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