the nucleon structure and the eos of nuclear matter jacek rozynek ins warsaw nuclear physics...
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The Nucleon Structure and the EOS of Nuclear Matter
Jacek Rozynek INS Warsaw
Nuclear Physics Workshop
KAZIMIERZ DOLNY 2006
Summary
• EMC effect• Relativistic Mean Field Problems• Hadron with quark primodial distributions• Pion contributions
• Nuclear Bjorken Limit - MN(x)
• Higher densities & EOS• Conclusions
PARTONS
IN
DIS
EMC effect
Historically ratio
R(x) = F2A(x)/ F2
N(x)
Three approaches to its description:x
Pion excess
Three approaches to EMC effect in term of nucleon degrees of freedom through the nuclear spectral function. (nonrelativistic off shell effects) G.A.Miller&J. Smith, O. Benhar, I. Sick, Pandaripande,E Oset
in terms of quark meson coupling model modification of quark propagation by direct coupling of quarks to nuclear envirovment A.Thomas+Adelaide/Japan group, Mineo, Bentz, Ishii, Thomas, Yazaki (2004)
by the direct change of the partonic primodial distribution. S.Kinm, R.Close Sea quarks from pion cloud. G.Wilk+J.R.,
Hit quark has momentum j + = x p +
ExperimentalyExperimentaly x =x = and is iterpreted as fraction of longitudinal nucleon momentum carried by parton(quark) for 2Q2
On light cone Bjorken x is defined as x = j+ /p+
where p+ =p0 + pz
e
p r(emnant)
Q2
,
Q2/2M
D I Sj
Light cone coordinates
fixedMQxMxq
QfixedxwithQ
qQQvq
pJJpedW iq
2/),0,0,(
0)/(
),,0,0,(
)0()(
2
222
2222
4
MxMx
Mx
qqq
Mxqbutq
qqq
/1||and/1||so
/2||but0
thenif
2/
limit Bjorken in)(2/1
30
30
Relativistic Mean Field Problems
In standard RMF electrons will be scattered on nucleons in average scalar and vector potential:
p +M+US) - (e -UV
where US=-gS /mSSUV =-gV /mV
US = 300MeV
UV = 300MeV
Relativistic Mean Field Problems
In standard RMF electrons will be scattered on nucleons in average scalar and vector potential:
p +M+US) - (e -UV
where US=-gS /mSSUV =-gV
/mV
US = -400MeV
UV = 300MeV
Gives the nuclear distribution f(y) of longitudinal nucleon momenta p+=yAMA
SN() - spectral fun. - nucleon chemical pot.
)(
)(1)p,(
)2(
4)( 3030
4
4 ppy
pE
ppS
pdy NA
A
Relativistic Mean Field Problemsconnected with Helmholz-van Hove theorem - e(pF)=M-
In standard RMF electrons will be scattered on nucleons in average scalar and vector potential:
p +M+US) - (e -UV
where US=-gS /mSSUV =-gV
/mV
US = -400MeV
UV = 300MeV
Gives the nuclear distribution f(y) of longitudinal nucleon momenta p+=yAMA
SN() - spectral fun. - nucleon chemical pot.
)(
)(1)p,(
)2(
4)( 3030
4
4 ppy
pE
ppS
pdy NA
A
Strong vector-scalar cancelation
*
3
22
/,)1(
4
3)( FFA
A
AAA
A Epvv
yvy
Hadrons with quark primodial distributions based on Heinserberg uncertainty relation
• Gaussian distribution of quark (u and d ) momenta j
Hadrons with quark primodial distributions based on Heinserberg uncertainty relation
• Gaussian distribution of quark momenta j
• Monte Carlo simulations
• Proton • Width - .18GeV
0 < (j+q) < W 0 < r < W’
W - invariant mass
Hadrons with quark primodial distributions based on Heinserberg uncertainty relation
• Gaussian distribution of quark momenta j
• Monte Carlo simulations
• Proton • Width - .18GeV
• • Pion • width -.18MeV
0 < (j+q) < W 0 < r < W'
W - invariant mass
Hadron with quark primodial distributions Good description - Edin, Ingelman Phys. Let. B432 (1999)
• Gaussian distribution of quark momenta j
• Monte Carlo simulations
• Proton • Width - .18GeV
• • Pion Component• width =52MeV • N =7.7 %
0 < (j+q) < W 0 < r < W’
W - invariant mass
Sea parton distribution is given by the pionic (fock) component of the nucleon
);/();();( 20
20
20 QyxfQyf
ydy
Qxf pionN
Change of nucleon primodial distribution inside medium
• Gaussian distribution of quark momenta j
• Monte Carlo simulations in medium
• pion cloud (mass) renormalization momentum sum rule
• Proton • Width - .18GeV• Pion width - 52MeV • N =7.7 %
• IN MEDIUM
• Proton • Width - .165GeV • Pion width =52MeV • N =7.7 %
0 < (j+q) < Wm 0 < r < W’m
W - invariant mass
Primodial Distributios and Monte –Carlo Simulations for NM
• Calculations for the realistic nuclear distributions
1
3
31
2
5.1
021.0
76..
