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Single-spin physics: experimental trends and their origin

Single-spin physics: experimental trends and their origin. V.V. Abramov Institute for High Energy Physics, Protvino, Russia. Outline. Introduction SSA and hadron polarization origin Data trends and model predictions Summary. Introduction.

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Single-spin physics: experimental trends and their origin

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  1. Single-spin physics: experimental trends and their origin V.V. Abramov Institute for High Energy Physics, Protvino, Russia

  2. Outline Introduction SSA and hadron polarization origin Data trends and model predictions Summary

  3. Introduction Globalanalysis of data:AN, PN, ρ00 & α = (σT – 2σL)/(σT + 2σL). (68 inclusive reactions for hh, hA, AA & lN-interactions). A↑ + B → C + X {Analyzing power, AN(pT, xF,√s) }. A + B → C↑ + X {polarization of C, PN(pT, xF,√s) }. In pQCD single-spin effects are small:AN SmQ/EQ  1%. The observed spin effects are much higher the pQCD predictions. Models: Sivers; Collins; Szwed;orbital quark motion (Liang Zuo-tang and C. Boros,Troshin, Tyurin et al.); semi-classical mechanisms (Anderson, De-Grand, Ryskin et al.). None of them is able to explain the experimental trends for the full set of the data. Single-spin processes.

  4. The global analysis The global analysis of single-spin data allows to reveal general regularities and data trends, which are otherwise not seen. To reveal and explain these regularities and the data trends in the framework of common mechanism, the effective color field model was developed. Data base for single-spin inclusive reactions was created in a unified format. It contains now data for 68 different reactions with more then 2100 data points and continue to grow. As a result of global analysis, many interesting phenomena have been found and they are explained below within framework of semi-classical mechanism of the effective color field model.

  5. Origin of SSA phenomena A semi-classical mechanism is proposed for single-spin phenomena. Effective color field (ECF, chromomagnetic & chromoelectric) is a superposition of string fields, created by moving spectator quarks & antiquarks after initial color exchange and new quark production. Constituent probe quark Q from the detected hadron interacts with non-uniform color field via its chromomagnetic moment μaQand its color charge gS. Microscopic Stern-Gerlach effect in chromomagnetic field and Thomas spin precession in chromoelectric field lead to SSA. ECF is considered as an external with respect to quark Q in observed hadron. Quark spin precession (BMT) in ECF is an additional phenomenon, which leads to a specific SSA dependence (oscillation) as a function of kinematical variables (xF, pT or scaling variables xA(B)=(xR±xF)/2).

  6. Color field between quark and antiquark There are longitudinal chromo-electric field Ea and a circular chromomagnetic field Ba. μaQ = sggs/2MQ – chromomagnetic constituent quark moment. A.B.Migdal, S.B.Khohlachev, JETP Lett. 41, 194 (1985). Also, Yu.Goncharov, Int.J.Theor.Phys.49, 1155 (2010). Field dependence on the distance rfrom the string axis: E(3)Z = -2αsνA /ρ2 exp(-r2/ρ2), (1) B(2)φ = -2αsνAr/ρ3 exp(-r2/ρ2), (2) where νA – number of quarks, ρ=1.25RC  2.08GeV-1, RC-1  0.6 GeV, RC –confinement radius,αs= gs2/4π 1.

  7. Stern-Gerlach-like force acts on a quark moving inside QCD string (flux tube) fx ≈ μax ∂Bax/∂x + μay ∂Bay/∂x(3) fy ≈ μax ∂Bax/∂y + μay ∂Bay/∂y.(4) SPECTATORS • Quark Q from the observed hadron C, which has pT kick of S-G force & spin precession is called a probe and it measures Ва& Ea. Ea~Ba ~ [2 + 2λ - 3τ λ ] Quark counting rules Effective color field (ECF): • Spectators are all quarks which are not constituents of hadron C. • In case of reaction pp→Ξ0+X theprobe s & u quarks from Ξ0 “feel” field, created by spectator quarks with weight νA= λ, created by antiquarks with νA= 1, and by target quarks with νB= -τλ, respectively. • λ = − |ψqq(0)|2 /|ψqq̃(0)|2 1-e1/8  -0.133color factor (5) • λ = −0.1321±0.0012, τ = 0.0562±0.0030 for 68 reactions.

