Masato Yamanaka (Saitama University)

collaborators

Shigeki Matsumoto Joe Sato Masato Senami

Phys.Rev.D76:043528,2007Phys.Lett.B647:466-471 and

Relic abundance of dark matter in universal extra dimension models

with right-handed neutrinos

Introduction

What is dark matter ?

http://map.gsfc.nasa.govSupersymmetric modelLittle Higgs model

Is there beyond the Standard Model ?

Universal Extra Dimension model (UED model) Appelquist, Cheng, Dobrescu PRD67 (2000)

Contents of today’s talk

Solving the problems in UED modelsCalculation of dark matter relic abundance

What is Universal

5-dimensions

compactified on an S /Z orbifold1 2

all SM particles propagatespatial extra dimension

(time 1 + space 4)

Extra Dimension (UED) model ?

R

4 dimension spacetime

S1

(1)

Standard model particle (2), , ,‥‥ (n)

KK particle

KK particle mass : m = ( n /R + m + m )(n) 222

m : corresponding SM particle mass2SM

1/2SM

2

m : 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

Lightest KK Particle

Next Lightest KK particle

G (1)KK graviton

KK photon (1)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(1) G (1)

high energy SM photon emission

It is forbidden by the observation !

Late time decay due to gravitational interaction

Solving the problems

Introducing the right-handed neutrino N

m N(1)

R1

+ 1/Rm 2

～ orderThe mass of the KK

right-handed neutrino N(1)

Dirac type with tiny Yukawa couplingMass type

Lightest KK Particle

Next to Next Lightest KK particle

G (1)KK graviton

KK photon (1)

Next Lightest KK particle KK right-handedneutrino N

(1)

Solving the problems

Branching ratio of the decay（ 1）

Br( )（ 1） =

( N )(1) (1)

( G )（ 1）

(1) = － 75 × 10

New decay mode of :（ 1）

（ 1）

N

(1)

Neutrino masses are introduced into UED models, and problematic high energy photon emission is highly suppressed !!

stable, neutral, massive,weakly interaction

KK right handed neutrino can be dark matter !

Change of dark matter

After introducing the neutrino mass into UED models

Before introducing the neutrino mass into UED models

Dark matter KK graviton

Dark matter KK right-handed neutrino N

(1)

G(1)

decay allowed by KK parityN (1)

G (1)N

(1) N

m N(1) m + mG(1) (0)N<Forbidden by kinematics

G(1) : Almost produced from decay(1)

N (1) (1)

When dark matter changes from G to N , what happens ?

(1)(1)

: Produced from decay and from thermal bath

Additional contribution to relic abundance

Total DM number density

DM mass ( ～ 1/R )

We must re-evaluate the DM number density !

1 From decoupled decay (1) (1) N(1)

2 From thermal bath (directly)

Thermal bath（ 1）N

3 From thermal bath (indirectly)

Thermal bath（ n）N

Cascade

decay

（ 1）N

（ 1）N

Production processes of new dark matter N（ 1）

N(n) Production process

In thermal bath, there are many N production processes(n)

N(n)N(n) N(n)N(n) N(n)

KK Higgs boson

KK gauge bosonKK fermionFermion mass term ( (yukawa coupling) (vev) )～ ・

t

x

N(n) Production process

N(n)N(n) N(n)

t

x

In the early universe ( T > 200GeV ), vacuum expectation value = 0

(yukawa coupling) (vev) = 0 ～ ・

N production needs processes including KK Higgs(n)

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 ]

2m (T)Any particle mass = 2m (T=0) + m (T)2

m (T) ～ m ・ exp[ ｰm / T ]

loop For m > 2Tloop

m (T) ～ T

For m < 2Tloop

m loop : mass of particle contributing to the thermal correction

Thermal correction

KK Higgs boson mass

m (T) = m (T=0) + [ a(T) 3+x(T)3y ]

2 2h t2 2 T2

12(n)(n) ・・

x(T) = 2[2RT] + 1

[ ] : Gauss' notation‥‥

a(T) = m=0

∞θ 4T － m R

ｰ22 2 [ a(T) 3+x(T)3y

]h t2 2・・ T2

12

T : temperature of the universe : quartic coupling of the Higgs bosony : top yukawa coupling

N(n) Production process

In thermal bath, there are many N production processes(n)

N(n)N(n) N(n)N(n)

N(n)

KK Higgs boson

KK gauge bosonKK fermionFermion mass term ( (yukawa coupling) (vev) )～ ・

t

x

Dominant N production process

(n)

UED model withright-handed neutrino

UED model withoutright-handed neutrino

Allowed parameter region changed much !!

