Possible Solution to the Li Problem by the Long-Lived Stau

1. Possible solution to the Li problem by the long lived stau 7 Masato Yamanaka ( Saitama University ) collaborators Toshifumi Jittoh, Kazunori Kohri, Masafumi Koike, Joe Sato, Takashi Shimomura arXiv:0704.2914[hep-ph]

2. Introduction ～ c ～ ～ t t Good candidate for beyond the standard model Supersymmetric model From dark matter physics Long lived charged particle stau Dark matter neutralino stau ＋ nuclear New processes ! Purpose 7 Solving the Li problem by using the new processesin a framework of MSSM

3. Li problem 7 D/H 7 Li problem p Baryon densityW h B 0.01 0.02 0.03 7 Predicted Li abundance ≠ observed Li abundance 4 He 0.26 7 Y p 0.24 7 We want to reduce the Li abundance !! 0.23 -3 10 B B N C M B -4 10 3 He/H p -5 10 -9 10 7 Li/H p 10 -10 1 8 2 3 4 5 6 7 -10 Baryon-to-photon ratio h ×10 Successful theory Big-Bang Nucleosynthesis Theory prediction －10 7 Li/H = 4.15 ×10 [ A.Coc, E.Vangioni-Flam, P.Descouvemont, A.Adahchour and C.Angulo (2003) ] Observation 7 Li/H = 1.7 ×10 －10 [ B.D.Fields and S.Sarkar (2006) ] [ B.D.Fields and S.Sarkar (2006) ]

4. Long lived charged particle ～ ～ c c ～ t Dark matter LSP neutralino coannihilation allowed region LSP mass NLSP mass coannihilation region Interesting case :dm = (NLSP mass) - (LSP mass) < (tau mass) ～ 1.7 GeV t [ J. Ellis (2002) ] Two-body decay LSP : Lightest Suparsymmetric Particle NLSP : Next Lightest Suparsymmetric Particle

5. Long lived charged particle BBN era ～ t life time can be long due to phase space suppression Possible decay processes t lifetime(s) ～ ～ t 10 10 survive until BBN era 6 10 2 10 ～ t provide additional -2 10 processes to reduce the primordial Li abundance 7 0.01 0.1 1 dm (GeV)

6. 7 Solving the Li problem Processes changing the light element abundance (1) Hadronic-current interaction (2) Stau-catalyzed fusion [ R.N.Cahn and S.L.Glashow (1981) ] [ M.Pospelov (2006) ] [ K. Hamaguchi, T. Hatsuda, M. Kamimura, Y. Kino and T. T. Yanagida (2007) ] (3) Internal conversion of stau-nucleus bound state [ C.Bird, K.Koopmans and M.Pospelov (2007) ] We re-predict the primordial abundance of the light element in consideration of these processes

7. Hadronic-current interaction 7 7 The abundance of the Li/ Be are changed by the new decay channels: n p t ～ c 0 t t ～ . . . . Emitted pion change the proton-neutron ratio Primordial abundance of the light element is changed

8. Stau-catalyzed fusion A nucleus has the Coulomb barrier The barrier is weakened when a stau is captured to a state bound to the nucleus While p p

9. Internal conversion of stau-nucleus bound state Stau and nucleus form bound state Interaction between stau and nucleus proceed much efficiently ～ ( t (nucleus) ) : bound state Reason ① The overlap of the wavefunctions of the stau and nucleus becomes large ② The small distance of the stau and nucleus allows virtual exchange hadronic current even if dm < m p

10. Our original chain processes ☆ Bound state The lifetime of internal conversion processes lifetime(s) 1 4 10 -2 10 1 -4 10 -4 10 -6 10 0.1 0.1 0.01 1 0.01 1 dm (GeV) dm (GeV)

11. Numerical calculation result 0.01 0.1 1 n /s Neutralino abundance which accounts for all the dark matter component -10 10 -12 10 Agreement with all the observational abundance including Li -15 10 7 -18 10 Blue, green, and purple region are excluded by the observations 0.01 0.1 1 dm (GeV) h=6.1 × 10 -10

12. Summary We have investigated a possible solution of the Li problem in a framework of MSSM 7 When the mass difference between stau NLSP and neutralino LSP is small, stau survive until the BBN era We have shown that long lived stau provide additional processes to reduce the primordial Li abundance 7 Hadronic-current interaction Stau-catalyzed fusion Internal conversion of stau-nucleus bound state Particularly, our original process ( internal conversion process ) is very important to solve the Li problem

13. Appendix

14. 2 (n/p) Y = p 1 + n/p Baryon density W = B Critical density Observational constraints Y = 0.2516 ± 0.0040 p -5 D/H = (2.82 ± 0.26) × 10 7 Log ( Li/H) = －9.63 ± 0.06 10 6 7 ( Li/ Li) < 0.046 ± 0.022 + 0.84

15. Lifetime of the internal conversion of stau-nucleus bound state Lagrangian The lifetime of the internal conversion The overlap of the wave function of the staus and the nucleus We estimate the overlap of the wave function by assuming that the bound state is in the S-state of a hydrogen-like atom

16. Lifetime of the internal conversion of stau-nucleus bound state Cross section The matrix element of the nuclear conversion appearing in this equation is evaluated by the ft-value of the corresponding b-decay obtained from the experiments. However the experimental ft-value is available for Li Be but not Li He 7 7 7 7 We assume that the two processes have the same ft-value owing the similarity of the two.

17. The qualitative feature of the white allowed region 0.01 0.1 1 n /s Stau need to have the long lifetime enough to survive when stau and nucleus form a bound state -10 10 dm < (100 ～ 200) MeV -12 10 -15 Stau number density needs to be large compared with that of Li 10 n /s > 10 -20 -18 10 The excessive destruction of Li by the process must be avoided due to the constraint . This condition requires that Li should not form a bound state with stau so much ☆ 0.01 0.1 1 dm (GeV) -10 h=6.1 × 10 n /s ～ 10 -20 dm > 100 MeV or ～