  8. Quark spin precession in string field dξ/dt≈ a[ξBa] + d[ξ [Eav]] (BMT-equation) (6) • a = gs(gaQ – 2 + 2MQ/EQ)/2MQ (mass MU ≈ MD ≈ 0.3 ГэВ) (7) • d = gs[gaQ – 2EQ/(EQ+MQ)]/2MQ (EQ is Q energy) (8) • ΔμaQ =(gaQ-2)/2(quark anomalous chromomagnetic moment). • Spontaneous chiral symmetry breaking leads to non-zero additional dynamical quark massΔMQ(q)&ΔμaQ(q). • In instanton model:ΔμaQ (0) ≈ –0.2 (N. Kochelev, 1998); • ΔμaQ (0) ≈ –0.744(D. Diakonov, 2003). • Both,ΔMQ(q) & ΔμaQ(q) tend to zero when q → ∞. • The second term in (6) is due to Thomas spin precession in Ea.

  9. Additional transverse momentum of quark Q is due to Stern-Gerlach type force in ECF Due to microscopic Stern-Gerlach effect quark Q gets an additional spin-dependent transverse momentum δpx, which causes an azimuthal asymmetry AN or transverse hadron polarization PN. δpx =gaQξ0y[(1 – cosφA)/φA + εφA]/2ρ/(gaQ – 2 + 2MQ/EQ),(9) φA= ωAxA spin precession angle in the fragmentation region of A. ωA= gsαsνAS0(gaQ – 2 + 2MQ/EQ)/(MQcρ2)«frequency» (10) xA(B)= (xR± xF)/2scaling variables (11) S0 ≈ 0.6 ± 0.2 fm (ECF length); ε = -0.00419 ± 0.00022. εis small due to subtraction of Thomas precession term from ε = 1/2 for chromomagnetic contribution to the δpx.

  10. Dependence of AN & PN on xF & pT AN≈ -δPxD; Fermi relation (Ryskin, 1988) (12) D≈ –∂/∂pT ln(d3σ/d3p); D = 5.68 ± 0.13 GeV–1(13) • In Ryskin modelδPx≈ 0.1 GeV/с is constant. • In the ECF model we have a dynamical origin of δPxdependence on kinematical variables (pT, xA(B), xF) & on a number of (anti)quarks in hadrons A, B & C, and also on quark colorgaQ–factor and its mass MQ. • This dependence is due to microscopic Stern-Gerlach mechanism and quark spin precession in the ECF.

  11. Generalized equations forAN&PN AN ≈C(√s)V(xF)F(pT,A)[G(φA) – σG(φB) ], (14) G(A) = [1 – cos A]/A + εφA, spin precession&S-G force.(15) C (√s) = v0/(1 – ER/√s), quark focusing in the ECF(16) F(pT,A) = {1 – exp[-(pT/p0T)3 ]}(1 – α lnA).Color form factor(17) ξ0y ≡ V(xF) ≈ ±θ(xF-x0) - u &d– polarization in a proton.(18) In totalthere are 8local parameters for each particular reaction: α, σ,E0, ER, f0, a0,x0,p0T.On average, 2 out of 8 can be written as functions of global parameters.Phys. At. Nucl. 72 (2009) 1872. There are 41 global parameters for 68 reaction (ε, λ,τ, MQ, ΔμaQ …).

  12. The meaning of φA &φB precession angles Precession angle φA(B)“measures”colorfield integral in the fragmentation region of hadron A(B). φA= ωAxA≈ ω0AyA = precession angle A (19) φB= ωBxB ≈ ω0ByB = precession angle B (20) whereω0A(B)= gsαsνA(B)S0(gaQ – 2)/(MQcρ2) - the limit of ωA(B) at high quark energy EQ. Variable yA(B)takes into account the quark motion inside proton and spin precession in the ECF: yA =xA – (E0/√s + f0)[1 +cosθcm ]+ a0[1 –cosθcm ],(21) yB =xB – (E0/√s + f0)[1 –cosθcm ] + a0[1 + cosθcm ],(22) where a0, f0 &E0– phenomenological parameters.

