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Quark Correlations and Single Spin Asymmetry G. Musulmanbekov JINR, Dubna, Russiae-mail:genis@jinr.ruContents

IntroductionStrongly Correlated Quark Model (SCQM)Spin in SCQMSingle Spin AsymmetryConclusions

SPIN05

IntroductionWhere does the Proton Spin come from?

Spin "Crisis:DIS experiments: =u+d+s1SU(6) 1

QCD sum rule for the nucleon spin:1/2 =(1/2)(Q)+Lq(Q)+g(Q)+Lg(Q)

QCD angular momentum operator (X. Ji, PRL 1997):

IntroductionWhere does the Proton Spin come from?

Spin "Crisis:DIS experiments: =u+d+s 1SU(6) 1

QCD sum rule for the nucleon spin:1/2 =(1/2)(Q)+Lq(Q)+g(Q)+Lg(Q)

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 SymmetrySU(2)L SU(2)R for L,R = u, dThe order parameter for symmetry breaking is quark or chiral condensate: - (250 MeV), = u,d As a consequence massless valence quarks (u, d) acquire dynamical masses which we call constituent quarksMC 350 400 MeV

Strongly Correlated Quark Model (SCQM)

Strongly Correlated Quark Model1. Constituent Quarks Solitons Sine- Gordon equationBreather 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 jr

The Strongly Correlated Quark ModelHamiltonian of the Quark AntiQuark System , are the current masses of quarks, = (x) the velocity of the quark (antiquark), is the quarkantiquark potential.

Conjecture:

where is the dynamical mass of the constituent quark and

IIIU(x) > I constituent quarksU(x) < II current(relativistic) quarks Quark Potential and Confining Force inside Light Hadons

Quark Potential inside Light HadronsUq = 0.36tanh2(m0x) Uq x

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

The ProtonOneQuark color wave functionWhere are orthonormal states with i = R,G,B Nucleon color wave function

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

Chiral Symmerty Breaking and its RestorationConsituent Current Quarks Consituent Quarks Asymptotic Freedom Quarkst = 0x = xmaxt = T/4x = 0t = T/2x = xmaxDuring the valence quarks oscillations:

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. 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. 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 0.64fSizes of the constituent quark: x,y 0.24f, z 0.12f Hadronic matter distributions inside nucleons are deformed (oblate).

Inelastic Overlap Function + energy momentum conservationMonte-Carlo Simulation of Inelastic Events

Spin in SCQMOur 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=cEB.Total angular momentum created by this Pointings vectoris associated with the entire spin angular momentum of the electron. Here if a = 2/3 r0.entiire mass of electron is contained in its field.

Spin in SCQM Now we accept that Sch = cEch Bch .3. Total angular momentum created by this Pointings vectoris associated with the entire spin angular momentum of the constituent quark. and intersecting Ech and Bch create around VQ color analog of Pointings vector4. 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.

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. Velocity field is irrotational:

Analogue from hydrodynamics(()/(t))+(v)=0,=v,v=0,This means that sea quarks are not polarized5. Quark spins are perpendicular to the plane of oscillation.

6. Quark spin module is conserved during oscillation:

Single Spin Asymmetry in proton proton collisionsIn the factorized parton modelwhere

Single Spin Asymmetry in proton proton collisionsIn the factorized parton modelwhere

Numerical Calculationsof Collins EffectLund model

Collins Effect in SSA

Single Spin Asymmetry in proton proton collisions

Collision of Vorticing QuarksAnti-parallel Spins Parallel Spins Single Spin Asymmetries Double Spin Asymmetries

Experiments with Polarized Protons