Musulm anbekov

On Nuclear Modification of Bound NucleonsG. Musulmanbekov JINR, Dubna, Russiae-mail:genis@jinr.ru: 

On Nuclear Modification of Bound Nucleons G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru Contents Introduction Strongly Correlated Quark Model Quark Arrangement inside Nuclei EMC – effect Color Transparency Conclusions

Introduction: 

Introduction EMC – effect F₂A(x)/F₂D(x) Regions of the effect * Shadowing * Antishadowing * EMC – effect * Fermi motion

Introduction: 

Introduction Color Transparency Quasielastic scattering p+A pp+X at θcm=900 Observable: T = σA/(Z σN)

Introduction: 

Introduction Color Transparency Quasielastic scattering e+A e`p+X Observable: T = σA/ σPWIA

Introduction: 

Introduction 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: 

Introduction

What is Chiral Symmetry and its Breaking?: 

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: andlt;ψψandgt; ≃ - (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) : 

Strongly Correlated Quark Model (SCQM)

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

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

The Strongly Correlated Quark Model: 

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.

Slide11: 

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

Quark Potential: 

Quark Potential I II U(x) andgt; I – constituent quarks U(x) andlt; II – current(relativistic) quarks

Generalization to the 3 – quark system (baryons): 

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

The Proton: 

The Proton

SCQM Chiral Symmerty Breaking : 

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

SCQM The Local Gauge Invariance Principle  : 

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

Slide17: 

Parameters of SCQM for Proton 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 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 : 

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: 

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

Quark Potential : 

Quark Potential Uq  x Uq = 0.36tanh2(m0x)

Structure Function of Valence Quark in Proton: 

Structure Function of Valence Quark in Proton

Summary on Quarks in Hadrons: 

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: 

Quark Arrangement inside Nuclei Nuclear Models

Two Nucleon System in SCQM: 

Two Nucleon System in SCQM Quark Potential Inside Nuclei

Deutron: 

Deutron

Three Nucleon Systems in SCQM : 

Three Nucleon Systems in SCQM 3H 3He

The closed shell n = 0, nucleus 4He : 

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

Binding Energy and Sizes of Nuclei: 

Binding Energy and Sizes of Nuclei

Hidden Color in NucleiDeuteron|6q> = c1|SS> + c2|CC>: 

Hidden Color in Nuclei Deuteron |6qandgt; = c1|SSandgt; + c2|CCandgt;

The closed shell n = 1, 16O : 

The closed shell n = 1, 16O

The closed shell n = 1, 16O: 

The closed shell n = 1, 16O

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

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

Face – Centered – Cubic Lattice: 

Face – Centered – Cubic Lattice n=(x + y +z – 3)/2 = (r sinq cosf + r sinq sinf + r cosq - 3) / 2 j = l + s = (x + y – 1) / 2 = (r sinq cosf + r sinq sinf - 1) / 2 m = x / 2 = (r sinq cosf) / 2

Conjecture: Current quark states in bound nucleons are suppressed: 

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

Method: Monte–Carlo Simulation : 

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

Slide36: 

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

Slide37: 

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: 

Comparison with experiments 1. EMC – effect

Comparison with experiments: 

Comparison with experiments Color Transparency 'Breaking' in quasielastic scattering p+A pp+X at θcm=900 Observable: T = σA/(Z σN)

Conclusions: 

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