BigBang Nucleosynthesis with Negatively Charged Massive Particles as

Big-Bang Nucleosynthesis with Negatively. Charged Massive Particles as a Cosmological Solution to the 6 Li and 7 Li Problems Motohiko Kusakabe 1, 2, †, Toshitaka Kajino 1, 2, 3, Richard N. Boyd 1, 4, Takashi Yoshida 1 & Grant J. Mathews 5 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 ar. Xiv: 0711. 3854 [astro-ph], PRD, in press MK et al. ② ar. Xiv: 0711. 3858 [astro-ph]

Introduction Constituents in the Universe 380, 000 years after the Big Bang NASA/WMAP Science Team Cosmological parameters (standard LCDM) H 0=70. 4 kms-1 Mpc-1 Wb=0. 0441 ? Wm=0. 268 (WMAP 3 years data : ? WL=0. 732 http: //lambda. gsfc. nasa. gov)

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 ~ m, ~ t) ~ including negatively-charged particles (e, • gravitino-slepton-lepton interaction MPl=1. 22× 1019 Ge. V • Decay-lifetime is M≈100 Ge. V-1 Te. V weak scale 105 s -108 s >>t. BBN

6 Li & 7 Li problems Metal-Poor Halo Stars (MPHSs) l 7 Li abundance is a factor of ~3 smaller than CMB+SBBN prediction. Asplund et al. (2006) 7 Li BBN problem New information will be presented by Kawanomoto (4 -2 -3), Aoki (4 -3 -2) l Possible high plateau of 6 Li abundance 7 Li/H=(1. 1 -1. 5)× 10 -10 6 Li/H ? ≿ 103 6 Li problem Old stars ~ primordial ≈ 6× 10 -12 -2. 0 Candidates of differences [7 Li] depletion in stellar atmosphere ? [6 Li] cosmic ray a+a ? / local spallation ? Poster by 　　　cosmological origin ? K. Nakamura (P-13) 6 Li 7 Li BBN depletion might be realized with large 6 Li depletion ! (Richard et al. 2005)

BBN with Negatively-Charged Massive Particles üCharged particle X- binds to a nucleus A to form AX üLarge enhancement of the 6 Li abundance by 4 He. X(d, X-)6 Li (Pospelov 2007) üSimilar enhancements of reaction rates of 4 He. X(t, X-), 4 He. X(3 He, X-), 6 Li. X(p, X-) (Cyburt et al. 2006) üDetailed study on recombination (Kohri & Takayama 2007) ü 7 Be destruction through 7 Be +p 8 B *a(n=2, l=1) 8 Be +g X X X (Bird et al. hep-ph/0703096) Goal of study Try to solve the 6 Li and 7 Li 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.

Model 1. Binding energy of nuclides with X[Assumptions] X- has spin 0, charge -e, mass m. X>>1 Ge. V 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 ØNeutron capture: (n, g) reaction rate SBBN value ØReaction of charged particles: We took S-factors of SBBN reactions and correct nuclear charges and reduced mass. We changed reaction Q-value.

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

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

Result Abundance Nuclear flow mx=50 Ge. V, nx=0. 1 nb, tx=∞ u. This corresponds to Wx=WDM~0. 2 u 4 He 7 Be(X-, g)7 Be X X(d, X -)6 Li 8 B *a 8 B +g (Bird et al. 2007) X X 7 Be +p 8 B*(1+, 0. 77 Me. V) 8 B +g X X X 7 Be ( X+p (MK et al. ①) is unimportant!) Temperature T 9=T/(109 K)

Parameter search 1 Contours of calculated Li abundance relative to the observed value: d(ALi)=ALi. Calc/ALi. Obs h=6. 1× 10 -10 Lifetime t. X 7 Li 6 Li destruction production Abundance YX=n. X/nb Possible parameter region leading to 7 Li destruction and 6 Li production !

Parameter search 2 When weak boson exchange reaction 7 Be 7 Li+X 0 (Bird et. al 2007) is included X 7 Li(p, a)4 He Contours of calculated Li abundance relative to the 7 Li(X-, g)7 Li (p, a)4 He observed value: d(ALi)=ALi. Calc/ALi. Obs X X h=6. 1× 10 -10 Lifetime t. X 7 Li 6 Li destruction production Abundance YX=n. X/nb Possible parameter region leading to 7 Li destruction and 6 Li production !

Summary We calculated light-element nucleosynthesis during BBN with negatively-charged X- particles in a fully dynamical manner. “ 6 Li problem (a factor of ~103) is resolved. ” As suggested in previous studies, X- particles greatly enhance the production of 6 Li through the recombination of 4 He, 4 He(X-, g)4 He. X followed by the X- transfer reaction 4 He. X(d, X-)6 Li. “ 7 Li problem (a factor of ~3) is also resolved simultaneously. ” Related parameter region: YX ≿ 0. 04 -1 and t. X≈(1 -3)x 103 s destruction reaction: 7 Be. X+p 8 BX*a 8 BX+g through the atomic excited state of 8 BX (Bird et al. 2007). [Constraint on the mass of CDM particles] If X- decays into a dark-matter Y 0 and any residues, the WMAP-CMB constraint of WCDM=0. 2, i. e. , YYm. Y ≲ 4. 5 Ge. V leads to m. Y ≲ 6 -100 Ge. V for YX ≿ 0. 04 -1 (the interesting parameter region). If m. X is close to m. Y, m. X ≲ O(100) Ge. V.