the nucleon structure and the eos of nuclear matter jacek rozynek ins warsaw nuclear physics...

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


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-


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


• Gaussian distribution of quark momenta j

• Monte Carlo simulations

• Proton • Width - .18GeV

0 < (j+q) < W 0 < r < W’

W - invariant mass





• • 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)




• • 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


• 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

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

qq

qqNm

fmeff

qq

qq22

1

for models)

<qq>m

Condensate Ratios in RMF

SF - Evolution in Density“no” free parameters

Saturation density


Saturation density

Walecka ( density- 6 fm-3)

Stiff EOS


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

the nucleon structure and the eos of nuclear matter jacek rozynek ins warsaw nuclear physics...

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