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Contents Introduction Strongly Correlated Quark Model (SCQM) Spin in SCQM Single Spin Asymmetry

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“:

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Contents Introduction Strongly Correlated Quark Model (SCQM) Spin in SCQM Single Spin Asymmetry

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  1. Quark Correlations and Single Spin Asymmetry G. MusulmanbekovJINR, Dubna, Russiae-mail:genis@jinr.ru Contents Introduction Strongly Correlated Quark Model (SCQM) Spin in SCQM Single Spin Asymmetry Conclusions SPIN’05

  2. 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):

  3. 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): SCQMAll nucleon spin comes from circulating around each valence quarks gluon and quark-antiquark condensate (term 4)

  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 MeV)³, ψ = u,d • As a consequence massless valence quarks (u, d) acquire dynamical masses which we call constituent quarks MC ≈ 350 – 400 MeV

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

  6. Strongly Correlated Quark Model1. 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

  7. Breather (soliton –antisoliton) solution of SG equation

  8. d=0.64 t = 0 d=0.05 t = T/4 d=0.05 d=0.64 t = T/2 Interplay Between Current and Constituent Quarks Chiral Symmetry Breaking and Restoration Dynamical Constituent Mass Generation r j

  9. is the potential energy of the quark. 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.

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

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

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

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

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

  15. Considering each quark separatelySU(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

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

  17. 1.Mass of Consituent Quark 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.

  18. Structure Function of Valence Quarks in Proton

  19. 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: • Maximal displacement of quarks in hadrons x 0.64f • Sizes of the constituent quark: x,y  0.24f, z 0.12f • Hadronic matter distributions inside nucleons are deformed (oblate).

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

  21. 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 Eand 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 ofelectron is contained in its field.

  22. Spin in SCQM • Now we accept that and intersecting Echand Bchcreate around VQcolor 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.

  23. 5. Quark spins are perpendicular to the plane of oscillation. • 6. Quark spin module is conserved during oscillation: Analogue from hydrodynamics 7. At small displacements spins of both u – quarks inside the proton are predominantly parallel. 8. Velocity field is irrotational: ((∂ξ)/(∂t))+∇×(ξ×v)=0, ξ=∇×v, ∇⋅v=0, This means that sea quarks are not polarized

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

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

  26. Numerical Calculationsof Collins Effect Lund model

  27. Collins Effect in SSA

  28. Single Spin Asymmetry in proton – protoncollisions

  29. Collision of Vorticing Quarks Single Spin Asymmetries Double Spin Asymmetries Anti-parallel Spins Parallel Spins

  30. Experiments with Polarized Protons

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