  13. Quark focusing in ECFBa Thedependenceof C(√s)= v0/(1 – ER/√s), AN and PN is due to focusing properties of circular chromomagnetic field Ba. Focusing Lorentz force F = gs[vBa]Ia leads to the prolongation of probe quark stay in a color field and enhance polarization effects in case of ER > 0. For opposite field direction we have a defocusing effect, ER < 0 and there is a decrease of AN or PN. The focusing effect is similar the one used in a Tokamak type thermonuclear reactor to keep plasma away off reactor’s walls.

  14. An example of quark focusing in field Ba p↑ + p(A) → π+ + X, focusingeffect when 0A = 1.85> 0; √s< 70 GeV ER = 3.31± 0.09 GeV √s= 200 GeV defocusing effect when 0A -11 <0 1/C(√s)~ (1-ER/√s); √s0 = 100GeV E704 √s =19.4GeV FODS-2 √s =8.77GeV √s =200GeV, BRAHMS √s =4.89GeV, BNL

  15. An example of quark defocusing in field Ba p +p(A) → Λ↑ + X, defocusingeffect when 0A = −2.41 < 0; ER = −2.95± 0.30 GeV Au+Au → Λ↑ + X, focusingeffect when 0A = +44.78 >0; √sNN =4.86GeV; ER =+4.805 ±0.016 GeV √s =4.86GeV, BNL √s =200GeV, STAR √s0 = 100ГэВ

  16. Dependence of frequency ω0A and ECF on √sand atomic weights A1, A2 At high energy √s new quark and antiquark production changes the ECF intensity. In case of ion collisions the effective number of spectator quarks in a projectile nucleus is equal to its number in a tube with transverse radius limited by the confinement: qA = 3(1+fN)Aeff ~ 3(1+fN)A1/3 (23) q̃A = 3fNAeff ~ 3fNA1/3 (24) New quark contribution fNis a suppressedat high pT & xF since fast probe quark leaves the ECF very quickly and is not influenced by it. fN = nqexp(-W1/√s)(1-XN)n, n = 1.38 ± 0.09; nq = 4.52 ± 0.32; (25) XN = [(pT/pN)2 + xF2 ]1/2; pN = 28 ±10GeV/с; W1 = 265±14 GeV.

  17. The case ofA1A2-collisions In case of А1А2-collisions the new quark contribution fNto ECF&string number νAat a given pT & xFis modified as: fN = nqexp(-W/√s)(1-XN)n, (26) XN = [(pT/pN)2 + xF2 ]1/2; (27) W = W2/(A1A2)1/6(28) n = n2(A1A2)1/6(fractality parameter) (29) n2 = 0.91 ± 0.37, W2 = 238± 54 ГэВ, nq = 4.52 ± 0.32, pN = 28 ±10 ГэВ/с; where A1 &A2areatomic weights of colliding nuclei.

  18. Predictions ofANfor√s = 130GeV, θCM= 4.1° AN scaling is violated at √s >70 GeV due to new quark production. p↑ + p → π+ + X Е704: √s =19.4 GeV BRAHMS: √s =62.4 GeV √s =200 GeV Solid red curve – predictions√s = 130GeV, θCM = 4.1°. Dashed blue curve – predictionsfor √s =200GeV, θCM = 4.1°.

  19. Predictions ofANfor√s =500GeV, θCM= 4.1° AN scaling violation at √s >70 GeV due to new quark production. p↑ + p → π+ + X Е704: √s =19.4 GeV BRAHMS: √s =62.4 GeV √s =200 GeV Solid red curve – prediction√s =500GeV, θCM = 4.1°. Dashed blue curve – predictionsfor√s =200GeV, θCM = 4.1°.

  20. Polarization in nuclei collisions Polarization ofΛinAu+Au–collisions. ExperimentSTAR: √s =62 и 200 GeV. Au+Au →Λ↑ + X There is energy dependent global Λ-hyperon polarization in heavy ion collisions at pT > 2.7 GeV/c.Combine effect of large color fields ~fNA1/3and correlation of production and reaction planes.

