On Nuclear Modification of Bound On Nuclear Modification of Bound NucleonsNucleons

G. Musulmanbekov JINR, Dubna, Russiae-mail:genis@jinr.ru

Contents•Introduction•Strongly Correlated Quark Model•Quark Arrangement inside Nuclei•EMC – effect •Color Transparency•Conclusions

Introduction

1. EMC – effect F₂A(x)/F₂D(x)

Regions of the effect * Shadowing * Antishadowing * EMC – effect * Fermi motion

Introduction

2. Color Transparency Quasielastic scattering

p+A pp+X at θcm=900

Observable:

T = σA/(Z σN)

4 6 8 10 12 14 160,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

Tra

nspa

renc

y

Beam Momentum, GeV/c

Introduction

2. Color Transparency Quasielastic scattering

e+A e`p+X

Observable:

T = σA/ σPWIA

Introduction

2. Color Transparency

Exclusive electroproduction of ρ0 in µA scattering

Observable: T = σA/(Aσ0)

Fit for specified Q2 region: σA = σ0Aα

Then T = Aα-1

Introduction

QCDQCD

Hadrons

Nuclei

Constituent Quarks Current Quarks

Chiral Symmetry BreakingChiral Symmetry Breaking

Quark ModelsQuark Models

Strongly Correlated Quark ModelG.Musulmanbekov, 1995

What is Chiral Symmetry and its Breaking?

• Chiral Symmetry

SU(3)L × SU(3)R for ψL,R = u, d, s

• The order parameter for symmetry breaking is quark or chiral condensate:

<ψψ> - (250 MeV)³, ψ = ≃ u,d,s.

• As a consequence massless valence quarks (u, d, s) acquie dynamical masses which we call constituent quarks

MC ≈ 350 – 400 MeV

Strongly Correlated Quark Model

(SCQM)

Attractive Force

Attractive Force

Vacuum polarization around single quark

Quark and Gluon Condensate

Vacuum fluctuations(radiation) pressure

Vacuum fluctuations(radiation) pressure

(x)

Interplay Between Current and Constituent Quarks Chiral Symmetry Breaking and Restoration Dynamical Constituent Mass Generation

2 0 21

0

1

x, fermi

Po

lari

zati

on

Fie

ld

2 0 20

0.5

1

x, fermi

Had

ron

ic M

att

er

Dis

trib

uti

on

d=0.64

t = 0

2 0 21

0

1

x, fermi

Po

lari

zati

on

Fie

ld

2 0 20

0.5

1

x, fermi

Had

ron

ic M

att

er

Dis

trib

uti

on

d=0.20

2 0 21

0

1

x, fermi

Po

lari

zati

on

Fie

ld

2 0 20

0.5

1

x, fermi

Had

ron

ic M

att

er

Dis

trib

uti

on

d=0.05

2 0 21

0

1

x, fermi

Po

lari

zati

on

Fie

ld

2 0 20

0.5

1

x, fermi

Had

ron

ic M

att

er

Dis

trib

uti

on

d=0.05

t = T/4

2 0 21

0

1

x, fermi

Po

lari

zati

on

Fie

ld

2 0 20

0.5

1

x, fermi

Had

ron

ic M

att

er

Dis

trib

uti

on

d=0.64 t = T/2

2 0 21

0

1

x, fermi

Po

lari

zati

on

Fie

ld

2 0 20

0.5

1

x, fermi

Had

ron

ic M

att

er

Dis

trib

uti

on

d=0.20

The Strongly Correlated Quark Model

Hamiltonian of the Quark – AntiQuark System

)2()1()1( 2/122/12 xV

mmH

qqq

q

q

q

, are the current masses of quarks, = (x) – the velocity of the quark (antiquark), is the quark–antiquark potential.

qm qm

qqV

)(

)1()(

)1( 2/122/12 xUm

xUm

Hq

q

q

q

)2(2

1)( xVxU

qq is the potential energy of the

quark.

Conjecture:

),(2),()(2 xMrxxdydzdxU Q

where is the dynamical mass of the constituent quark and

)()(

xMQQ

),,(),,(

),(),(

zyxxzyxxC

rxCrx

QQ

QQ

For simplicity

XAXA

rT

exp)(det

)(2/3

2/1

Quark Potential

I

II

U(x) > I – constituent quarksU(x) < II – current(relativistic) quarks

Generalization to the 3 – quark system (baryons)

ColorSU )3(

3 RGB,

_ 3 CMY

qq 1 33-

qqq 3 3

3

3

3

31- -

-

_ ( 3)Color

qq

The Proton

SCQM Chiral Symmerty Breaking

Consituent Current Quarks Consituent Quarks Asymptotic Freedom Quarks

t = 0x = xmax

t = T/4x = 0

t = T/2x = xmax

During the valence quarks oscillations:

...321332123211 gqqqcqqqqqcqqqcB

SCQM The Local Gauge

Invariance Principle  

Destructive Interference of color fields Phase rotation of the quark w.f. in color space:

Colorxig

Color xex )()( )(

Phase rotation in color space dressing (undressing) of the quark the gauge transformation );()()( xxAxA here

)0,0,0,( A

Parameters of SCQM for Proton

tot pp_

2.Amplitude of VQs oscillations : xmax=0.64 fm,

3.Constituent quark sizes (parameters of gaussian distribution): x,y=0.24 fm, z =0.12 fm

,36023

1)( max)(

MeVmm

xM NQQ

Parameters 2 and 3 are derived from the calculations of Inelastic Overlap Function (IOF) and in and pp – collisions.

