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Single Spin Asymmetry of Charged Hadron Production by 40 GeV/c polarized protons

Single Spin Asymmetry of Charged Hadron Production by 40 GeV/c polarized protons. V . V . Abramov, P . I . Goncharov, A.Yu. Kalinin, A . V . Khmelnikov, A . V . Korablev, Yu . P . Korneev, А .V . Kostritsky, А .N . Krinitsyn, V . I . Kryshkin, A . A . Markov,

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Single Spin Asymmetry of Charged Hadron Production by 40 GeV/c polarized protons

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  1. Single Spin Asymmetry of Charged Hadron Production by 40 GeV/c polarized protons V.V. Abramov, P.I. Goncharov,A.Yu. Kalinin, A.V. Khmelnikov, A.V. Korablev, Yu.P. Korneev,А.V. Kostritsky, А.N. Krinitsyn, V.I. Kryshkin,A.A. Markov, V.V. Talov, L.K. Turchanovich, A.A. Volkov Institute for High Energy Physics, Protvino, Russia Single transverse spin asymmetries(AN) were measuredforreactions p + Ас X, where с = ,  ,K, K, p and p, in central and forwardregionsusing 40 GeV/c IHEP polarizedproton beam.

  2. Outline Beam & FODS-2 experimental setup Measurements Results Summary

  3. Polarized Proton Beam Line 22 at IHEP MH, MV – magnets; P1 – absorber; K– collimator; T – target. Primary proton beam:60-70 GeV/c, 1013 ppp, hits Be target T. Polarized protons from Λ-decays:P = 39 ± 2 %, 3.5∙107 ppp, 40 GeV/c, Δp/p = ± 4.5 %, spill ≈ 1.3 s., π+ admixture ≤ 1.5 %, beam polarization was changing each 18 minutes during 30 s.

  4. Secondary Target Region & Beam Monitoring Q – magnetic lens; MV – vertical corrector; T1 – target; Č – beam cherenkov counter; S – scintillation counter; IC – ionization chamber; HB – beam hodoscope. Beam monitoring: Intensity (S, IC); Composition (Č); Position (IC, HB). Targets: Liquid H2 – 0.05 λint; Carbon, Copper, Lead – 0.10 λint.

  5. FODS-2 – Rotating Double Arm Spectrometer T1– Target H– Hodoscope Č– cherenkov counter S– Trigger counter DC– Drift chamber PC– Prop. chamber SCOCH– Ring imaging cherenkov spectrometer HCAL– Hadron calorimeter STEEL– Muon detector MAGNETabsorbs beam Two arms allowed to cancel some apparatus biases.

  6. SCOCH – cherenkov Ring Imaging Spectrometer HPM – Hodoscope photomultipliers Identification: π+, π–, K+, K–, p, p̃ 24 HPMs

  7. SCOCH – cherenkov Ring Imaging Spectrometer Identification range: π+, π– (2-40 GeV/c); K+, K– (5-40 GeV/c); p, p̃ (10-40 GeV/c).

  8. Measurements Region 1:θcm = 105o –0.25 ≤ xF ≤ –0.05 0.7 ≤ pT ≤ 3.0 GeV/c Region 2:θcm = 86o –0.15 ≤ xF ≤ +0.20 0.5 ≤ pT ≤ 4.0 GeV/c Region 3:θcm = 48o +0.05 ≤ xF ≤ 0.70 0.5≤ pT ≤ 2.5 GeV/c

  9. Measurements • In case of symmetric FODS position analyzing powers from two arms were averaged to cancel some systematic uncertainties. • Measurements have been performed at two signs of magnetic field B to reduce systematic errors. • Measurements have been performedat two values of magnetic field (B & B/2) to increase hadron momentum range and equalize statistics at different pT. • The presented results are based on 22.8M events, recorded in two runs in 2003 using carbon and copper targets.

  10. Difference in mean coordinates for Up and Down beam polarizations • Beam coordinates are measured in each event by X and Yhodoscope planes. • The mean beam coordinates, averaged over spill time, have difference for UP and Down beam polarizations. • The cuts are applied to UP and Down beam coordinates to level their mean values and to remove false asymmetry.

