1. YET ANOTHER TALK ON BIG BANG NUCLEOSYNTHESIS G. Mangano, INFN Naples STATUS OF BIG BANG NUCLEOSYNTHESIS

2. Atlas Coelestis Main new developments in Big Bang Nucleosynthesis (BBN): Baryon density measurement by CMB experiments (WMAP)  b h 2 = 0.023  0.001 New analysis of weak and nuclear rates Neutron lifetime accurate at the 0.1 % level  n = 885.7  0.8 s Future: Analysis of systematics in experimental estimates of light nuclei New data on some key nuclear processes in the BBN energy range ( 0.01  1 MeV)

3. Summary standard BBN neutrino decoupling weak rates nuclear rates present status: theory versus experiments outlook work in collaboration with S. Esposito, F. Iocco, G. Miele, O. Pisanti and P.D. Serpico astro-ph/0408076, astro-ph/0307213

4. Standard BBN: 3 standard neutrinos 1.Decoupling of weak rates which keep n and p in chemical equilibrium 2.Neutrino decoupling 3.D formation 4.Nuclear chain a: scale factor  : energy density of relativistic species (m < 1 MeV)  e : electron chemical potential

5. X i =n i /n B

6. Neutrino decoupling neutrinos are in chemical equilibrium with the e.m. plasma till weak reactions freeze out at T  1 MeV First approximation: instantaneous decoupling. Neutrino decoupling has no overlap in time with e + -e - annihilation More accurate calculation by solving the kinetic equations Partial entropy transfer during e + -e - annihilation phase f=f v (p,T ν )[1+δf(p)] T ν 0.15% larger ρ(ν e ) 1% larger ρ(ν μ,τ ) 0.5% larger

7. z = m e /T

8. How distortion in neutrino distribution affects BBN ? change in v energy density: 1 % change in n-p weak rates  (n  p): v e distribution enters the thermal averaged rate very tiny effects !!

9. Weak rates Freeze out of weak rates determines the eventual n/p ratio (crucial for 4 He) Big improvements in the last decade: QED radiative corrections Finite nucleon mass corrections Plasma effects Neutrino distortion Rates are accurate at the 0.1 % level

10. Check: the neutron lifetime QED radiative effects inner corrections outer corrections Perturbativ e QCD Leading log resummatio n Coulomb correction: rescattering of electron in the proton field Weak magnetism  n exp = 885.7  0.8 s  n th = 886.5 s

11. Plasma effects: Interactions with photons/electrons of the plasma Change in the e.m. equation of state due to photon/electron thermal masses P=P(  ) Very small (0.1 %) corrections

12. Nuclear rates Main problem: extract the cross section from data in the low energy range of interest for BBN (0.01  1 MeV) 1.Data from different experiments with different systematics 2.For several crucial reactions present data show evidence for ununderstood systematics 3.Experimental results typically overlap only partially in energy 4.Cross section for some (at the moment) sub-leading process is still poorly known

13. Data analysis: Fowler and Hoyle 1964 Wagoner 1969 Caughlan and Fowler 1988 Smith, Kawano and Malaney 1993 Important recent steps in the field NACRE Coll. Database: pntpm.ulb.ac.be/nacre.htm New data on D(p,  ) 3 He by LUNA Collaboration 2002 Recent compilations: Cyburt 2004 Descouvement et al 2004 Serpico et al 2004

14. Some examples D(p,  ) 3 He LUNA data

15. D-D reactions: leading source of uncertainty for Deuterium Small statistical errors but quite large systematics due to scale normalization poor  2 D(d,n) 3 He D(d,p) 3 H

16. 4 He( 3 He,  ) 7 Be: dominant channel for 7 Be production and 7 Li synthesis New measurements in progress or planned ERNA, LUNA 7 Be(n,  ) 4 He relevant role in 7 Be destruction and main source of uncertainty of 7 Li abundance theoretical estimate Recent data only for E>0.6 MeV Still large uncertainty (10%)

17. Fit method and error estimates S ik S factor at E i of k-th experiment  ik statistical uncertainty  k normalization uncertainty S th polynomial fit of the S factor depending on coefficients a n to be determined by the fit Pull approach  k offset of the k-th experiment (free parameter determined by the fit)

18. Rate estimate Boltzmann/Gamow kernel best fit values error estimate for reduced  v 2 larger than 1 the error is inflated by a factor

19. From nuclear rates to nuclide abundances BBN evolution equations numerically solved via a FORTRAN code Theoretical uncertainties on X i due to the rates  k : linear propagation Fiorentini, Lisi, Sarkar and Villante 1998

20. Improved analysis of 4 He(d,  ) 6 Li, 6 Li(p, 3 He) 4 He, 3 H(p,  ) 4 He, 7 Li(p,  ) 4 He 4 He, 7 Be(n,  ) 4 He, 7 Li(d,n) 4 He 4 He, 7 Be(d,p) 4 He 4 He

21. Results nuclidecentral value (exp)  (rates) (b)(b) D/H (10 -5 )2.44 (2.78  0.4)  0.04+0.19 -0.16 3 He/H(10 -5 )1.01  0.03+0.02 -0.03 4 He (mass fraction)0.2486 (0.245  0.007) +0.0002 –0.0001 +0.0005 -0.0004 6 Li/H(10 -14 )1.1  1.7  0.07 7 Li/H(10 -10 )4.9 (2.19  0.5)  0.4

23. rate  D 2 /  D 2 (%) D(p,  ) 3 He49 D(D,n) 3 He37 D(D,p) 3 H14 rate  4He 2 /  4He 2 (%) weak p-n98.5 D(D,n) 3 He1 D(D,p) 3 H0.25 D(n,  ) 3 H0.25 rate  3He 2 /  3He 2 (%) 3 He(D, p) 4 He80.7 D(p,  ) 3 He16.8 D(D,p) 3 H1.3 D(D,n) 3 He1.2 rate  Li 2 /  Li 2 (%) 7 Be(n, 4 He) 4 He40.9 4 He( 3 He,  ) 7 Be25.1 7 Be(D,p) 4 He 4 He16.2 3 He(D,p) 4 He8.6 D(p,  ) 3 He4 others5.2 6 Li large uncertainty due to 4 He(D,  ) 6 Li

24. Baryon density from CMB or BBN?

25. Neutrinos? 1 extra effective degree of freedom still allowed at 2  D+WMAP D+ 4 He

26. Summary Present status of standard BBN D in good agreement with experimental results from QSAS 4 He slightly higher than the values found by regression to zero metallicity in Blue compact object 7 Li evidence for strong depletion of primordial material Main achievements Weak rates well under control Carefuls analysis of neutrino decoupling Nuclear rate uncertainties strongly reduced by an updated re-analysis of available data including most recent results

27. Outlooks Astrophysicists: better understanding of possible systematics affecting 4 He measurement and 7 Li At this stage it is impossible to severely bound neutrino number from BBN (1.5 < N v < 4 at 95 C.L.) Nuclear physicists: new measurements in the energy range of interest for BBN (0.01  1 MeV) needed for 4 He( 3 He,  ) 7 Be, 7 Be(n, 4 He) 4 He, 3 He(D, p) 4 He 4 He(D,  ) 6 Li Astroparticle physicists: can rest for a while