1. Single Spin Asymmetry in Correlated Quark Model 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

2. 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(Q 2 ) q+g SCQM: Total nucleon spin comes from circulating around each of three valence quarks gluon and quark-antiquark condensate.

3. 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)

4. 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

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

6. 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.

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

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

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

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

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

12. 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

13. 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 total spin angular momentum of the constituent quark. and intersecting E ch and B ch 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.

14. Analogue from hydrodynamics Helmholtz laws for velocity field ((∂ξ)/(∂t))+ ∇ ×(ξ×v)=0, ξ=∇×v,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 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. lead to

15. 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

16. Structure Function of Valence Quarks in Proton

17. 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.

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

19. Determination of PDFs

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

22. Determination of cross sections

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

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

25. Collins Effect in SSA

26. Inclusion of “Sivers” Effect

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

28. Collins & “Sivers” Effect in SSA Single Spin Asymmetries

29. Experiments with Polarized Protons Anti-parallel Spins Double Spin Asymmetries Parallel Spins

30. Experiments with Polarized Protons