A Solution to the Li Problem by the Long Lived Stau
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A Solution to the Li Problem A Solution to the Li Problem by the Long Lived Stauby the Long Lived Stau
Masato YamanakaMasato YamanakaCollaborators Collaborators
Toshifumi Jittoh, Kazunori Kohri, Toshifumi Jittoh, Kazunori Kohri, Masafumi Koike, Joe Sato, Takashi ShimomuraMasafumi Koike, Joe Sato, Takashi Shimomura
7
Phys. Rev. D78 : 055007, 2008 and arXiv : 0904.××××Phys. Rev. D78 : 055007, 2008 and arXiv : 0904.××××
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Contents
1, Introduction
2, The small m scenario and long lived stau
3, Solving the Li problem by the long lived stau7
4, Relic density of stau at the BBN era
5, Summary
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Introduction
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[ B.D.Fields and S.Sarkar (2006) ]
Big Bang Nucleosynthesis (BBN) Yellow box
Observed light element abundances
[CMB] vertical bandCosmic baryon density obtained from WMAP data
Color lines Light element abundances as predicted by the standard BBN
Prediction of the light elements abundance
Primordial abundance obtained from observations
consistent !
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Li problem7
Theory
( 4.15 )×10+ 0.49- 0.45
- 10
A. Coc, et al., astrophys. J. 600, 544(2004)
Observation
( 1.26 )×10+ 0.29- 0.24
- 10
P. Bonifacio, et al., astro-ph/0610245
Predicted Li abundance ≠ observed Li abundance7 7
Li problem7
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Requirement for solving the Li problem7
Requirement for solving the Li problem
Able to destroy a nucleus
To occur at the BBN era
Not a Standard Model (SM) process
Possible to be realized in a framework of minimal supersymmetric standard model !
Stau ~Superpartner of tau lepton
Coupling with a hadronic current Coupling with a hadronic current
Able to survive still the BBN era Able to survive still the BBN era
Exotic processes are introducedExotic processes are introduced
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The small m scenario and long lived stau
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Setup
Minimal Supersymmetric Standard Model (MSSM) with R-parity
Lightest Supersymmetric Particle (LSP)Lightest neutralino ~
~ = N1 N3N2 N4B~
+ + +~W
~Hu
0 ~Hd
0
Next Lightest Supersymmetric Particle (NLSP)
Lighter stau ~~ = cos
~L~R+ sin e-i
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Dark matter and its relic abundance
http://map.gsfc.nasa.gov
Dark Matter (DM)
Neutral, stable (meta-stable), weak interaction, massive
Good candidate : LSP neutralino
DM relic abundance
DMh 2= 0.1099 ± 0.0062
m n× DMDM∝
mDM = (constant) 1nDM
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Naïve calculation of neutralino relic density
~
~
SM particle
SM particle
DM reduction process
Neutralino pair annihilation
Not enough to reduce the DM number density
[ PDG 2006 (J. Phys. G 33, 1 (2006)) ]
mDM = (constant) 1nDM
m ~ > 46 GeV
Not consistent !
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Coannihilation mechanism [ K. Griest and D. Seckel PRD43(1991) ]
~
~
SM particle
SM particle
DM reduction process
Neutralino pair annihilation
+
+ stau-neutralino coannihilation
~ SM particle
SM particle~
Requirement for the coannihilation to work
Possible to reduce DM number density efficiently !
mLSPmNLSP
mLSP
–<~ 10 %
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Attractive parameter region in coannihilation case
m ≡ NLSP mass ー LSP mass < tau mass (1.77GeV)
NLSP stau can not two body decay
Stau has a long Stau has a long lifetime due to phase lifetime due to phase space suppression !!space suppression !!
Long lived stau
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Stau lifetime
~~ survive until BBN era
BBN era
Stau provides additional processes to reduce the primordial Li abundance !!7
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7Solving the Li problem by the long lived stau
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Destruction of nuclei with free stau
~ ± A(Z)
A(Z±1)~
Interaction time scale (sec)
Negligible due toCancellation of destruction
Smallness of interaction rate
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Stau-nucleus bound state
nuclear radius~
・・ stau ・・nucleus
New processes
Key ingredient for solving the Li problemKey ingredient for solving the Li problem
Negative-charged stau can form a bound state with nuclei Negative-charged stau can form a bound state with nuclei
77
Formation rate
Solving the Boltzmann Eq.
