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Dynamical Model of Hadron Structure and Diffractive Processes G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru: 

Dynamical Model of Hadron Structure and Diffractive Processes G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru Contents Introduction Strongly Correlated Quark Model (SCQM) SCQM and Diffractive Processes

Introduction: 

Introduction

Slide3: 

Constituent Quarks – Solitons Sine- Gordon equation Breather – oscillating soliton-antisoliton pair, the periodic solution of SG: The density profile of the soliton-antisoliton pair (breather) Effective soliton – antisoliton potential

Breather (soliton –antisoliton) solution of SG equation: 

Breather (soliton –antisoliton) solution of SG equation

What is Chiral Symmetry and its Breaking?: 

What is Chiral Symmetry and its Breaking? Chiral Symmetry U(3)L × U(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) acquire 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.

Slide9: 

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

Slide10: 

I II U(x) > I – constituent quarks U(x) < II – current(relativistic) quarks Quark Potential and “Confining Force” inside Light Hadons

Quark Potential inside Light Hadrons: 

Quark Potential inside Light Hadrons Uq = 0.36tanh2(m0x) Uq  x

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

Chiral Symmerty Breaking and its Restoration: 

Chiral Symmerty Breaking and its Restoration 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

Slide16: 

Parameters of SCQM 2.Maximal Displacement of Quarks: 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

Structure Function of Valence Quarks in Proton: 

Structure Function of Valence Quarks 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. Explicit manifestation of these fluctuations is single diffraction. There are no strings stretched 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.

SCQM and Diffractive Processes 1. Hadronic Collisions: 

SCQM and Diffractive Processes 1. Hadronic Collisions The probability of finding any quark configuration inside a hadron Possible quark configurations inside colliding hadrons

Inelastic Overlap Function : 

Inelastic Overlap Function + energy – momentum conservation Monte-Carlo Simulation of Inelastic Events

Inelastic Overlap Functions for (anti)proton – proton collisions: 

Inelastic Overlap Functions for (anti)proton – proton collisions

Cross Sections: 

Cross Sections Total Cross Section Single Diffraction Cross Section

Deep Inelastic Scattering: 

Deep Inelastic Scattering SCQM + VDM

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