On Nuclear Modification of Bound Nucleons On Nuclear Modification of Bound Nucleons G. Musulmanbekov JINR, Dubna, Russia Contents Introduction Strongly Correlated Quark Model Quark Arrangement inside Nuclei EMC – effect Color Transparency Conclusions

Introduction 1.EMC – effect F ₂ A (x)/F ₂ D (x) Regions of the effect * Shadowing * Antishadowing * EMC – effect * Fermi motion

Introduction 2.Color Transparency Quasielastic scattering p+A pp+X at θ cm =90 0 Observable: T = σ A /(Z σ N )

Introduction 2.Color Transparency Quasielastic scattering e+A e`p+X Observable: T = σ A / σ PWIA

Introduction 2.Color Transparency Exclusive electroproduction of ρ 0 in µA scattering Observable: T = σ A /(Aσ 0 ) Fit for specified Q 2 region: σ A = σ 0 A α Then T = A α-1

Introduction QCD Hadrons Nuclei Constituent QuarksCurrent Quarks Chiral Symmetry Breaking Quark Models Strongly Correlated Quark Model G.Musulmanbekov, 1995

What is Chiral Symmetry and its Breaking? Chiral Symmetry SU(3) L × SU(3) R for ψ L,R = u, d, s The order parameter for symmetry breaking is quark or chiral condensate: ≃ - (250 MeV)³, ψ = u,d,s. As a consequence massless valence quarks (u, d, s) acquie dynamical masses which we call constituent quarks M C ≈ 350 – 400 MeV

Strongly Correlated Quark Model (SCQM) 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 d=0.64 t = 0 d=0.20 d=0.05 t = T/4 d=0.64 t = T/2 d=0.20  

The Strongly Correlated Quark Model Hamiltonian of the Quark – AntiQuark System, are the current masses of quarks,  =  (x) – the velocity of the quark (antiquark), is the quark–antiquark potential. is the potential energy of the quark.

Conjecture: where is the dynamical mass of the constituent quark and For simplicity

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

Generalization to the 3 – quark system (baryons) 3 RGB, _ 3 CMY qqq _ ( 3) Color qq

The Proton

SCQM Chiral Symmerty Breaking Consituent Current Quarks Consituent Quarks Asymptotic Freedom Quarks t = 0 x = x max t = T/4 x = 0 t = T/2 x = x max During the valence quarks oscillations:

SCQM The Local Gauge Invariance Principle Destructive Interference of color fields  Phase rotation of the quark w.f. in color space: Phase rotation in color space dressing (undressing) of the quark  the gauge transformation here

Parameters of SCQM for Proton 2.Amplitude of VQs oscillations : x max =0.64 fm, 3.Constituent quark sizes (parameters of gaussian distribution):  x,y =0.24 fm,  z =0.12 fm 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 Breather – oscillating soliton-antisoliton pair, the periodic solution of SG: The evolution of density profile of the soliton- antisoliton pair (breather) is identical to that one of our quark-antiquark system.

Breather (soliton –antisoliton) solution of SG equation Soliton – antisoliton potential Here M is the soliton mass

Quark Potential Quark Potential U q  x U q = 0.36tanh 2 (m 0 x)

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 QCD 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

Three Nucleon Systems in SCQM 3H3H 3 He

The closed shell n = 0, nucleus 4 He p p n d d u u u u d u d He n u d d n 3 He + neutron or 3 H + proton p n n u d u u u d u d u u d d p d p d u u d d u u u d u d u d n p n Connections 1  1 2  2 3  3

Binding Energy and Sizes of Nuclei Nucleus E B, MeV 1/2, fm deuteron H He He He 29.27

Hidden Color in Nuclei Deuteron |6q> = c 1 |SS> + c 2 |CC> c 1 c 2 deuteron (6q) 15% 85% triton (9q) 9% 91% 4 He (12q) 2% 98%

The closed shell n = 1, 16 O He n d d u p d u u p u d u p d u u p u u d u n d d n d du p u d u n d d u 3H3H d u n d u p d u n d d u 3H3H 1 3 2

The closed shell n = 1, 16 O

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

Face – Centered – Cubic Lattice n=(x + y +z – 3)/2 = (r sin  cos  + r sin  sin  + r cos  - 3) / 2 j = l + s = (x + y – 1) / 2 = (r sin  cos  + r sin  sin  m = x / 2 = (r sin  cos 

Conjecture: Current quark states in bound nucleons are suppressed Bound Nucleon, N * suppressed Bound Nucleon, N *

Method: Monte–Carlo Simulation 1. The Model of DIS: SCQM + VDM

 Heisenberg inequality: 2. Calculation of cross sectons  Inelastic Overlap Function:

Parameters of SCQM Free Nucleon  Amplitude of VQs oscillations:  x max = 0.64 fm Bound (distorted) nucleon:  Reduced amplitude of VQs oscillations  Displacement of the origin of VQs oscillations to the nucleon perephery Adjusted values: x min = 0.32 fm, x max = 0.64 fm

Comparison with experiments 1. EMC – effect

Comparison with experiments 2.Color Transparency “Breaking” in quasielastic scattering p+A pp+X at θ cm =90 0 Observable: T = σ A /(Z σ N )

Conclusions EMC effect could be explained by valence quark momentum distribution reaggangements. Quasielastic proton – proton and lepton – proton scattering at high Q 2 are not adequate reactions to observe Color Transparency Favorable reaction for CT observation is the Vector meson production in lepton – nucleus scattering at Q 2