Masato Yamanaka (Saitama University)
description
Transcript of 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
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 ?
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
What is UniversalExtra Dimension (UED) model ?
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
Serious problems in UED models
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
Serious problems in UED models
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
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 !
KK right-handed neutrino dark matter and relic abundance calculation of that
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
KK right-handed neutrino dark matter and relic abundance calculation of that
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 !
KK right-handed neutrino dark matter and relic abundance calculation of that
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
KK right-handed neutrino dark matter and relic abundance calculation of that
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)
KK right-handed neutrino dark matter and relic abundance calculation of that
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 right-handed neutrino dark matter and relic abundance calculation of that
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
KK right-handed neutrino dark matter and relic abundance calculation of that
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)
KK right-handed neutrino dark matter and relic abundance calculation of that
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
What is UniversalExtra Dimension (UED) model ?
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) ]
What is UniversalExtra Dimension (UED) model ?
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)
Serious problems in UED models
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
KK right-handed neutrino dark matter and relic abundance calculation of that
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 !!