Stau catalyzed fusion
Internal conversion in the bound state
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Stau catalyzed fusion
Nuclear fusionWeakened coulomb
barrier
・・ stau ・・nucleus
( ): bound state
[ M. Pospelov, PRL. 98 (2007) ]
Ineffective for reducing 7Li and 7Be
∵ stau can not weaken the barrieres of Li3+ and Be4+ sufficiently
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Constraint from stau catalyzed fusion
Standard BBN process Catalyzed BBN process
Constraint on stau life time
Catalyzed BBN cause over production of Li
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Internal conversion
Closeness between stau and nucleus
Overlap of the wave function : UPUPInteraction rate of hadronic current : UPUP
Hadronic current
~+ does not form a bound state
No cancellation processes
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The decay rate of the stau-nucleus bound state
IC | | 2・= ( ) v: The overlap of the wave functions
: Cross section × relative velocity
| | 2
( ) v
The bound state is in the S-state of a hydrogen-like atom
| | 2 =1
anucl3
Internal conversion rate
anucl = nuclear radius = 1.2 × A 1/3~
( ) v is evaluated by using ft-value
( ) v ∝ ( ft )– 1
7Be → 7Li ・・・ ft = 103.3 sec (experimental value)
ft-value of each processes
7Li → 7He ・・・ similar to 7Be → 7Li (no experimental value)
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Interaction rate of Internal conversionIn
tera
ctio
n ti
me
scal
e (s
)
Very short time scale
significant process for reducing Li abundance !significant process for reducing Li abundance !77
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Scattering with background particles
Internal conversion
Internal conversion
Be7 7Li
He7
He,4 He,3
proton, etcD, etc
~~ ,
~ ~ ,
New interaction chain reducing Li and BeNew interaction chain reducing Li and Be7 7
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Numerical result for solving the Li problem7
10.01 0.1Mass difference between stau and neutralino (GeV)
10
10
10
10
10
10
-16
-12
-13
-14
-15
-11
Y~
m = 300 GeVDM
Y~ ~ns
~n : number density of stau
s : entropy density
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Allowed region
100 - 120 MeV
(7 – 10) 10× -13
The Li problem is solved7
Strict constraint on m and Y~
m = (100 – 120) MeV Y~ = (7 – 10) 10× -13
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Allowed region
Produced Li are destructed by energetic proton
7
Internal conversion of occur when back ground protons are still energetic
Back ground particles are not energetic when Li are emitted 7
Produced Li are destructed by internal conversion
7
( Be)7~
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Over production of Lidue to stau catalyzed fusion
6
Forbidden region
Bound states are not formed sufficiently
Insufficient reduction
Overclosure of the universe
Stau decay before forming a bound state
• Lifetime of stau
• Formation time of
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Relic density of stau at the BBN era
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For the prediction of parameter point
Stau relic density at the BBN era
Not a free parameter !
Value which should be calculated from other parameters
For example
DM mass, mass difference between stau and neutralino, and so on
Calculating the stau relic density at the BBN era
We can predict the parameters more precisely, which provides the solution for the Li problem7
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The evolution of the number density
Boltzmann Eq. for neutralino and stau
i, j : stau and neutralino
X, Y : standard model particle
n (n ) : actual (equilibrium) number density
H : Hubble expansion rate
eq
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The evolution of the number density
Boltzmann Eq. for neutralino and stau
Annihilation and inverse annihilation processes
i j X Y
Sum of the number density of SUSY particles is controlled by the interaction rate of these processes
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The evolution of the number density
Boltzmann Eq. for neutralino and stau
Exchange processes by scattering off the cosmic thermal background
i X j Y
These processes leave the sum of the number density of SUSY particles and thermalize them
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The evolution of the number density
Boltzmann Eq. for neutralino and stau
Decay and inverse decay processes
i j Y
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Can we simplify the Boltzmann Eq. with ordinal method ?
In the calculation of LSP relic density
All of Boltzmann Eq. are summed up
Single Boltzmann Eq. for LSP DM
Absence of exchange terms ( cancel out )
∴
In the calculation of relic density of long lived stau
( all of SUSY particles decay into LSP )
∴
Obviously we can not use the method !
We are interesting to relic density of NLSP
We must solve numerically a coupled set of differential Eq. for stau and neutralino
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Significant process for stau relic density calculation
Due to the Boltzmann factor, n i n j n X n Y, ,<<
Annihilation process
Exchange process
Annihilation process rate << exchange process rate
Boltzmann Eq. for neutralino and stau
≠Freeze out temperature of sum of number density of SUSY particles
Freeze out temperature of number density ratio of stau and neutralino
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Exchange process
~ ~ ~ ~
( DM mass 100 GeV - 1000 GeV )
DM freeze out temperature
TDM ~ mDM 205 GeV - 50 GeV
Exchange process for NLSP stau and LSP neutralino
After DM freeze out, number density ratio is still varying
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Boltzmann Eq. for the number density of stau and neutralino
Numerical calculation
Y n si i
s : entropy densityn : number density of particle ii
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Numerical result (prototype)
Tau decoupling temperature (MeV)
Mass difference between tau and neutralino (MeV)Ratio of stau relic density and current DM density
Significant temperature for the calculation of stau number density
Tau decoupling temperature
Freeze out temperature of exchange processes・・
6060 80 80
50 50100 100
15 % 3 % 8 % 1.5 %
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Tau decoupling temperature
Condition ( tau is in thermal bath )
[ Production rate ] > [ decay rate, Hubble expansion rate ]
Production processes of tau
l l
q q
Tau decoupling temperature
~ 120 MeV
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Summary
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We investigated solution of the Li problem in the MSSM, in which the LSP is lightest neutralino and the NLSP is lighter stau
Long lived stau can form a bound state with nucleus and provides new processes for reducing Li abundance
Stau-catalyzed fusionStau-catalyzed fusionInternal conversion processInternal conversion process
We obtained strict constraint on the mass difference between stau and neutralino, and the yield value of stau
Stau relic density at the BBN era strongly depends on the tau decoupling temperature and mass difference between stau and neutralino
Our goal is to predict the parameter point precisely by calculating the stau relic density and nucleosynthesis including new processes
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Appendix
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mixing angle between and
CP violating phase
Weak coupling
Weinberg angle
Effective Lagrangian
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Bound ratio
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Red : consistent region with DM abundance and mass difference < tau mass
Yellow : consistent region with DM abundance and mass difference > tau mass
The favored regions of the muon anomalous magnetic moment at 1, 23confidence level are indicated by solid lines