Possible solution to the Li-7 problem by the long lived stau Masato - PowerPoint PPT Presentation

Possible solution to the Li-7 problem by the long lived stau Masato Yamanaka ( Saitama University ) collaborators Toshifumi Jittoh, Kazunori Kohri, Masafumi Koike, Joe Sato, Takashi Shimomura Phys.Rev.D73:055009,2006. and arXiv:0704.2914 [hep-ph]

Big-Bang nucleosynthesis [ B.D.Fields and S.Sarkar (2006) ] 7 and Li problem Successful theory Big-Bang Nucleosynthesis Theory prediction � 10 Li / H = 4.15 � 10 7 [ A.Coc, E.Vangioni-Flam, P.Descouvemont, A.Adahchour and C.Angulo (2003) ] Observation � 10 Li / H = 1.7 � 10 7 [ B.D.Fields and S.Sarkar (2006) ]

7 Li problem 7 Predicted Li abundance 7 �� observed Li abundance 7 We have to reduce the Li abundance !! Purpose 7 Solving the Li problem by using the new processes in a framework of MSSM

Long lived charged particle Dark matter � neutralino � : allowed region Present from coannihilation coannihilation region appropriate neutralino dark matter abundance [ J. Ellis (2002) ] Requirement of coannihilation � NLSP mass LSP mass =

Long lived charged particle Interesting case : � m �� NLSP mass � LSP mass < tau mass (1.77GeV) stau tau + neutralino Two-body decay Allowed stau stau decay processes decay processes Allowed � � � � � � � � � � � � � � � � l � � l

Long lived charged particle m μ m π 10 16 � � lifetime (s) 10 14 10 12 10 10 10 10 BBN era 10 8 lifetime(s) 10 6 10 6 10 4 10 2 10 2 1 10 -2 10 -2 10 -4 10 -6 0.01 0.1 1 0.01 0.1 1 δ m (GeV) � m (GeV) � survive until BBN era � � Stau provide additional processes to 7 reduce the primordial Li abundance !!

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) ]

Hadronic-current interaction The staus can interact with the nuclei through the hadronic current and thereby change the BBN processes � � � � � � � � � Emitted pion change the proton-neutron ratio Primordial abundance of the light element is changed

Stau-catalyzed fusion stau + nucleus Forming a bound state In the nuclear fusion, Coulomb barrier becomes weak Time scale of these � � � � � 7 7 Be + ( Be ) + processes > � 1 sec � � � � � 7 7 Li + ( Li ) + � � � � � 7 8 ( Be ) + p ( B ) + Longer than time scale � � of dominant process � � 7 8 ( Be ) + n ( Li ) + n � � � � 7 4 ( Li ) + p + 2 He or Stau-catalyzed fusion � � 4 + 2D + He is subdominant

Internal conversion of stau-nucleus bound state stau + nucleus Forming a bound state Interaction between stau and nucleus proceed much efficiently Why ? �� The overlap of the wavefunctions of the stau and nucleus becomes large �� The small distance of the stau and nucleus allows virtual exchange hadronic current even if � m < m �

Internal conversion of stau-nucleus bound state � Internal conversion chain processes � � � 7 Li � � � � � 7 Be Internal conversion cross section The matrix element of the nuclear conversion is evaluated by the ft- value of the corresponding � -decay obtained from the experiments

The lifetime of internal conversion processes lifetime(s) μ π μ π 10 6 10 1 10 4 1 10 4 10 -1 10 2 -2 10 10 -2 1 lifetime(s) lifetime(s) 1 10 -3 10 -2 -4 10 10 -4 10 -4 10 -4 10 -5 -6 10 -6 10 10 -6 10 -7 10 -8 0.01 0.1 1 0.01 0.1 1 0.1 0.1 0.01 1 0.01 1 δ m (GeV) δ m (GeV) � m (GeV) � m (GeV) Time scale of internal conversion is shorter than that of another two type processes ! Internal conversion process is most important to solve the Li problem in a framework of MSSM !!

Numerical result The constraints from the light-element abundance shown in � m-(n_stau/s) plane 0.01 0.1 1 n /s Neutralino abundance which accounts for all the 10 -10 dark matter component 10 -12 Agreement with all the 10 -15 observational abundance 7 including Li 10 -18 Blue, green, and purple region are excluded by 0.01 0.1 1 the observations � m (GeV) � = 6.1 � 10 -10

The constraints from the light-element Why excluded ? abundance shown in � m-(n_stau/s) plane 0.01 0.1 1 6 7 n /s ( Li/ Li) < 0.046 ± 0.022 + 0.84 Li should not form a bound state with stau so much 10 -10 10 -12 Stau should decay before it form a bound state with Li, or stau number 7 density should be small enough 10 -15 n /s n /s > � � = Li 10 -18 > Required stau lifetime 10(s) = 0.01 0.1 1 � m (GeV) < Mass difference � m 150 MeV = � = 6.1 � 10 -10

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 7 processes to reduce the primordial Li abundance Hadronic Hadronic-current interaction -current interaction Stau-catalyzed fusion -catalyzed fusion Stau Internal conversion of stau stau-nucleus bound state -nucleus bound state Internal conversion of Particularly, our original process, internal conversion process is very important to solve the Li problem

Appendix

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

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 � -decay obtained from the experiments. However the experimental ft-value is available for 7 7 7 7 Li Be but not Li He We assume that the two processes have the same ft-value owing the similarity of the two.

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

Introduction Shortcoming in the Big-Bang Nucleosynthesis (BBN) 7 Li problem Good candidate for beyond the standard model Minimal Supersymmetric Standard Model (MSSM) Purpose 7 Solving the Li problem by using the new processes in a framework of MSSM