________________________________
)(
)()(
%12
050.0
172.0
fmp
fm
AfmN
BLettPhys
EiZabolitsky
ppforeNpN
A
pNpNpN
N
GeV
GeV
C
C
Cp
Ctail
tailmf
ex
N
The Change of the primodial disribution in medium
Results
Results
with G. Wilk Phys.Lett. B473, (2000), 167
Today - Convolution modelToday - Convolution model for x <0.15
• We We willwill show that in deep inelastic show that in deep inelastic scattering the magnitude of the scattering the magnitude of the nuclear Fermi motion is sensitive to nuclear Fermi motion is sensitive to residual interaction between partons residual interaction between partons influencing both the Nucleon influencing both the Nucleon Structure Function Structure Function
• and nucleon mass in th and nucleon mass in th NMNM
• MMBB (x) (x)
• We We willwill show that in deep inelastic show that in deep inelastic scattering the magnitude of the scattering the magnitude of the nuclear Fermi motion is sensitive to nuclear Fermi motion is sensitive to residual interaction between partons residual interaction between partons influencing both the Nucleon influencing both the Nucleon Structure Function Structure Function
• and nucleon mass in th and nucleon mass in th NMNM
• MMBB (x) (x)
• Relativistic Mean Field problems
• Primodial parton distributions
• Bjorken x scaling in nuclear medium
F2N(x)
)()()()(1
22 xFyxyxx
dxdyAxF
xN
AA
AAAAA
A
N O S H A D O W I N G
Nuclear Deep Inelastic limit
Fermi
23
1
e
1
NB
BNAnA
i Ai
MM
pMpdMA
Mj
A
Nuclear Deep Inelastic limit
Fermi
23
1
e
1
NB
BNAnA
i Ai
MM
pMpdMA
Mj
A
Nuclear Deep Inelastic limit
Fermi
23
1
e
1
NB
BNAnA
i Ai
MM
pMpdMA
Mj
A
To much pions
RMF failure &Where the nuclear pions are
• M Birse PLB 299(1985), JR IJMP(2000), G Miller J Smith PR (2001)• GE Brown, M Buballa, Li, Wambach , Bertsch, Frankfurt, Strikman
z=9fm
TTwo resolutions scales in deep inelastic scattering
1 1/ Q 2 connected with virtuality of probe . (A-P evolution equation - well known)
1/Mx = z distance how far can propagate the quark in the medium. (Final state quark interaction - not known)
For x=0.05 z=4fm
•
Nuclear final state interaction
z(x)
Effective nucleon Mass M(x)=M( z(x) , rC ,rN )
J.R. Nucl.Phys.A in print
rN - av. NN distance
rC - nucleon radius
if z(x) > rN
M(x) = MN
if z(x) < rC
M(x) = MB
Nuclear deep inelastic limit revisitedx dependent nucleon „rest” mass in NM
• Momentum Sum Rule violation
NNx
NNN
Vxf
MM
FxfxFxfx
2
)(1
))(1()()()( 22
22F
)1(]1)(
)(1
2
2
M
V
dxxF
dxxFA N
N
AAA
C[f
f(x) - probability that struck quark originated from correlated nucleon
M(x) & in RMF solution the nuclear pions almost
disappear
Nuclear sea is slightly enhanced in nuclear medium - pions have bigger mass according to chiral restoration scenario BUT also change sea quark contribution to nucleon SF
rather then additional (nuclear) pions appears
Because of Momentum Sum Rule in DIS
The pions play role rather on large distances?
Results
Fermi Smearing
Results
Fermi Smearing
Constant effective nucleon mass
Results“no” free paramerers
Fermi Smearing
Constant effective nucleon mass
x dependent effective nucleon mass
with G. Wilk Phys.Rev. C71 (2005)
Drell Yan Calculations
Good description due to the x dependence of nucleon mass
(no nuclear pions in Sum Rules)
The QCD vacuum
is the vaccum state of quark & gluon system. It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as
the gluon <gg> & quark <qq> condensates.
These condensates characterize the normal phase or the confined phase of quark matter.
Unsolved problems in physics: QCD in the non-perturbative regime: confinement The equations of QCD remain unsolved at energy scale relevant for describing atomic nuclei. How does QCD give rise to the physics of nuclei and nuclear constituents?
In vacuum
In nuclear medium
Phys.Rev.C45 1881
Derivative Coupling for scalars RMF Models ZMA. Delfino, CT Coelho and M. Malheiro, Phys. Rev. C51, 2188 (1995).
{Tensor coupling vector (Bender, Rufa)} Review J. R. Stone, P.-G. Reinhard nucl-th/0607002 (2006).
