YET ANOTHER TALK ON BIG BANG NUCLEOSYNTHESIS
G. Mangano, INFN Naples
STATUS OF
BIG BANG NUCLEOSYNTHESIS
Atlas Coelestis
Main new developments in Big Bang Nucleosynthesis (BBN):
Baryon density measurement by CMB experiments (WMAP)
bh2= 0.023 0.001New 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)
Summary
•standard BBN
•neutrino decoupling
•weak rates
•nuclear rates
•present status: theory versus experiments
•outlookwork in collaboration with S. Esposito, F. Iocco, G. Miele, O. Pisanti and P.D. Serpico
astro-ph/0408076, astro-ph/0307213
Standard BBN: 3 standard neutrinos1. Decoupling of weak rates which keep n and p in
chemical equilibrium
2. Neutrino decoupling
3. D formation
4. Nuclear chain
!!)(
!!)(
)(),(
),(
3
3
8
,,
b
Nb
a
Na
dcb d
Nd
c
Nc
aa
abaryonelepton
a
b
b
be
N
X
N
Xdcba
N
X
N
XbadcNX
XQTQ
XtT
a
a
n
n
G
a
a
ba
dc
a: scale factor
: energy density
of relativistic
species (m < 1 MeV)
e: electron chemical
potential
Xi=ni/nB
Neutrino decouplingneutrinos 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
3/1
11
4
T
Tv
More accurate calculation by solving the kinetic equationsPartial entropy transfer during e+-e- annihilation
phase
f=fv(p,Tν)[1+δf(p)]Tν 0.15% largerρ(νe) 1% larger ρ(νμ,τ) 0.5% larger
423/4
0
3011
4
4
7
1)/exp(
1
T
TEf
v
vv
z = me/T
i
iipav pac
eapf )(1
1
1),(
How distortion in neutrino distribution affects BBN ?
change in v energy density: 1 %
change in n-p weak rates (np): ve distribution enters the thermal averaged rate
very tiny effects !!
Weak rates
npe
enp
pen
e
e
e
Freeze out of weak rates determines the eventual n/p ratio (crucial for 4He)
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
Check: the neutron lifetime
QED radiative effects
),( )(2
)3()( 22
3
222
EpGEEpdp
ccGepn eee
AVFe
),(),(2
)(2log
21),( ZpQCDve
p
A
pve mmSAEpg
mC
m
mEpG
inner corrections
outer corrections
Perturbative QCD
Leading log resummation
Coulomb correction: rescattering of electron in the proton field
Weak magnetismn
exp = 885.7 0.8 s nth =
886.5 s
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
Nuclear ratesMain problem: extract the cross section from data in the low energy range of interest for BBN (0.01 1 MeV)
)/exp()(
)( EEE
ESE G
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
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,)3He by LUNA Collaboration 2002
Recent compilations:Cyburt 2004
Descouvement et al 2004
Serpico et al 2004
Some examples
D(p,)3He
LUNA data
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
4He(3He,)7Be: dominant channel for 7Be production and 7Li synthesis
New measurements in progress or planned
ERNA, LUNA
7Be(n,)4He relevant role in 7Be destruction and main source of uncertainty of 7Li abundance theoretical estimateRecent data only for E>0.6 MeVStill large uncertainty (10%)
Fit method and error estimates
Sik S factor at Ei of k-th experiment
ik statistical uncertainty
k normalization uncertainty
Sth polynomial fit of the S factor depending on coefficients an to be determined by the fit
Pull approach
ki k
k
ki ikk
ikknikth SaES
,2
2
,
2
222 1)),((
k offset of the k-th experiment (free parameter determined by the fit)
Rate estimate
),( ),( )( naESTEKdETf
Boltzmann/Gamow kernel
best fit values
error estimate
),cov( ),'( ),'( '),( ),( )( 2jin
jn
i
aaaEa
STEKdEaE
a
STEKdETf
for reduced v2 larger than 1 the error is
inflated by a factor
2
From nuclear rates to nuclide abundances
!!)(
!!)(
,,
b
Nb
a
Na
dcb d
Nd
c
Nc
aa
N
X
N
Xdcba
N
X
N
XbadcNX
ba
dc
BBN evolution equations numerically solved via a FORTRAN codeTheoretical uncertainties on Xi due to the rates k: linear propagation Fiorentini, Lisi, Sarkar and Villante
1998
k
kkjkkjkkikkiij ffXffXffXffX )()()()(4
12
Improved analysis of
4He(d,)6Li, 6Li(p,3He)4He, 3H(p, )4He, 7Li(p, )4He4He, 7Be(n,)4He, 7Li(d,n)4He4He, 7Be(d,p)4He4He
Results
nuclide central value (exp)
(rates) (b)
D/H (10-5) 2.44 (2.78 0.4)
0.04 +0.19-0.16
3He/H(10-5) 1.01 0.03 +0.02-0.03
4He (mass fraction) 0.2486 (0.245 0.007)
+0.0002–0.0001
+0.0005-0.0004
6Li/H(10-14) 1.1 1.7 0.07
7Li/H(10-10) 4.9 (2.19 0.5)
0.4 0.4
7Li (x1010)
4,9
1,731,23
2,07 2,19123456
CMB
(N=3.04)
Bonifacio &
Molaro '97
Ryan,
Norris &
Beers '99
Bonifacio
et al stelle
di fondo
Bonifacio
et al 2003
NGC6397
4He (Yp)
0,23
0,235
0,24
0,245
0,25
0,255
CMB
(N=3.04)
high 4He low 4He conservative
D (x105)
1234567
Theo
ry
Q22
06-1
99
Q10
09-2
956
HS010
5-16
19
Q01
30-4
021
Q03
47-3
819
Q03
47-3
819
PKS1
937-
1009
Aver
age
rate D2/ D
2 (%)
D(p,)3He 49
D(D,n)3He 37
D(D,p)3H 14
rate 4He2/ 4He
2 (%)
weak p-n 98.5
D(D,n)3He 1
D(D,p)3H 0.25
D(n, )3H 0.25
rate 3He2/ 3He
2(%)3He(D, p)4He 80.7
D(p,)3He 16.8
D(D,p)3H 1.3
D(D,n)3He 1.2
rate Li2/ Li
2(%)7Be(n,4He)4He 40.94He(3He, )7Be 25.17Be(D,p)4He4He 16.23He(D,p)4He 8.6
D(p,)3He 4
others 5.2
6Li large uncertainty due to 4He(D, )6Li
Baryon density from CMB or BBN?
Neutrinos?
1 extra effective degree of freedom still allowed at 2
D+WMAP
D+4He
SummaryPresent status of standard BBN
D in good agreement with experimental results from QSAS
4He slightly higher than the values found by regression to zero metallicity in Blue compact object
7Li evidence for strong depletion of primordial materialMain 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
Outlooks
Astrophysicists: better understanding of possible systematics affecting 4He measurement and 7Li
At this stage it is impossible to severely bound neutrino number from BBN (1.5 < Nv < 4 at 95 C.L.)Nuclear physicists: new measurements in the energy range of interest for BBN (0.01 1 MeV) needed for4He(3He, )7Be, 7Be(n,4He)4He, 3He(D, p)4He 4He(D, )6LiAstroparticle physicists: can rest for a while