  11. False asymmetry due to difference in X or Y for Up and Down polarized beam • False asymmetry is minimal near maximum (plateau) of PT distribution. • We have to level UP and Down coordinates with 4 μm accuracy to have false asymmetry less than0.002. • The remaining systematic uncertainty 0.04 is estimated from run to run AN variation and is added in quadratureto the statistical error.

  12. Analyzing Power for p + Aπ+ X • There is no significant A-dependence of AN. • There is a breakdown in pT-dependence with maximum near 2.5 GeV/c. • First π+data for pT≥ 2.2 GeV/c. • The AN breakdown at 2.5 GeV/c could indicate a transition to the pQCD regime, where AN 0.

  13. Analyzing Power for p + Aπ– X • AN≈ 0for θcm≈ 85o. • Firstπ– data for pT≥ 2.2 GeV/c. • There is no significant A-dependence of AN. • The measurements at other angles are required in order to disentanglethe PTand xFdependences. We plan to do these measurements in future.

  14. Analyzing Power for p + A K+ X • There is breakdown in pT-dependence near 2.2 GeV/c. • First K+data for pT≥ 1 GeV/c. • There is no significant A-dependence of AN. • There is similarity with π+ asymmetry. In both casesvalence u-quark contributes to the hadron production.

  15. Analyzing Power for p + AK– X • There is no significant A-dependence of AN. • First K–data for pT≥ 1 GeV/c. • AN for K– data ≈ 0, as expected due to small sea quark polarization.

  16. Analyzing Power for p + A p  X • AN≈ 0forθcm ≈88o. • AN oscillates as a function of pT with minimum at 1.3 GeV/c and maximum near 2.2 GeV/c forθcm≈50o. • First protondata for pT ≥ 1 GeV/c. • Data are consistent with other experiments, all of which have pT < 1 GeV/c and AN 0.

  17. Analyzing Power for p + A p X • There is no significant • A-dependence of AN. • First p data. • AN for p data ≈ 0, as expected due to small sea quark polarization.

  18. AN for p + Aπ+ X at 104.4o • There is no significant A-dependence of AN. • There is no pT-dependence of AN. • AN 0.05 for pC and pCu. • First π+data for θcm > 90o.

  19. AN for p + Aπ─ X at 104.4o • There is no significant A-dependence of AN. • There is no pT-dependence of AN. • AN 0 for pC and pCu. • First π─data for θcm > 90o.

  20. AN for p + A p  X at 108.2o • There is no significant A-dependence of AN. • AN 0 for pC and pCu. • First pdata for θcm > 90o.

  21. AN scaling for π+ production at high xF At high energies and PT scaling is expected: AN ~F(PT)[GA(XA–X0)-GB(XB –X0)] XA= (XR +XF)/2 -u/s; XB= (XR─ XF)/2 -t/s; X0= 0.075NQ+ 2NQMQ(1+cosθcm)/s MQ= 0.3 GeV, quark mass. NQ=2 in π+ XS = XA – X0 ; In forward region (θcm<50o) XB 0; AN rises for XS > 0, where it shows a scaling behaviour.

  22. AN scaling for π─ production at high xF AN~F(PT)[GA(XA–X0)-GB(XB–X0)] X0= 0.075NQ+2NQMQ(1+cosθcm)/s XS = XA– X0; AN start to rise at XS = 0; Agreement with E925 for PT > 0.6 GeV/c. Some AN dependence on angle (PT), target and energy is possible at PT below 0.6 GeV/c. Other examples of AN scaling: V.V.Abramov, Eur.Phys.J. C14(2000)427; Physics of Atomic Nucl., 68(2005)385.

  23. AN energy dependence for protons • AN~F(PT)[GA(XA–X0)-GB(XB– X0)] • X0= 0.075NQ+2NQMQ(1+cosθcm)/s • XS = XA – X0; NQ=3 for proton; • AN start to rise at XS = 0; • Agreement with E925 for PT > 0.6 GeV/c. • Some AN dependence on angle (PT), target and energy is possible at lower PT.

