ビッグバン元素合成における スタウ原子衝突

1. ビッグバン元素合成におけるスタウ原子衝突 東北大・理・化学 木野康志 上村正康九大理、理研 肥山詠美子理研 初田哲男東大理 浜口幸一東大理 柳田　勉東大理

2. 1 What is stau ( ) ? Wikipedia Stau may refer to one of the following: • In particle physics, stau is a slepton which is the hypothetical superpartner of a taulepton • An obsolete letter Stigma in the GreekAlphabet • In German language, Stau is a word meaning 'traffic jam' Lepton(spin 1/2) Slepton(spin 0) selectron Supersymmetric pair smuon stau (scalar tau)

3. 2 Why the stau is so important ? Large Hadron Collider@CERNThe first beam (10 Sep. 2008) Objectives of LHC • Higgs mechanism • Supersymmetry, supersymmetric particles • Gravitino (dark matter) • etc. Perspective of LHC Finding evidence for a supersymmetric particle might be possible as early as the year 2009. Finding the Higgs might be possible by 2010. By A. Seidan (California) at APS meeting 2008

4. 3 In this talk… I do not discuss the supersymmetry (and cosmology), but atomic physics. I denote the Long lived scalar lepton as The X particle has Long lifetime ≈ 1,000-100,000 s Heavy mass: ≈ 100-1,000 GeV/c2 Interaction: Coulomb M(stau) ≥ M(Fe) X(Stau): negatively charged point-like heavy particle The stau can form an exotic atom/molecule

5. 4 (for example; hydrogen like atom) Stau atom mX = 100 GeV/c2 mp = 0.94 GeV/c2 Reduced mass Binding energy and Bohr radius (point nuclear charge) Root mean charge radius of nucleus

6. 5 Nuclear charge density Gaussian distribution X4He : Hydrogen-like ion wavefunction Pure Coulombic potential b = 1.37 fm for 4He b = 1.75 fm for d b = 2.576 fm for 7Be b = 0.7144 fm for p

7. 6 M. Pospelov (PRL 98, 231301, 2007) 6Li production by X-particle atomic collision Lifetime: more than 1,000 s nucleosynthesis (the first three minutes) catalyzed nuclear fusion Cf. muon catalyzed fusion

8. 7 Nucleosynthesis in Big Bang and the Li problem Observed value Li problem 7Li (X 1/3) 6Li (X 1000) 6Li (= 4He + D) Very slow（E1:forbidden）

9. “The Economist” (June, 2007) Dr Pospelov's catalytic mechanism, by contrast, explains both discrepancies in one fell swoop. It also makes predictions about the detailed properties of the supersymmetric partners—and, as luck would have it, suggests that although they cannot be made on Earth at the moment, they should be in range of the Large Hadron Collider, a particle accelerator being built near Geneva, which should open for business later this year. It should not, therefore, take long to find out if his explanation for the lithium problem is correct. If it is, he can claim to have found SUSY's traces before the particle physicists did. Posperov’s result significantly limited the current understanding of stau.

10. Is it true? … Pospelov employed a simple scaling, and paid no attention to the nuclear interaction and low energy atomic collision. Particle phys. (U. Tokyo) Nuclear Phys. Atomic Phys.(Exotic Atom) Maybe yes, but… Stau could be created at big ban,

11. Catalyzed reactions Submitted to Prog. Theo. Phys. arXiv:0809.4772v1

12. 11 6Li production (4HeX)1s + D → 6Li + X +1.137 MeV (6Li ≈4He + D) Phys. Lett. B 650, 268, 2007 7Li destruction (7BeX)1s + H → (8BX)2p → (8BX)1s +  Feshbach-type resonance 7Be → 7Li 8B → 8Be → 24He electron capture electron capture 53 d 0.77 s 10–16 s Submitted to Prog. Theo. Phys.

13. 12 a a a r2 r1 R3 R2 R1 r3 c = 2 c = 1 c = 3 X– b X– b X– b Numerical method Gaussian Expansion Method (GEM) Prog. Part. Nucl. Phys. 51. 223, 2003. 3,4-Nucleons, Nuclei, Hyper Nuclei, 3,5-Quarks Exotic atom/molecule (positronic, muonic, antiprotonic,…) Hamiltonian (a, b) = (D, 4He) (7Be, H)

14. 13 Wave function Incident channel Reaction channel Molecular and 3-body continuum states Incident channel Molecular and 3-body continuum states Incl.resonance states Boundary conditions

15. 14 discretization Continuum state Resonance stateBound state Resonance state Ecm Closed channel Expanded in terms of L2 basis Diagonarize the 3-body Hamiltonian Rapid convergence max≈50

16. Scattering wavefunction Coupled integro-differential equations Non local potential Numerical calculation *Variation method *Difference method

17. 16 Potential between 4He and D; Vd(r2) Reproduces the root mean square radius of 6Li (2.54 fm) the binding energy of 6Li (1.474 MeV) b = 1.37 fm for 4He, b = 1.75 fm for d 4He + D Li + e– 原子核電荷分布：ガウス型 b = 1.37 fm for 4He, b = 1.75 fm for d Charge form factor S-wave phase shift

18. 17 Nuclear potentialVd(r2) The nuclear reaction occurs by tunneling effect between the 4He and D. Coulomb Coulomb barrior Relative energy Vdr2) (MeV) VX Nuclear reaction Ecm ≈ 0.036 MeV KXHe Coulomb + Nuclear -10 MeV Internuclear distancer2 (fm) Different mechanism from electron screening

19. 18 Reaction cross section Full Coupled Channel DWBA 　mb) 2-channel CC (w/o closed channel) Gamow peak@36.4 keV (T=10 keV) E (keV)

20. DWBA 2-channel CC Full CC

21. Energy levels of the 7BeX + p reaction 8B[p(3/2–),7Be(3/2–)](2+) Vp-Be = VWS + Vls + VMC 7Be + X + p 0 MeV 8B + X -0.1375 MeV (8BX)2p J– E,  Ein Gamov peak ≈ 114 keV (kT ≈ 35 keV) (7BeX)1s + p  -1.33 MeV Incident channel -1.86 MeV 2+ (8BX)1s

22. 21 (7BeX)1s + H → (8BX)2p → (8BX)1s +  Reaction rate J–→ 2+ Er, p T = 0.3x109 K (mX) Maxwell(E) Strong mX dependence!

23. 22 Resonance parameters J– (8BX)2p J–→ 2+ E,  (820 keV) 2+ (8BX)1s

24. 23 Summary † Low energy stau atomic collision is precisely calculated based on full quantum mechanics. † Three-body closed channel (Stau molecular states HeDX and resonance state 8BX) plays an important role. † Present calculation supports the Posperov’s pioneering idea, but reduces his reaction rate by one order of magnitude. (The present result is in the current prediction of SUSY.) † Accurate theoretical predictions of nuclear reaction rate are important in the study of big ban nucleosynthesis. ‡ Stau opens a new page of exotic atom/molecule research, and will provide fruitful results for few-body physics. Stau catalyzed big ban nucleosynthesis => supersymmetry

25. 24 Stau atomic/molecular system Stau atom Electronic atom XHe He Heliocentric System Geocentric System Nuclei move around the heavy electron (stau)!!