[ Kakizaki, Matsumoto, Senami PRD74(2006) ]

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

Produced from decay (m = 0)

(1)

Produced from decay + from the thermal bath

(1)

Summary

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.

We have solved two problems in UED models (absence of the neutrino mass, forbidden energetic photon emission) by introducing the right-handed neutrino

Appendix

KK parity

(3)

(1)

φ (2)

(1)

(0)

(0)

φ

5th dimension momentum conservationQuantization of momentum by compactification

P = n/R5 R : S radius n : 0, 1, 2,….1

KK number (= n) conservation at each vertex

KK-parity conservation

n = 0,2,4,… ＋ 1n = 1,3,5,… － 1

At each vertex the product of the KK parity is conserved

t

m = R1

G(1)Mass of the KK graviton

Mass matrix of the U(1) and SU(2) gauge boson

: cut off scale v : vev of the Higgs field

Radiative correction[ Cheng, Matchev, Schmaltz PRD66 (2002) ]

Dependence of the ‘‘Weinberg’’ angle

[ Cheng, Matchev, Schmaltz (2002) ]

sin 2W～～ 0 due to 1/R >> (EW scale) in the

mass matrix

～～B(1) (1)

Solving cosmological problemsby introducing Dirac neutrino

We investigated some decay mode(1)

(1)N(1)

(1)

G(1)

(1)N(1)h(1)

llW

etc.

Dominant decay mode from (1)

Dominant photon emission decay mode from (1)

= 2×10 [sec ]－ 9 － 1 500GeV

（ 1）

m3 m

10 eV－ 2

2 m1 GeV

2

m = mN（ 1 ）m － m : SM neutrino mass（ 1 ）

Decay rate for （ 1） N（ 1

）

Solving cosmological problemsby introducing Dirac neutrino

(1)

N (1)

= 10 [sec ]－ 15 － 1

3

1 GeVm´

m = m － m(1) G(1)

Decay rate for （ 1） G（ 1

）

(1)

G(1)

Solving cosmological problemsby introducing Dirac neutrino

[ Feng, Rajaraman, Takayama PRD68(2003) ]

We expand the thermal correction for UED model

Thermal correction

We neglect the thermal correction to fermionsand to the Higgs boson from gauge bosons

Gauge bosons decouple from the thermal bath at once due to thermal correction

Higgs bosons in the loop diagrams receive thermal correctionIn order to evaluate the mass correction correctly,

we employ the resummation method[P. Arnold and O. Espinosa (1993) ]

The number of the particles contributing to the thermal mass is determined by the number of the particle lighter than 2T

Boltzmann equation

dTdY

(n)

=s T Hm

C(m)(n)

1 +dT

dg (T)*s

3g (T)s*

T

C(m)(n)

= 4 g (2)3d k3 (m)

(m)N(n)

f(m)< 1 ｰ f >

L

s, H, g , f : entropy density, Hubble parameter, relativistic degree of freedom, distribution function

*s

Relic abundance calculation

g= 3= 2= 1 The normal hierarchy

The inverted hierarchyThe degenerate hierarchy

Y(n) = ( number density of N ) ( entropy density )(n)

Result and discussion

N abundance from Higgs decay depend on the y (m )(n)

Degenerate case

m = 2.0 eV

[ K. Ichikawa, M.Fukugita and M. Kawasaki (2005) ]

[ M. Fukugita, K. Ichikawa, M. Kawasaki and O. Lahav (2006) ]