ]

(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

< 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) ]

Dotted line : (1) N abundance produced directly from thermal bath Dashed line : (1) N abundance produced indirectly from higher mode KK right-handed neutrino decay Reheating temperature dependence of relic density from thermal bath Determination of relic abundance and 1/R We can constraint the reheating temperature !!

Masato Yamanaka (Saitama University)