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
arXiv0704.2914 hep-ph
2
Introduction
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
processes in a framework of MSSM
3
Li problem
7
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
Li/H 1.7 10
7
-10
B.D.Fields and S.Sarkar (2006)
B.D.Fields and S.Sarkar (2006)
4
Long lived charged particle
Dark matter
LSP neutralino
coannihilation
allowed region
LSP mass NLSP mass
coannihilation region
Interesting case dm (NLSP mass) - (LSP mass)
lt (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

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
? 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 dm lt 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
0.01
1
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
7
6
( Li/ Li) lt 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
-12
dm lt (100 200) MeV
10
-15
10
Stau number density needs to be large compared
with that of Li
-18
n /s gt 10
-20
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 gt 100 MeV or