Quark Correlations and Single Spin Asymmetry G Musulmanbekov

Quark Correlations and Single Spin Asymmetry 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’ 05

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):

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)

What is Chiral Symmetry and its Breaking? • Chiral Symmetry SU(2)L × SU(2)R for ψL, R = u, d • The order parameter for symmetry breaking is quark or chiral condensate: <ψψ> ≃ - (250 Me. V)³, ψ = u, d • As a consequence massless valence quarks (u, d) acquire dynamical masses which we call constituent quarks MC ≈ 350 – 400 Me. V

Strongly Correlated Quark Model (SCQM) (x) Vacuum fluctuations (radiation) pressure Vacuum polarization around single quark Quark and Gluon Condensate Attractive Force

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

Interplay Between Current and Constituent Quarks Chiral Symmetry Breaking and Restoration Dynamical Constituent Mass Generation r j d=0. 64 t=0 d=0. 05 t = T/4 d=0. 05 d=0. 64 t = T/2

The Strongly Correlated Quark Model Hamiltonian of the Quark – Anti. Quark System , are the current masses of quarks, = (x) – the velocity of the quark (antiquark), is the quark–antiquark potential. is the potential energy of the quark.

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

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

Quark Potential inside Light Hadrons Uq = 0. 36 tanh 2(m 0 x) Uq x

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

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

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

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

Parameters of SCQM 1. Mass of Consituent Quark 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.

Structure Function of Valence Quarks in Proton

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. 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: 1. 2. • Maximal displacement of quarks in hadrons x 0. 64 f Sizes of the constituent quark: x, y 0. 24 f, z 0. 12 f Hadronic matter distributions inside nucleons are deformed (oblate).

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

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 r 0. entiire mass of electron is contained in its field.

Spin in SCQM 1. Now we accept that and intersecting Ech and Bch create around VQ color analog of Pointing’s vector Sch = c²Ech× Bch. 2. Circulating flow of energy carrying along with it hadronic matter is associated with hadronic matter current. 3. Total angular momentum created by this Pointing’s vector is associated with the entire spin angular momentum of the constituent quark. 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: Analogue from hydrodynamics ((∂ξ)/(∂t))+∇×(ξ×v)=0, ξ=∇×v, ∇⋅v=0, 7. At small displacements spins of both u – quarks inside the proton are predominantly parallel. 8. Velocity field is irrotational: This means that sea quarks are not polarized