1. (Tokyo university, ICRR)
Solving the Li problem by long lived stau in a stau-neutralino coannihilation scenario
Masato Yamanaka
(Tokyo university, ICRR)
Collaborators
Toshifumi Jittoh, Kazunori Kohri, Masafumi Koike, Joe Sato, Takashi Shimomura
Phys. Rev. D78 : , 2008

2. Li problem 7 Theoretical prediction ( 4.15 )×10 Observation
( )×10
＋0.49
－10
－0.45
A. Coc, et al., astrophys. J. 600, 544(2004)
Observation
( )×10
＋0.29
－10
－0.24
P. Bonifacio, et al., astro-ph/
Predicted Li abundance ≠ observed Li abundance 7 7 7
Li problem
Purpose
Soving the Li problem in a framework of Minimal Supersymmeteric Standard Model (MSSM) 7

3. Neutralino dark matter and Coannihilation scenario
Setup
Lightest Supersymmetric Particle (LSP)
Neutralino
Dark matter R-parity conservation ∴
Next Lightest Supersymmetric Particle (NLSP)
Stau
DM abundance and Connihilation
Coannihilation mechanism predicts observed DM abundance
Requirement for the coannihilation to work

4. Long lived stau Attractive parameter region in coannihilation scenario
dm ≡ NLSP mass － LSP mass < tau mass
(1.77GeV)
NLSP stau can not two body decay
Stau has a long lifetime due to phase space suppression !!

5. t BBN era Stau lifetime survive until BBN era～ t
survive until BBN era
Stau provides additional processes to reduce the primordial Li abundance !! 7

6. Stau-nucleus bound state
Key ingredient for solving the Li problem 7
Negative-charged stau can form a bound state with nuclei ~
nuclear radius
Formation rate
Solving the Boltzmann Eq.
･･ stau ･･ nucleus
New processes
Stau catalyzed fusion
Internal conversion in the bound state

7. Weakened coulomb barrier
Stau catalyzed fusion
[ M. Pospelov, PRL. 98 (2007) ]
･･ stau ･･ nucleus
Weakened coulomb barrier
Nuclear fusion
( ): bound state
Ineffective for reducing 7Li and 7Be
∵ stau can not weaken the barrieres of Li3+ and Be4+ sufficiently

8. UP UP Internal conversion t Hadronic current
Closeness between stau and nucleus UP
Overlap of the wave function : UP
Interaction rate of hadronic current : t ~ +
does not form a bound state
No cancellation processes

9. Interaction rate of Internal conversion
Lifetime of bound state (s) 1 10 4 10 －1 2 10 10 －2 1 10 －3 －2 10 10 －4 －4 10 10 －5 －6 10 －6 10
0.01
0.1 1
0.01
0.1 1 d
m(GeV) d
m(GeV)
Rapid interaction
significant process for reducing Li abundance ! 7

10. Numerical result for solving the Li problem7
-11 10
Allowed region as a function of stau relic density and mass difference 10
-12
-13 10
-14 10
-15 10
Allowed region
Consistent with all the observational abundance of light-elements
0.01
0.1 1

11. Allowed region and prediction
-12 10
-13 10
-14 10
-13
(7 – 10) 10 ×
-15 10
MeV
Strict constraint on m and d Y ~ t

12. Insufficient reduction
Forbidden region
Overclosure of the universe
-12 10
-13 10
Stau decays before forming a bound state
-14
Lifetime of stau　
Formation time 10
-15 10
Bound states are not formed sufficiently
Over production of Li due to stau catalyzed fusion 6
Insufficient reduction

13. Summary Stau-catalyzed fusion Internal conversion process
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 fusion
Internal conversion process
We obtained strict constraint on the mass difference between stau and neutralino, and the yield value of stau

14. Appendix

15. Convention and Lagrangian
mixing angle between 　 and
CP violating phase
Weak coupling
Weinberg angle

16. Naïve calculation of neutralino DM abundance
DM reduction process without coannihilation processes ～ c
SM particle
Cross section is too weak to reduce the number density of neutralino DM ～ c
SM particle
Neutralino pair annihilation 1 m =
(constant) DM n DM
Observed DM abundance
Not consistent ! m c ～
> 46 GeV
[ PDG (J. Phys. G 33, 1 (2006)) ]

17. Destruction of nuclei with free stau～ c n t
A(Z±1)
Negligible due to
Cancellation of destruction
Smallness of interaction rate
Interaction time scale (sec) ～ t
A(Z)

18. Bound ratio

19. Constraint from stau catalyzed fusion
Standard BBN process
Catalyzed BBN process
Catalyzed BBN cause over production of Li
Constraint on stau life time

20. Internal conversion rate
The lifetime of the stau-nucleus bound state
The bound state is in the S-state of a hydrogen-like atom
nuclear radius
( ) s v
is evaluated by using
ft-value
ft-value of each processes
7Be → 7Li ・･･ ft = sec (experimental value)
7Li → 7He ･･･ similar to 7Be → 7Li (no experimental value)

21. Scattering with background particles
New interaction chain reducing Li and Be 7 7
Internal conversion 7 He
Internal conversion ～ ～ t c , n t 7 Be 7 Li
Scattering with background particles ～ ～ t c n , t 4
He, 3
He,
D, etc
proton, etc