Single Spin Asymmetry in Correlated Quark Model G. Musulmanbekov JINR, Dubnae-mail:genis@jinr.ru:

Single Spin Asymmetry in Correlated Quark Model G. Musulmanbekov JINR, Dubna e-mail:genis@jinr.ru Contents
Introduction
Strongly Correlated Quark Model (SCQM)
Single Spin Asymmetry in hadronic reactions
Collins Effect
Sivers Effect
Conclusions
SPIN2006

Introduction:

Introduction Where does the Proton Spin come from?
Spin "Crisis“:
DIS experiments: ΔΣ=Δu+Δd+Δs ≪ 1
SU(6) 1
Sum rule for the nucleon spin:
1/2 =(1/2)ΔΣ(Q²)+Δg(Q²)+L(Q2)q+g
SCQM:
Total nucleon spin comes from circulating
around each of three valence quarks gluon
and quark-antiquark condensate.

Strongly Correlated Quark Model (SCQM) :

Strongly Correlated Quark Model (SCQM)

Slide4:

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

Breather (soliton –antisoliton) solution of SG equation:

Breather (soliton –antisoliton) solution of SG equation

Slide6:

Hamiltonian of the Quark – AntiQuark System , are the current masses of quarks,
= (x) – the velocity of the quark (antiquark),
is the quark–antiquark potential.

Slide7:

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

Slide8:

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

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

The Proton:

The Proton One–Quark color wave function Where are orthonormal states with i = R,G,B Nucleon color wave function

Considering each quark separatelySU(3)Color U(1) :

Considering each quark separately SU(3)Color U(1)
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
chiral symmetry breaking (restoration)
here

Slide13:

Spin in SCQM Now we accept that Sch = c²Ech× Bch . 3. Total angular momentum created by this Pointing’s vector is associated with the total spin angular momentum of the constituent quark. and intersecting Ech and Bch create around VQ circulating flow of energy, color analog of the Pointing’s vector Classical analog of electron spin
– F.Belinfante 1939; R. Feynman 1964;
H.Ohanian 1986; J. Higbie 1988.
2. Circulating flow of energy carrying along with it hadronic matter is associated with hadronic matter current.

Slide14:

Analogue from hydrodynamics
Helmholtz laws for velocity field ((∂ξ)/(∂t))+∇×(ξ×v)=0, ξ=∇×v, ∇⋅v=0, 5. Quark spins are perpendicular to the plane of oscillation.
6. Quark spin module is conserved during oscillation: 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. lead to

Slide15:

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 vortical solitons.
Hadronic matter distribution inside hadrons is fluctuating quantity resulting in interplay between constituent and current quarks.
Hadronic matter distribution inside the nucleon is deformed;
it is oblate in relation to the spin direction.

Single Spin Asymmetry in proton – proton collisions:

Single Spin Asymmetry in proton – proton collisions In the factorized parton model where

Determination of PDFs:

Determination of PDFs

Geometrical view of possible quark configurations inside colliding protons at the instant of collision:

Geometrical view of possible quark configurations inside colliding protons at the instant of collision

Geometrical view of possible quark configurations inside colliding protons at the instant of collision:

Geometrical view of possible quark configurations inside colliding protons at the instant of collision

Slide22:

Determination of cross sections

Slide23:

Calculation of cross section with the use of Inelastic Overlap Fuction + energy – momentum conservation Monte-Carlo simulation of inelastic events
using modified Heisenberg picture:

Calculationsof Collins Effect:

Calculations of Collins Effect Pure Collins Effect: leading quark is a spectator

Collins Effect in SSA:

Collins Effect in SSA

Inclusion of “Sivers” Effect:

Inclusion of “Sivers” Effect

Slide27:

“Sivers” Effect in SSA Single Spin Asymmetries Spin-up polarized quark - vortex Chou & Yang 1976
Hadronic matter current distributions inside
polarized hadrons and nuclei

Slide28:

Collins & “Sivers” Effect in SSA Single Spin Asymmetries

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