1.Mass of Consituent Quark

Constituent Quarks – Solitons SCQM Breather Solution of Sine- Gordon

equation 0),(sin),( txtx

Breather – oscillating soliton-antisoliton pair, the periodic solution of SG:

2

21

1/cosh

1/sinhtan4),(

uxu

uuttx ass

The evolution of density profile of the soliton-antisoliton pair (breather)

x

txtx ass

ass

),(),(

is identical to that one of our quark-antiquark system.

Breather (soliton –antisoliton) solution of SG equation

Soliton – antisoliton potential

)(tanh2)( 2 mxMxV

Here M is the soliton mass

Quark PotentialQuark Potential

Uq xUq = 0.36tanh2(m0x)

Structure Function of Valence Quark in Proton

Summary on Quarks in Hadrons

  

• Quarks and gluons inside hadrons are strongly correlated;

• Hadronic matter distribution inside hadrons is fluctuating quantity;

• There are no strings stretching between quarks inside hadrons;

• Strong interactions between quarks are nonlocal: they emerge as the vacuum response on violation of vacuum homogeneity by embedded quarks;

• Maximal displacement of quarks in hadrons x 0.64f

• Sizes of the constituent quark: x,y 0.24f, z

0.12f

• Constituent quarks are identical to solitons.

Quark Arrangement inside Nuclei

QCDQCD

Hadrons Nuclei

Nuclear Models

Shell Models

Liquid Drop Model

Crystalline Models of Nuclei

Cluster Models

Two Nucleon System in SCQM

Quark Potential Inside Nuclei

Deutron

Spin Flip l = 2

qcNcNcD 622 3*

21

Three Nucleon Systems in SCQM

3H

3He

The closed shell n = 0, nucleus 4He

pp

n

d

d uu

u

u

d u

d

1

2 3

3He

4 5

6

n

u

d d

1

2 3

n

3He + neutron or 3H + proton

p n

n

u

du

u

u d

u

d

u

udd

12

3

6 5

4

pd

pd

u

ud

du

u

u

d u

d

u

5

6

2

13

dn

p

n

Connections 1 1 2 2 3 3

Binding Energy and Sizes of Nuclei

Nucleus EB, MeV < r2 >1/2, fm

deuteron 2.22 2.4

3H 8.48 1.7

3He 7.72 1.88

4He 28.29 1.67

6He 29.27

Hidden Color in Nuclei

Deuteron|6q> = c1|SS> + c2|CC>

c1 c2

deuteron

(6q)

15% 85%

triton

(9q)

9% 91%

4He

(12q)

2% 98%

The closed shell n = 1, 16O

6

1

3He

ndd

u

pd

u

up

u d

u

3He

p

d

uu

pu

u

d

u

nd d

n

d

dup

u d

u

n

d

du

3H

54

32

d un

d

up

d

u

n

d

du

3H

1

32

The closed shell n = 1, 16O

3

6

5

2

4

Face – Centered – Cubic Lattice Model (FCC) (N. Cook, 1987)

Face – Centered – Cubic Lattice

n - value j - value m - value

s - value i - value - clusters

40Ca

n=(x + y +z – 3)/2 =(r sincos + r sin sin + r cos - 3) / 2

j = l + s = (x + y – 1) / 2 = (r sincos + r sin sin

m = x / 2 = (r sincos

Conjecture: Current quark states in bound nucleons are suppressed

...321332123211* gqqqcqqqqqcqqqcN

)(/)()(/)( 22 xdxdxFxF DADA

Bound Nucleon, N*

suppressed

),(/)()(/)(**

22 xdxdxFxF NNNN

Bound Nucleon, N*

Method: Monte–Carlo Simulation

1. The Model of DIS: SCQM + VDM

Xpqqp

22 1

Qr qq

p

sxxM 212

Heisenberg inequality:

2. Calculation of cross sectons

Inelastic Overlap Function:

b2),(112)( dbsGs intot

Parameters of SCQM

Free Nucleon

Amplitude of VQs oscillations: xmax= 0.64 fm

Bound (distorted) nucleon:

Reduced amplitude of VQs oscillations

Displacement of the origin of VQs oscillations to the nucleon perephery

Adjusted values:xmin= 0.32 fm, xmax= 0.64 fm

Comparison with experiments

1. EMC – effect

)(/)( 22 xFxF DA

Comparison with experiments

2. Color Transparency “Breaking” in quasielastic scattering

p+A pp+X at θcm=900

Observable:

T = σA/(Z σN)

Conclusions

• EMC effect could be explained by valence quark momentum distribution reaggangements.

• Quasielastic proton – proton and lepton – proton scattering at high Q2 are not adequate reactions to observe Color Transparency

• Favorable reaction for CT observation is the Vector meson production in lepton – nucleus scattering at Q2