A Solution to the Li Problem by the Long Lived Stau

1. 7 A Solution to the Li Problem by the Long Lived Stau Masato Yamanaka Collaborators Toshifumi Jittoh, Kazunori Kohri, Masafumi Koike, Joe Sato, Takashi Shimomura Phys. Rev. D78 : 055007, 2008 and arXiv : 0904.××××

2. Contents 1, Introduction 2, The small m scenario and long lived stau d 3, Solving the Li problem by the long lived stau 7 4, Relic density of stau at the BBN era 5, Summary

3. Introduction

4. Big Bang Nucleosynthesis (BBN) Yellow box Observed light element abundances [CMB] vertical band Cosmic baryon density obtained from WMAP data Color lines Light element abundances as predicted by the standard BBN Prediction of the light elements abundance consistent ! Primordial abundance obtained from observations [ B.D.Fields and S.Sarkar (2006) ]

5. 7 Li problem Theory ＋0.49 －10 ( 4.15 )×10 －0.45 A. Coc, et al., astrophys. J. 600, 544(2004) Observation －10 ( 1.26 )×10 ＋0.29 －0.24 P. Bonifacio, et al., astro-ph/0610245 7 7 Predicted Li abundance ≠ observed Li abundance 7 Li problem

6. ~ t Requirement for solving the Li problem 7 Able to destroy a nucleus Requirement for solving the Li problem To occur at the BBN era Not a Standard Model (SM) process Possible to be realized in a framework of minimal supersymmetric standard model ! Coupling with a hadronic current Stau Able to survive still the BBN era Superpartner of tau lepton Exotic processes are introduced

7. The small m scenario and long lived stau d

8. ～ ～ c c N 1 ～ N W 2 N 3 ～ 0 ～ H ～ u B 0 H d N 4 ～ ～ ～ ～ t t t t q q t t g -i e t Setup Minimal Supersymmetric Standard Model (MSSM) with R-parity Lightest Supersymmetric Particle (LSP) Lightest neutralino = + + + Next Lightest Supersymmetric Particle (NLSP) Lighter stau cos sin = + L R

9. W h 2 = 0.1099 ± 0.0062 DM 1 m (constant) = n DM DM Dark matter and its relic abundance Dark Matter (DM) Neutral, stable (meta-stable), weak interaction, massive Good candidate : LSP neutralino DM relic abundance m n × ∝ DM DM http://map.gsfc.nasa.gov

10. SM particle ～ ～ c c SM particle 1 m m (constant) = > 46 GeV ～ n DM c DM Naïve calculation of neutralino relic density DM reduction process Neutralino pair annihilation Not enough to reduce the DM number density Not consistent ! [ PDG 2006 (J. Phys. G 33, 1 (2006)) ]

11. SM particle SM particle ～ ～ ～ c c c SM particle SM particle ～ t – < ~ 10 % m m LSP LSP m NLSP Coannihilation mechanism [ K. Griest and D. Seckel PRD43(1991) ] DM reduction process + stau-neutralino coannihilation Neutralino pair annihilation + Possible to reduce DM number density efficiently ! Requirement for the coannihilation to work

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

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

14. Solving the Li problem by the long lived stau 7

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

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

17. 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

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

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

20. : The overlap of the wave functions : Cross section × relative velocity G = ・ IC 2 2 2 | | | | | | y y y 1 = p a 3 nucl a – 1 ( ft ) ∝ nucl 1/3 1.2 × A ( ) ( ) ( ) ( ) s s s s v v v v Internal conversion rate The decay rate of the stau-nucleus bound state The bound state is in the S-state of a hydrogen-like atom ～ = nuclear radius = 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)

21. Interaction rate of Internal conversion Interaction time scale (s) Very short time scale significant process for reducing Li abundance ! 7

22. 7 7 New interaction chain reducing Li and Be Internal conversion 7 He ～ Internal conversion ～ c t n , t 7 Be 7 Li Scattering with background particles ～ ～ c t n , t 4 He, 3 He, D, etc proton, etc

23. -11 10 -12 10 Y ~ t -13 10 n n m = 300 GeV Y ~ ~ ~ DM t t t -14 10 -15 10 -16 10 0.01 0.1 Mass difference between stau and neutralino (GeV) Numerical result for solving the Li problem 7 s : number density of stau s : entropy density 1

24. ~ ~ t t -13 (7 – 10) 10 × Allowed region 100 - 120 MeV 7 The Li problem is solved Y Strict constraint on m and d -13 Y (7 – 10) 10 (100 – 120) MeV = d m = ×

25. ( Be) 7 ~ t Allowed region Internal conversion of occur when back ground protons are still energetic 7 Produced Li are destructed by energetic proton Back ground particles are not energetic when Li are emitted 7 7 Produced Li are destructed by internal conversion

26. Forbidden region Overclosure of the universe Stau decay before forming a bound state • Lifetime of stau • Formation time of Bound states are not formed sufficiently 6 Over production of Lidue to stau catalyzed fusion Insufficient reduction

27. Relic density of stau at the BBN era

28. 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 problem 7

29. The evolution of the number density Boltzmann Eq. for neutralino and stau i, j : stau and neutralino : standard model particle X, Y n (n ) eq : actual (equilibrium) number density : Hubble expansion rate H

30. 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

31. 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

32. The evolution of the number density Boltzmann Eq. for neutralino and stau Decay and inverse decay processes i j Y

33. Can we simplify the Boltzmann Eq. with ordinal method ? In the calculation of LSP relic density All of Boltzmann Eq. are summed up ( all of SUSY particles decay into LSP ) ∴ Single Boltzmann Eq. for LSP DM Absence of exchange terms ( cancel out ) ∴ In the calculation of relic density of long lived stau We are interesting to relic density of NLSP Obviously we can not use the method ! We must solve numerically a coupled set of differential Eq. for stau and neutralino

34. n i n Y n n X j , << , Significant process for stau relic density calculation Boltzmann Eq. for neutralino and stau Annihilation process Exchange process Due to the Boltzmann factor, Annihilation process rate << exchange process rate ≠ Freeze out temperature of sum of number density of SUSY particles Freeze out temperature of number density ratio of stau and neutralino

35. m ~ T 20 DM DM ~ ~ ~ g c t t t ~ t c g Exchange process DM freeze out temperature 5 GeV - 50 GeV ( DM mass 100 GeV - 1000 GeV ) Exchange process for NLSP stau and LSP neutralino After DM freeze out, number density ratio is still varying

36. n Y i s i : number density of particle i Numerical calculation Boltzmann Eq. for the number density of stau and neutralino n i s : entropy density

37. Numerical result (prototype) Tau decoupling temperature (MeV) 60 60 80 80 Mass difference between tau and neutralino (MeV) 50 100 50 100 Ratio of stau relic density and current DM density 15 % 3 % 8 % 1.5 % Significant temperature for the calculation of stau number density ・ Tau decoupling temperature ・ Freeze out temperature of exchange processes

38. g g t t t t l l t t q q Tau decoupling temperature Condition ( tau is in thermal bath ) [ Production rate ] > [ decay rate, Hubble expansion rate ] Production processes of tau Tau decoupling temperature ~ 120 MeV

39. Summary

40. 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 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

41. Appendix

42. Effective Lagrangian mixing angle between and CP violating phase Weak coupling Weinberg angle

43. Bound ratio

44. 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 1s, 2s, 2.5s, 3s confidence level are indicated by solid lines