  21. Global data analysis: AN Inclusive reactions, in which analyzing power was measured inhр &hA–collisions. 23 reactions, 876points.

  22. Global data analysis: AN AN(xF) and GA(φA) oscillate due to spin precession in color field. √s =200GeV The best studied reactions: AN inhр &hA–collisions.14 reactions № 1÷14, 510 points. High precision data. p↑p→n √s <70GeV p↑p→π±K± Model: Solid curve: G(φA) = (1- cosφA)/φA+εφA

  23. Global data analysis: PN Reactions, in which analyzing power was measured inhр &hA–collisions. 25 reactions, 916points.

  24. Baryon polarization oscillation The best studied reactions: PN inhр &hA–collisions.19 reactions № 24÷42, 691points. High precision data. K- p →Λ↑ + X We can seeoscillation forK- p →Λ↑ + X Model – solid curve: G(φA) = (1- cosφA)/φA+εφA

  25. Data for 46most studied reactions, -10< φA < 40. For anti-hyperon production in pp or pA collisions the effective color field and the precession angle φA are high due to large number of spectator anti-quarks. As a result the polarization oscillates as a function of xF or φA. Ξ̃+ Σ̃− Ξ̃0 Model: Solid curve: G(φA) = (1- cosφA)/φA+εφA

  26. Λ̃ polarization in pp, pA-collisions For Λ̃ production in pp or pA collisions most of the data are at high energy, √s >27 GeV and PN is compatible with zero (blue diamonds). The only non-zero data, J. Felix (1995), reported at ICTP, Trieste, Italy, have √s = 7.31 GeV (red points). In the ECF model the large PN values are explained by quark focusing effect with ER=7.2±0.2 GeV. BNL, E766.

  27. Summary A semi-classical mechanism is proposed for single-spin phenomena. Effective color field of QCD strings, created by spectator quarks & antiquarks is described by quark counting rules. Microscopic Stern-Gerlach effect in chromomagnetic field and Thomas spin precession in chromoelectric field lead to large SSA. The energy and atomic weight dependence of effective color fields, combined with quark spin precession phenomenon, lead to oscillating behaviour of AN and PN as a function of kinematical variables. Additional anti(quark) production at high √s > 70 GeV changes the dependence on kinematical variables and violate AN(xF) or PN scaling. Quark focusing or defocusing in the effective color field leads to an additional resonance like energy dependence of AN or PN.

  28. Global data analysis : AN, PN, ρ00 Reactions, in which PN was measured inAuAu–collisions, vector meson polarization, PN &AN in lepton-nucleon collisions. 20 reactions, 308points.

  29. Vector meson polarization The best studied reactions: Polarization inhр &hA–collisions.9 reactions № 51÷59, 116points. High precision data. pCu→Y(S2) ρ0 K*+ φ K*- pp→Y(S1) Model: Solid curve: G(φA) = (1- cosφA)/φA+εφA Ј/ψ pCu→Y(S1)

  30. Quark counting rules for frequency ω0A Quarks&antiquarksspectatorsfrom projectilecontribute toω0А, with weightsλ & 1 respectively.Spectatorsfrom target have additional factor –τ. SPECTATORS p↑ + p → π+ + X Ea~Ba~ω0A= ω0U[3λ - 3τ λ ] > 0; AN > 0; ω0U~ (gaU – 2) < 0. General frequencyω0Aequations forq и q̃probesfrom hadron С: ω0A(q)= ω0Q{q̃new +λqnew – q̃used - λqused +λqA + q̃A –τ(λqB+q̃B)} (27) ω0A(q̃)= ω0Q{λq̃new +qnew – λq̃used - qused +qA + λq̃A –τ(qB+ λq̃B)} (28)

