Masato Yamanaka (Saitama University)

Masato Yamanaka (Saitama University)

collaborators

Shigeki Matsumoto Joe Sato Masato Senami

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

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 modelsDetermination of UED model parameter

http://map.gsfc.nasa.gov/






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

5. Summary

4. Numerical result

What is UniversalExtra Dimension (UED) model ?


5-dimensions

Extra dimension is compactified on an S /Z orbifold1 2

all SM particles propagate spatial extra dimension

(time 1 + space 4)

R

4 dimension spacetime

S1

Feature of UED models

Interaction rule same as SM


Periodic condition of S manifold1

(1)

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

Kaluza-Klein (KK) particle

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

m : corresponding SM particle mass2SM

1/2SM

2

m : radiative correction

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

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 ?

1/R >> m SM

degeneration of KK particle masses

Origin of mass difference

Radiative correction

For 1/R < 800 GeV～For 1/R > 800 GeV～

NLKP : (1)

NLKP : G (1)

NLKP : Next Lightest Kaluza-Klein Particle

LKP : G (1)

LKP : (1)LKP :

m = m (1) m G(1)－

Mass difference between the KK graviton and the KK photon

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 !!

Problem 2 Case : LKP NLKP (1)G (1)

KK number conservation and kinematics

Possible decay mode(1)(1) G (1)

high energy SM photon emission

It is forbidden by the observation !

Late time decay due to gravitational interaction


Case : LKP NLKP(1)

G

(1)

[ Feng, Rajaraman, Takayama PRD68(2003) ]

(1)G (1) Same problem due to the late time decay

G (1)

Constraining the reheating temperature, we can avoid the problem


Solving the problems by introducing the right-handed neutrino

To solve the problems

Introducing the right-handed neutrino N

Dirac type with tiny Yukawa couplingMass type

Lagrangian = y N L + h.c.

m N(1)

R1

+ 1/Rm 2～ order

Mass of the KK right-handed neutrino

Lightest KK Particle

Next Lightest KK particle

G (1)KK graviton

KK photon (1)

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)

Introducing the right-handed neutrino

Solving the problems by introducing the right-handed neutrino

（ 1） N

(1)

Appearance of the new decay（1）

（1）

N(1)

N(1)

（1）

（1）

W

G(1)

(1)

Fermion mass term ( (yukawa coupling) (vev) )～・

（1）

Many decay mode in our model

Dominant decay mode from (1)

Dominant photon emission decay mode from (1)

Branching ratio of the decay（ 1）

= ( )(1) (1)

( )（ 1）

(1) = － 75 × 10

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

Decay rate of dominantphoton emission decay

Decay rate of new decay mode

G

N

Serious problems in UED model and solving the problems

Introducing the right-handed neutrino

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


Possible N decay from the view

point of KK parity conservation

G (1)N

(1) N

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

m G> m> m (1)N (1)(1)Mass relation

(1)

stable, neutral, massive,weakly interaction

KK right handed neutrino

can be 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)

G(1) : Produced from decay(1)

N (1) (1): Produced from decay and from thermal bath

Additional contribution to relic abundance


timeKK photon decouple from thermal bath

Relic number density of KK photon at this time constant

KK photon decay into KK right-handed neutrino (or KK graviton)

KK right-handed neutrino production from thermal bath

N (1) number density from decay (our model)

(1) = G (1) number density from

decay (previous model)

(1)

Total DM number density

DM mass ( ～ 1/R )

We must re-evaluate the DM number density !


h ～ (number density) × (DM mass)～ constant

2DM

N production processes in thermal bath(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)N(n) N(n)

t

x

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

(yukawa coupling) (vev) = 0 ～・

N must be produced through the coupling with KK Higgs (n)


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

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 ]


KK Higgs boson mass

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

2 2h t2 2 T2

12(n)(n) ・・

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

N must be produced through the coupling with KK Higgs (n)

a(T)[ x(T) ] : Higgs [top quark] particle number contributing to thermal correction loop


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 production processes in thermal bath(n)


Dominant N production process

(n)

Numerical result

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)

Neutrino mass dependence of the DM relic abundance

UED model withright-handed neutrino

UED model withoutright-handed neutrino

Allowed parameter region changed much !!

[ Kakizaki, Matsumoto, Senami PRD74(2006) ]

Excluded

Summary

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


Hierarchy problem

Candidate for the theory beyond the standard model

Large extra dimensions [ Arkani-hamed, Dimopoulos, Dvali PLB429(1998) ]

Warped extra dimensions [ Randall, Sundrum PRL83(1999) ]

Extra dimension model

Existence of dark matter

etc.

LKP dark matter due to KK parity [ Servant, Tait NPB650(2003) ]


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

5-dimensional kinetic term

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

m : corresponding SM particle mass2SM

1/2

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)

Thermal bath

（ 1）

decoupleG（ 1

）decay

early universe

High energy photon

～M

2planck

m3（ 1） G（ 1

）

decays after the recombination（ 1）


Allowed

[ Kakizaki, Matsumoto, Senami PRD74(2006) ]

Excluded

Allowed region in UED models

Because of triviality bound on the Higgs mass term, larger Higgs mass is disfavored

In collider experiment, smaller extra dimension scale is favored

We investigated :

『 The excluded region is truly excluded ? 』

= 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) ]

Total injection photon energy from decay(1)

Br( )(1) Y (1) < 3 × 10 － 18GeV

500GeV

2

m0.1 eV 2 m

1 GeV1 / R

0.10DM h22

×

The successful BBN and CMB scenarios are not disturbed unless this value exceeds 10 - 10 GeV－ 9 － 13

[ Feng, Rajaraman, Takayama (2003) ]

: typical energy of emitted photon

Y (1) : number density of the KK photon normalized by that of background photons

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）

We expand the thermal correction for UED model

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


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

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) ]

Reheating temperature dependence of relic density from thermal bath

Dotted line : N abundance produced directly from thermal bath

(1)

Dashed line :N abundance produced indirectly from higher mode KK right-handed neutrino decay

(1)

Determination of relic abundance and 1/R

We can constraint the reheating temperature !!

Masato Yamanaka (Saitama University)

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