SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia Contents Introduction Strongly Correlated Quark Model (SCQM) Spin in SCQM Single Spin Asymmetry Conclusions SPIN’04

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)

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

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

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)

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  

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.

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

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

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

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

The Proton

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:

SCQM The Local Gauge Invariance Principle 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 here

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

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. Explicit manifestation of these fluctuations is single diffraction. There are no strings stretched between quarks inside hadrons; 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

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

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 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.

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. 5. Quark spins are perpendicular to the plane of oscillation. 6. Quark spin module is conserved during oscillation: 2. Circulating flow of energy carrying along with it hadronic matter is associated with hadronic matter current.

7. At small displacements spins of both u – quarks inside the proton are predominantly parallel. 8. At large displacements there is a spin – flip of d and one of u quarks (according to spin-flavor SU(6)). 9. Velocity field is irrotational: Analogue from hydrodynamics ((∂ξ)/(∂t))+ ∇ ×(ξ×v)=0, ξ= ∇ ×v, This means the suggestion that sea quarks are not polarized

Single Spin Asymmetry in proton – proton collisions In the factorized parton model In our model the second term is dominating in SSA (Szwed mechanism)

Single Spin Asymmetry in proton – proton collisions

Collision of Vorticing Quarks Anti-parallel Spins Parallel Spins Single Polarized Quark

Experiments with Polarized Protons