M. Baldo, Nuclear Methods and the Nuclear Equation of State (World Scientific, 1999)
Effective Mass in RMF
• W - Nucleon bare mass in the Walecka mean field approach
• ZM - constructed by changing of covariant derivative in W model. Langrangian describes the motion of baryons with effective mass and the density dependent scalar (vector) coupling constant.
ZM - Zimanyi Moszkowski
Relativistic Mean Field & EOSquark condensate < qq>m in the medium 0
• Delfino, Coelho, Malheiro
22
2
22
2
2
2
22)()1(
)(
1 *
*
m
g
MMMg
m
MMgm
fm NNN
NN
qqNm
fmeff
qq22
1
for models)
<qq>m
Condensate Ratios in RMF
SF - Evolution in Density“no” free parameters
Saturation density
SF - Evolution in Density“no” free parameters
Saturation density
Walecka ( density- 6 fm-3)
Stiff EOS
SF - Evolution in Density“no” free parameters
Saturation density
Soft EOS (density- .6 fm-3)
pions take 5% of nuclear
longitudinal momenta
Chiral instability
Walecka ( density- 6 fm-3)
Stiff EOS
EOS in NJL
• pion mass in the medium in chiral symmetry restoration
• Nucleon mass in the medium ?
Bernard,Meissner,Zahed PRC (1987)
EMC effect
MeVif 92222
• For such pionic cutoff Λ fluctuation of pion field pola shift the ground state out of magic circle to <σ2>=0 .
• In our model : Λ>700MeV for ρ=5ρ0 (chiral symmetry restoration)
• For NJL Chiral Restoration occures when Λ >0.8 Λq.. where Λq cutoff for quark momenta
• In our model : Λ >0.8 Λq for ρ=(4-5)ρ0 .
fi
222216/3
Estimate of Chiral StabilityH.Kleinert, B. Vanden Bossche Phys. Lett. B474 (2000)
Conclusions• Good fit to data for Bjorken x>0.1 by modfying the nucleon mass
in the medium (~24 MeV depletion) will correct the EOS for NM. Although such subtle changes of nucleons mass is difficult to measure inside nuclear medium due to final state interaction this reduction of nucleon mass is compatible with recent observation of similar reduction in Delta invariant mass in the decay spectrum to (N+Pion)T.Matulewicz Eur. Phys. J A9 (2000)
• (~ 1% only) of nuclear momentum is carried by sea quarks nuclear pions) due to x dependent effective nucleon mass supported by Drell-Yan nuclear experiments for higher densities increase for soft EOS towards chiral phase transition.
• Increase of the „additional nuclear pion mass” 5% means that nuclear density is about 2 times smaller than critical .
• x – dependent correction to the distribution• for higher density SF strongly depend from EOS• correction to effective NN interaction for high density?
kT2
x dependent nucleon effective mass
• it is possible to show that in DIS <kT2> M2
22 / TMediumT kk
In the x>0.6 limit
(no NN interaction)
<kT2> Nuclear= <kT
2> Nukleon
Bartelski Acta Phys.Pol.B9 (1978)
Dependence from initial in p-A collision
2kT
X-N Wang Phys. Rev.C (2000)
Chiral solitons in nuclei
Miller, Smith, Phys. Rev. Lett. 2003
0)()0(
( )()(_
5
rnriMeiL
EENM vCN
)(
)(arctan)(
r
rr
qs
qps
)'()'()()( '30 rrrrdrr v
svs
qs
)(
)(4
2
3
vsN
vsN
kNs
qMk
Mkd
F
)()()2()(
42
222
3
3
FBv
vFN
k
FB
km
gkMk
kd
kA
E F
nNnn
nNC xMpEMNxq |)()1(|)( 330
_
Chiral Quark Soliton Model Petrov- Diakonov So far effect to strong
Nuclear Vector Potential in DIS• Free Nucleon
ciq PJJPedW |)]0(),([|4 4
)()()(_
QJ
/)])([()( 22212Fq
qPq
qPF
q
qqgW
0,0
222/
1 |)()0()0()(|)(
PPQPQPedxF iMx
Quark inside nucleus
)()()())(( 0 nnn qVEqrmi
0,0
2
22/
~
1
|)()0(
)0()(|)(
PPQe
PQePedxF
iV
iViMx
QMC model
0,00
2
0
0
2
02/
~
1
|)()0(
)0()(|)(
PPQe
PQePedxF
iV
iViMx
Deep inelastic scattering
fixedMQxMxq
qQQvq
ScalingBjorkenxFqWM
qWqqMpqqMvp
MqWqqqgW
pJJpedW
pJXXJprqpW
Wld
T
T
v
iq
x
2/),0,0,(
),,0,0,(
)(),(lim)/(
),())/()()/((
/1),()/(
)0()(
)0()0()(
2
2222
22
2
22
22
221
2
4