1. Quark Correlations and 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

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)+L q (Q²)+Δg(Q²)+L g (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)+L q (Q²)+Δg(Q²)+L g (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)

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

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

6. 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

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

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

9. 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. is the potential energy of the quark.

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

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

12. Quark Potential inside Light Hadrons U q = 0.36tanh 2 (m 0 x) U q  x

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

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

17. Parameters of SCQM 2.Maximal Displacement of Quarks: x max =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

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: 1.Maximal displacement of quarks in hadrons x  0.64f 2.Sizes of the constituent quark:  x,y  0.24f,  z  0.12f Hadronic matter distributions inside nucleons are deformed (oblate).

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

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 E and B fields creates circulating flow of energy: S= ɛ₀ c²E×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.

22. Spin in SCQM 1. Now we accept that S ch = c²E ch × B ch. 3. Total angular momentum created by this Pointing’s vector is associated with the entire spin angular momentum of the constituent quark. and intersecting E ch and B ch create around VQ color analog of Pointing’s vector 4. Quark oscillations lead to changing of the values of E ch and B ch : 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. 2. Circulating flow of energy carrying along with it hadronic matter is associated with hadronic matter current.

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

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. Lund model Numerical Calculations of Collins Effect

27. Collins Effect in SSA

28. Single Spin Asymmetry in proton – proton collisions

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

30. Experiments with Polarized Protons