SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russiae-mail:genis@jinr.ru:

SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru Contents
Introduction
Strongly Correlated Quark Model (SCQM)
Spin in SCQM
Single Spin Asymmetry
Conclusions
SPIN’04

Introduction:

Introduction Where does the Proton Spin come from?
Spin "Crisis“:
DIS experiments: ΔΣ=Δu+Δd+Δs≪1
SU(6) 1
QCD sum rule for the nucleon spin:
1/2 =(1/2)ΔΣ(Q²)+Lq(Q²)+Δg(Q²)+Lg(Q²)
QCD angular momentum operator (X. Ji, PRL 1997):
SCQM All nucleon spin comes from circulating around each valence quarks gluon and quark-antiquark condensate (term 4)

Slide3:

Strongly Correlated Quark Model 1. 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

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 SCQM:

Summary on SCQM
Quarks and gluons inside hadrons are strongly correlated;
Constituent quarks are identical to solitons.
Hadronic matter distribution inside hadrons is fluctuating quantity resulting in interplay between constituent and current quarks.
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 (radiation field) on violation of vacuum homogeneity by embedded quarks.
Parameters of SCQM:
Maximal displacement of quarks in hadrons x 0.64f
Sizes of the constituent quark: x,y 0.24f, z 0.12f

Inelastic Overlap Function :

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

Spin in SCQM:

Spin in SCQM Our conjecture: spin of consituent quark is entirely
analogous to the angular momentum carried by
classical circularly polarized wave: Classical analog of electron spin – F.Belinfante 1939;
R. Feynman 1964; H.Ohanian 1986; J. Higbie 1988.
Electron surrounded by proper electric E and B
fields creates circulating flow of energy: S=ɛ₀c²E×B. Total angular momentum created by this Pointing’s vector is associated with the entire spin angular momentum of
the electron. Here if a = 2/3 r0.entiire mass of electron is
contained in its field.

Spin in SCQM:

Spin in SCQM Now we accept that Sch = c²Ech× Bch . 3. Total angular momentum created by this Pointing’s vector is associated with the entire spin angular momentum of the constituent quark. and intersecting Ech and Bch create around VQ color analog of Pointing’s vector 4. Quark oscillations lead to changing of the values of Ech
and Bch : at the origin of oscillations they are concentrated
in a small space region around VQ. As a result hadronic
current is concentrated on a narrow shell with small radius.
5. Quark spins are perpendicular to the plane of oscillation.
6. Quark spin module is conserved during oscillation: 2. Circulating flow of energy carrying along with it hadronic
matter is associated with hadronic matter current.

Slide22:

7. At small displacements spins of both u – quarks inside the proton are predominantly parallel.
8. At large displacements there is a spin – flip of d
and one of u quarks (according to spin-flavor SU(6)).
9. Velocity field is irrotational:
Analogue from hydrodynamics ((∂ξ)/(∂t))+∇×(ξ×v)=0, ξ=∇×v, This means the suggestion that sea quarks
are not polarized

Single Spin Asymmetry in proton – proton collisions:

Single Spin Asymmetry in proton – proton collisions In the factorized parton model In our model the second term is dominating
in SSA (Szwed mechanism)

Single Spin Asymmetry in proton – proton collisions:

Single Spin Asymmetry in proton – proton collisions

Collision of Vorticing Quarks:

Collision of Vorticing Quarks Anti-parallel Spins Parallel Spins Single Polarized Quark

Experiments with Polarized Protons:

Experiments with Polarized Protons

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