1. Big-Bang Nucleosynthesis with Negatively-Charged Massive Particles as a Cosmological Solution to the 6Li and 7Li Problems
Motohiko Kusakabe1,2,†, Toshitaka Kajino1,2,3, Richard N. Boyd1,4,
Takashi Yoshida1 & Grant J. Mathews5
1) Division of Theoretical Astronomy, National Astronomical Observatory of Japan
2) Department of Astronomy, Graduate School of Science, University of Tokyo
3) Department of Astronomical Science, The Graduate University for Advanced Studies
4) Lawrence Livermore National Laboratory, University of California
5) Department of Physics and Center for Astrophysics, University of Notre Dame
†) Research Fellow of the Japan Society for the Promotion of Science
MK et al.① arXiv: [astro-ph], PRD, in press
MK et al.② arXiv: [astro-ph]

2. Constituents in the Universe
Introduction
Constituents in the Universe
380,000 years after the Big Bang
NASA/WMAP Science Team
Cosmological parameters (standard LCDM) ?
H0=70.4kms-1Mpc-1
Wb=0.0441
Wm=0.268
WL=0.732
(WMAP 3 years data :

3. Possible presence of long-lived (charged) particles
Feng et al. (2003)
Stable particles in supersymmetry or universal extra-dimension
models possibly have Wm-values consistent with observation
candidates of dark matters (DMs)
Unstable particles might have existed in the early Universe
including negatively-charged particles (e, m, t)
gravitino-slepton-lepton interaction
Decay-lifetime is ~
MPl=1.22×1019GeV
M≈100GeV-1TeV
105 s -108 s
>>tBBN
weak scale

4. ? ≿103 6Li problem 6Li & 7Li problems 7LiBBN 6LiBBN 7Li problem
-2.0
6LiBBN
? ≿103
Old stars ~ primordial
6Li problem
7Li problem
Asplund et al. (2006)
Metal-Poor Halo Stars
(MPHSs)
7Li abundance is a factor of ~3 smaller than CMB+SBBN prediction.
Possible high plateau of
6Li abundance
New information will be presented
by Kawanomoto (4-2-3), Aoki (4-3-2)
7Li/H=( )×10-10
6Li/H ≈ 6×10-12
Candidates of differences
[7Li] depletion in stellar atmosphere ?
[6Li] cosmic ray a+a ?/ local spallation ?
　　　cosmological origin ?
7Li depletion might be realized
with large 6Li depletion !
(Richard et al. 2005)
Poster by
K. Nakamura (P-13)

5. BBN with Negatively-Charged Massive Particles
Charged particle X- binds to a nucleus A to form AX
Large enhancement of the 6Li abundance by 4HeX(d,X-)6Li
(Pospelov 2007)
Similar enhancements of reaction rates of 4HeX(t,X-), 4HeX(3He,X-), 6LiX(p,X-)
(Cyburt et al. 2006)
Detailed study on recombination (Kohri & Takayama 2007)
7Be destruction through 7BeX+p8BX*a(n=2,l=1)8BeX+g
(Bird et al. hep-ph/ )
Goal of study
Try to solve the 6Li and 7Li problems
in fully dynamical BBN calculation taking account of
recombination of X- by nuclei as well as many possible
nuclear reactions of X-bound nuclei.

6. Model 1. Binding energy of nuclides with X-
[Assumptions]
X- has spin 0, charge -e, mass mX>>1 GeV
Nuclides have Gaussian charge distributions.
We solved two-body Shrödinger equations by variational calculation
and obtained binding energies.
(Gaussian expansion method, f.e. Hiyama et al. 2003)
2. (non-resonant) Nuclear reactions of X-bound nuclei
Neutron capture: (n,g) reaction rate SBBN value
Reaction of charged particles:
We took S-factors of SBBN reactions
and correct nuclear charges and reduced mass.
We changed reaction Q-value.

7. 3. X- transfer reaction 4HeX(d,X-)6Li
Pospelov (2007) suggested that the rate of X- transfer reaction 4HeX(d,X-)6Li is enhanced by 7 orders of magnitude more than that of 4He(d,g)6Li
We adopted the precise cross section for 4HeX(d,X-)6Li calculated in a quantum three-body model by Hamaguchi et al. (2007).
4. 7BeX(p,g)8BX through atomic excited state of 8BX
Bird et al. (2007) suggested that the resonant reaction 7BeX+p8BX*a(n=2,l=1)8BX+g contribute to destruction of 7Be.
We adopted this process, and added the 8BeX(p,g)9BX reaction through atomic excited state of 9BX.

8. (2nd order Runge-Kutta)
Calculation
t : time
radiation dominant
T(t)  r, p , , (g, e±, n, baryon)
Hubble expansion rate
reaction rate ・・・・・・・・・
: abundance change rate
SBBN(88)
recombination
new BBN
T(t), h(t), fe(t),Yi(t)
time integration
(2nd order Runge-Kutta)
SBBN i e
(Kawano 1992)
new processes
recombination process of X- (16) E
Vcoul
・・・
recombination
ionization r
new BBN reactions of X-bound
nuclides (42)
Including
4HeX(d,X-)6Li
7BeX+p8BX*a8BX+g
8BeX+p9BX*a9BX+g
Solve fully dynamically!

9. Result Nuclear flow Abundance mx=50GeV, nx=0.1nb, tx=∞ 4HeX(d,X-)6Li
This corresponds to Wx=WDM~0.2
4HeX(d,X-)6Li
7BeX+p8BX*a8BX+g (Bird et al. 2007)
( 7BeX+p8B*(1+,0.77MeV)X8BX+g
(MK et al.①) is unimportant!)
7Be(X-,g)7BeX
Temperature T9=T/(109 K)

10. Parameter search 1 h=6.1×10-10 Possible parameter region leading to
Abundance YX=nX/nb
Lifetime tX
7Li destruction
6Li production
Contours of calculated Li abundance relative to the
observed value: d(ALi)=ALiCalc/ALiObs
h=6.1×10-10
Possible parameter region leading to
7Li destruction and 6Li production !

11. Parameter search 2 h=6.1×10-10 Possible parameter region leading to
When weak boson exchange reaction
7BeX7Li+X0 (Bird et. al 2007) is included
7Li destruction
Abundance YX=nX/nb
Lifetime tX
Contours of calculated Li abundance relative to the
observed value: d(ALi)=ALiCalc/ALiObs
h=6.1×10-10
6Li production
7Li(p,a)4He
7Li(X-,g)7LiX(p,a)4HeX
Possible parameter region leading to
7Li destruction and 6Li production !

12. Summary
We calculated light-element nucleosynthesis during BBN with negatively-charged X- particles in a fully dynamical manner.
“6Li problem (a factor of ~103) is resolved.”
As suggested in previous studies, X- particles greatly enhance the production of 6Li through the recombination of 4He, 4He(X-,g)4HeX followed by the X- transfer reaction 4HeX(d,X-)6Li.
“7Li problem (a factor of ~3) is also resolved simultaneously.”
Related parameter region: YX ≿ and tX≈(1-3)x103s
destruction reaction: 7BeX+p8BX*a8BX+g through the atomic excited state of 8BX (Bird et al. 2007).
[Constraint on the mass of CDM particles]
If X- decays into a dark-matter Y0 and any residues, the WMAP-CMB constraint of WCDM=0.2, i.e., YYmY ≲ 4.5GeV leads to mY ≲ GeV for YX ≿ (the interesting parameter region).
If mX is close to mY, mX ≲ O(100) GeV.