(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 : 055007, 2008

Li problem 7 Theoretical prediction ( 4.15 )×10 Observation ( 4.15 )×10 ＋0.49 －10 －0.45 A. Coc, et al., astrophys. J. 600, 544(2004) Observation ( 1.26 )×10 ＋0.29 －10 －0.24 P. Bonifacio, et al., astro-ph/0610245 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

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

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 !!

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

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

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

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

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

Numerical result for solving the Li problem 7 -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

Allowed region and prediction -12 10 -13 10 -14 10 -13 (7 – 10) 10 × -15 10 100 - 120 MeV Strict constraint on m and d Y ~ t

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

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

Appendix

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

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 2006 (J. Phys. G 33, 1 (2006)) ]

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)

Bound ratio

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

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 = 103.3 sec (experimental value) 7Li → 7He ･･･ similar to 7Be → 7Li (no experimental value)

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