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

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]

Possible solution to the Li-7 problem by the long lived stau

Big-Bang nucleosynthesis and Li problem

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Big-Bang Nucleosynthesis Successful theory Theory prediction Li/H = 4.15 10

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Observation Li/H = 1.7 10

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[ A.Coc, E.Vangioni-Flam, P.Descouvemont, A.Adahchour and C.Angulo (2003) ] [ B.D.Fields and S.Sarkar (2006) ]

[ B.D.Fields and S.Sarkar (2006) ]

Li problem

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Predicted Li abundance

• bserved Li abundance

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We have to reduce the Li abundance !!

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Solving the Li problem by using the new processes in a framework of MSSM

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Long lived charged particle

coannihilation region allowed region

[ J. Ellis (2002) ]

Dark matter

neutralino

• :

Present from coannihilation appropriate neutralino dark matter abundance Requirement of coannihilation

NLSP mass LSP mass

=

Long lived charged particle

Two-body decay stau tau + neutralino Allowed Allowed stau stau decay processes decay processes

• l

l

• Interesting case :

m NLSP mass LSP mass < tau mass (1.77GeV)

10-6 10-4 10-2 1 102 104 106 108 1010 1012 1014 1016 1 mπ mμ 0.1 0.01

lifetime(s)

δm (GeV)

0.01 0.1 1 m (GeV)

• lifetime (s)

10 10 10 6 10 2 10 -2

BBN era

Long lived charged particle

• survive until BBN era

Stau provide additional processes to reduce the primordial Li abundance !!

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Solving the Li problem

7 (1) Hadronic-current interaction (3) Internal conversion of stau-nucleus bound state (2) Stau-catalyzed fusion

Processes changing the light element abundance

[ R.N.Cahn and S.L.Glashow (1981) ] [ M.Pospelov (2006) ] [ C.Bird, K.Koopmans and M.Pospelov (2007) ] [ K. Hamaguchi, T. Hatsuda, M. Kamimura, Y. Kino and

• T. T. Yanagida (2007) ]

Hadronic-current interaction

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

Stau-catalyzed fusion

stau + nucleus Forming a bound state

In the nuclear fusion, Coulomb barrier becomes weak Be + ( Be ) +

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• Li + ( Li ) +
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• ( Be ) + p ( B ) +

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( Be ) + n ( Li ) + n

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• 8

( Li ) + p + 2 He or

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• 4

+ 2D + He

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Time scale of these processes >

1 sec

Longer than time scale

• f dominant process

Stau-catalyzed fusion is subdominant

Internal conversion of stau-nucleus bound state

stau + nucleus Forming a bound state Interaction between stau and nucleus proceed much efficiently 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

Why ?

Internal conversion of stau-nucleus bound state

The matrix element of the nuclear conversion is evaluated by the ft- value of the corresponding -decay obtained from the experiments

• Be

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Li

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Internal conversion chain processes Internal conversion cross section

10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 10 1 π μ 0.1 0.01 lifetime(s) δm (GeV) 10-8 10-6 10-4 10-2 1 102 104 106 1 π μ 0.1 0.01 lifetime(s) δm (GeV)

The lifetime of internal conversion processes

m (GeV) m (GeV) 0.1 0.1 0.01 0.01 1 1

10 10 1 10

• 6
• 2
• 4

lifetime(s)

10 4 1 10 -4

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

m (GeV)

0.01 0.1 1 0.01 0.1 1 10 -10 10 -12 10 -15 10 -18

n /s

= 6.1 10 -10

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Agreement with all the

• bservational abundance

including Li Neutralino abundance which accounts for all the dark matter component Blue, green, and purple region are excluded by the observations

The constraints from the light-element abundance shown in m-(n_stau/s) plane

Why excluded ?

m (GeV)

0.01 0.1 1 0.01 0.1 1 10 -10 10 -12 10 -15 10 -18

n /s

= 6.1 10 -10 Required stau lifetime 10(s)

>

=

<

=

Mass difference m 150 MeV

n /s n /s

• >

=

Li

( Li/ Li) < 0.046 ± 0.022 + 0.84

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Li should not form a bound state with stau so much Stau should decay before it form a bound state with Li, or stau number density should be small enough

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The constraints from the light-element abundance shown in m-(n_stau/s) plane

Summary

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

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Hadronic Hadronic-current interaction

• current interaction

Stau Stau-catalyzed fusion

• catalyzed fusion

Particularly, our original process, internal conversion process is very important to solve the Li problem

Internal conversion of Internal conversion of stau stau-nucleus bound state

• nucleus bound state

We have investigated a possible solution of the Li problem in a framework of MSSM

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Appendix

Y =

p

1 + n/p 2 (n/p)

=

B

Critical density Baryon density Observational constraints Observational constraints Y = 0.2516 ± 0.0040

p

D/H = (2.82 ± 0.26) 10 Log ( Li/H) = 9.63 ± 0.06

7 10

• 5

( Li/ Li) < 0.046 ± 0.022 + 0.84

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Definition and

• bservational constraints

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 Li Be but not Li He We assume that the two processes have the same ft-value

• wing the similarity of the two.

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Lifetime of the internal conversion of stau-nucleus bound state

The lifetime of the internal conversion Lagrangian

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 Lifetime of the internal conversion of stau-nucleus bound state

Introduction

Minimal Supersymmetric Standard Model (MSSM) Good candidate for beyond the standard model Purpose

Solving the Li problem by using the new processes in a framework of MSSM

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Shortcoming in the Big-Bang Nucleosynthesis (BBN)

Li problem

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