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