  31. Thomas precession effect in effective color field U= s·ωT - an additional term in the effective Hamiltonian(12) ωT≈ [F v]/MQ - Thomas frequency forEQ»MQ. (13) δP = -ωT/ΔE – polarization for pp→Λ+X, where ΔE >0. (14) • Direction and magnitude of the force F= gsEa is determined by quark counting rule for ECF. FZ ~ -[2 + 2λ - 3τ λ ]<0 for Q=s in pp→Ξ0+X, • FZ =gSEaZ = -2gSαS [1 + λ - 3τ λ ]/ρ2 < 0 for Q=s in pp→Λ+X, (15) • FZ ~ -[3λ - 3τ λ ]>0 for Q=u in pp→π++X. • Force FZ is processes dependent! δPN > 0 for Q=s in pp→Λ+X. • Additional Thomas precession term δPN > 0 is opposite in sign to the DeGrand model predicted negative polarization for pp→Λ+X. In ECF model dominates chromomagnetic field contribution with δPN < 0 .

  32. Data for 46most studied reactions, -20< φA <20. xF > x0, pT > 0.3 GeV/с.46 reactions, 1427points. Model: Solid cureve: G(φA) = (1- cosφA)/φA+εφA 11.41

  33. Predictions ofPNinAu+Au-collisions Polarization ofΛin Au+Au–collisions. Reaction: Au+Au →Λ↑ + X It is possible to vary «frequency» ω0A by a factor ~103varying energy and atomic weight in reaction A1+A2→Λ↑ +X. Predictionsfor√s = 9 &7GeV: Au + Au →Λ↑ + X рТ = 2.35 GeV/с

  34. Predictions ofPNinS+S-collisions Reaction: S+S →Λ↑ + X Polarization ofΛinS+S–collisions. At low energy «frequency» ω0A >0 andthere is quark focusing effect, which enhance polarization. η = -ln tan(θCM/2) Predictions for√s = 9 &7GeV: S + S →Λ↑ + X рТ = 2.35 GeV/с

  35. Predictions ofPNinCu+Cu-collisions Reaction: Сu+Сu →Λ↑ + X Polarization ofΛin Сu+Сu–collisions. At low energy «frequency» ω0A >0 andthere is quark focusing effect, which enhance polarization. Predictionsfor √s = 9 &7GeV: Cu + Cu →Λ↑ + X рТ = 2.35 GeV/с

  36. Constituent quark mass estimates Dynamical masses, q = 0. Global analysis: MU = 0.254 ± 0.027 GeV/с2 MD = 0.330 ± 0.047 GeV/с2 MS = 0.541 ± 0.065GeV/с2 MC = 1.45 ± 0.11 GeV/с2 MB = 5.95 ± 0.37 GeV/с2 (2 solutions) MB = 4.27 ± 0.78 GeV/с2 Charged pion form factors: MU ≈ MD ≈ 0.25 GeV/с2; A.F.Krutov, V.E.Troitsky, Eur. Phys. J. C20 (2001) 71. (JLAB data) MQ = (2/3)1/2πFπ = 0.24 ГэВ/с2; S.B.Gerasimov, YF 29(1979)513. MU = 0.263ГэВ/с2; M.Mekhfi, Phys.Rev. D72(2005)114014. 11.45

  37. Constituent quark chromomagnetic moment estimates Δμa =(ga -2)/2 Anomalous chromomagnetic moments atq=0: ΔμaU(0) = -0.64 ± 0.12 Instanton model: ΔμaD(0) = -0.56 ± 0.13 Kochelev: Δμa = -0.2;ΔμaS(0) = -0.61 ± 0.12 Diakonov: Δμa = -0.744; ΔμaC(0) = -0.78 ± 0.09 ΔμaB(0) = -0.76 ± 0.09(2 solutions) ΔμaB(0) = -1.44 ± 0.21 N.I. Kochelev, Phys. Lett. B426(1998) 149. D. Diakonov, Prog. Part. Nucl. Phys. 51(2003)173. 11.46

  38. Dependence ofMQ &ΔμaQonq In instanton model dynamical quark mass MQ&anomalous chromomagnetic moment ΔμaQdepend on momentum transfer q: D.I.Diakonov, 2003 (62) (63) (64) Data analysis: q0 = 1.03 ± 0.40 GeV/c. 11.22

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