Transcript Document

STATUS OF
YET ANOTHER TALK ON
BIG BANG NUCLEOSYNTHESIS
G. Mangano, INFN Naples
Atlas Coelestis
Main new developments in Big
Bang Nucleosynthesis (BBN):
Baryon density measurement by
CMB experiments (WMAP)
bh2= 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)
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
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
a
8 G


   e    b   
a
3
nb
a
 3
nb
a
T   (t , X a )
Qlepton (  e , T )  Qbaryon ( X a )
Nc
Nd





X
X
d
X a   N a  (c  d  a  b) c
Nc!
Nd !
b ,c , d

N
N

X a  X b 
 (a  b  c  d )
a
Na!


N b ! 
b
Xi=ni/nB
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
1
1/ 3
fv 
Tv  4 
exp(E / Tv )  1
 
T
 11
More accurate calculation by
solving the kinetic equations

0
v
7 4 
  
4  11
4/3
Partial entropy transfer during e+-e- annihilation phase
f=fv(p,Tν)[1+δf(p)]
Tν 0.15% larger
ρ(νe) 1% larger ρ(νμ,τ) 0.5% larger
2
30
T4
z = me/T
1 
i
f v ( p, a)  pa 1   ci ( pa) 
e 1 
i

How distortion in neutrino distribution affects BBN ?
change in v energy density: 1 %
change in n-p weak rates (np): ve distribution enters the
thermal averaged rate
very tiny effects !!
Weak rates
 e  n  e  p
 e  p  n  e
Freeze out of weak rates determines the
eventual n/p ratio (crucial for 4He)
 e  e  p  n
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
GF (cV  3c A )
2
2

( n  p  e   e ) 
dp
p
E
e e
 ( E ) G ( pe , E )
3

2
2
 
G ( pe , Ev )  1 
 2
2
2

m

  (m p )
 log p  2C  
g ( pe , Ev )  AQCD  S (m p , mZ )
mA
2



inner corrections
outer corrections Perturbative
QCD
Leading log
resummation
Coulomb correction: rescattering of electron in the proton field
Weak magnetism
nexp = 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 rates
Main problem: extract the cross section from data in the
low energy range of interest for BBN (0.01 1 MeV)
S (E)
 (E) 
exp(  EG / E )
E
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) subleading 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,p)3H
D(d,n)3He
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 estimate
Recent data only for E>0.6 MeV
Still 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
 
2
i ,k
( S ( Eik , an )  k Sik )
th
k 
2
2
ik
2

i ,k
k  1
2
k
2
k offset of the k-th experiment (free parameter determined
by the fit)
Rate estimate
f (T )   dE K ( E , T ) S ( E , an )
Boltzmann/Gamow kernel
best fit values
error estimate
 f 2 (T )   dE K ( E, T )
S
S
( E, an )  dE' K ( E ' , T )
( E ' , an ) cov(ai , a j )
ai
a j
for reduced v2 larger than 1 the error is inflated by a factor  2
From nuclear rates to nuclide abundances
Nc
Nd





X
X
d
X a   N a  (c  d  a  b) c
Nc!
Nd !
b ,c , d

N
N

X a  a X b  b 

 ( a  b  c  d )
Na!
N b ! 
BBN evolution equations numerically solved via a FORTRAN code
Theoretical uncertainties on Xi due to the rates k:
linear propagation
Fiorentini, Lisi, Sarkar and Villante 1998
 2ij 
1
 X i ( f k  f k )  X i ( f k  f k )X j ( f k  f k )  X j ( f k  f k )

4 k
Improved analysis of
4He(d,)6Li, 6Li(p,3He)4He, 3H(p,
7Li(d,n)4He4He, 7Be(d,p)4He4He
)4He, 7Li(p, )4He4He, 7Be(n,)4He,
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
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
(mass fraction)
4
He (Yp)
0,255
0,25
0,245
0,24
0,235
D (x105)
0,23
high 4He
low 4He
conservative
(N=3.04)
7
10
Li (x10 )
6
5
4
3
2
1
4,9
1,73
2,07
2,19
Bonifacio
Bonifacio
1,23
CMB
Bonifacio &
Ryan,
(N=3.04)
Molaro '97
Norris &
Beers '99
et al stelle et al 2003
di fondo
NGC6397
ve
ra
ge
Th
e
or
y
Q
22
06
-1
99
Q
10
09
-2
95
H
S0
6
10
516
19
Q
01
30
-4
02
Q
1
03
47
-3
81
Q
9
03
47
-3
PK
81
S
9
19
37
-1
00
9
7
6
5
4
3
2
1
A
CMB
D2/ D2 (%)
rate
49
weak p-n
D(D,n)3He
37
D(D,n)3He
1
D(D,p)3H
14
D(D,p)3H
0.25
D(n, )3H
0.25
rate
D(p,)3He
3He2/ 3He2(%)
rate
3He(D,
p)4He
80.7
D(p,)3He
16.8
D(D,p)3H
1.3
D(D,n)3He
1.2
6Li
large uncertainty due to
4He(D,
)6Li
4He2/ 4He2 (%)
98.5
rate
7Be(n,4He)4He
4He(3He,
)7Be
Li2/ Li2(%)
40.9
25.1
7Be(D,p)4He4He
16.2
3He(D,p)4He
8.6
D(p,)3He
4
others
5.2
Baryon density from CMB or BBN?
Neutrinos?
D+WMAP
1 extra effective
degree of freedom
still allowed at 2
D+4He
Summary
Present 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 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
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 for
4He(3He,
)7Be, 7Be(n,4He)4He,
3He(D, p)4He
4He(D, )6Li
Astroparticle physicists: can rest for a while