  24. Summary • AN was measured for π +, π –, K+, K–, p̃ & protons at FODS-2 setup. The mean angle θcm was near 48o, 86o & 105o. • The data were obtained with pT up to 4 GeV/c in central region and with xF up to 0.7 in forward regions for pC & pCu collisions. • There is no significant A-dependence for AN. • First data for K– & p̃ show near zero AN for pC & pCu collisions as expected due to small sea quarks polarization. • Breakdown in pT–dependence of analyzing powers for π +, K+ & protons in pC & pCu collisions could indicate a transition to the pQCD regime above 2.5 GeV/c, where AN tends to zero. • The asymmetry for θcm = 105o is close to zero. • Scaling behavior of AN in the forward region & pT > 0.6 GeV/c.

  25. xF -dependence of ANfor π+ and π─ production

  26. AN energy dependence for protons

  27. Dimensional SSA analysis and scaling Scaling for largeofs, -t и –u: AN = AN (PT/PTh, PT/PTQ, MQ/s, xA, xB) (4) PT < PTh 1/Rh 0.35 GeV (quarks are not seen inside hadrons) PTh<PT < PTQ(constituent quarks revealed) PT > PTQ  3/RQ2.7 ГэВ (transition to current quarks) Scalingvariables: xA= -u/s  (xR+ xF)/2  EC/EA(in B rest frame) (5) xB= -t/s  (xR–xF)/2 EC/EB (in A rest frame) (6) Thresholdenergy (ETh) of hadron С in c.m.: ETh  NQ[MQ + XMINs/2],(7) whereNQ – number of quarks in С; XMIN – minimal momentum fraction carried by constituent quarkQ.

  28. Energy dependence of hadron C threshold energy (ETh) in c.m. ETh NQ[MQ + XMINs/2], δPZ ≥ħ/2RP 0.113 δX/X  δPZ/MQ0.312 XMIN= 1/3 - 2 δX 0.129 MQ= 0.37 ± 0.03 GeV XMIN = 0.118 ± 0.008 AN~ F(PT)[G(XA – XTh) - G(XB – XTh)]; XTh  NQ[2MQ /s + XMIN]

  29. Quark interaction with color flux tube in QCD Longitudinal chromoelectricandcircular chromomagnetic fieldsin the color flux tube. μ = sggs/2MQ – chromomagneticmoment of constituent quark. В dependence ondistancerfrom tube axes: B = -2αsνr/ρ3 exp(-r2/ρ2) (12) whereν – number of quarks, ρ 1.25RC  2.08GeV-1, RC-1  0.6 GeV, RC –confinement radius. Stern-Gerlach force: (Ryskin, 1987) fx = μx ∂Bx/∂x + μy ∂By/∂x(13) fy = μx ∂Bx/∂y + μy ∂By/∂y(14)

  30. Polarization effects in color flux tube field Quark path length(S) incolor flux tubeat fixedpT S~ RT/sin(θLab) ~ p/pT ~PAXA/pT S~ lf ~ p ~ PAXA (if formation lengthis less thanS) AN~δPx~μ sin(kS)/a~sin(kS)/(g – 2) (20) kS ~ XAν/MQ~ωAXA(21) G(XA) ~ sin[ωA(XA - XTh)], (22) whereXThtakes into account threshold energyETh.

  31. Experimental dataand dependence on kinematical variables (A + B → C + X) ANandPNdependence: AN = F(PT)[G(A, xA) - ()G(B, xB )] (23) G(A, xA) = C(s) sin[ωA(xA - xTh)](24) () = χ sin() + 1 – χ(forA ≡ B) (25) xTh = 2E0 /s + x0(26) C(s)= C0/[1 - ER /s ](27) xA = -u/s ≈ (xR + xF)/2 ≈ EC/EA(in B rest frame)(28) xB= -t/s ≈ (xR - xF)/2 ≈ EC/EB(in A rest frame)(29)

  32. Energy dependence of normalization parameter • C(s)= C0/[1 - ER /s]; • ER= 3.73± 0.13 ГэВ; • C0 = 0.267 ± 0.011 • C(s)decrease with s rise. • Singularity at s = 3.73 ГэВ. • Betatron type oscillation in color flux tube?

  33. Resonance and energy dependence of normalization parameter • Quark focusing in color flux tube field: • BX = -B0y/ρ; BY= B0x/ρ; B0 = 2αsν/ ρ2; • ∂BY/∂x = B0/ρ; ρ = 2.08 GeV-1; • Ω = (gsB0/pQρc) –oscillation frequency • Где pQ = pp/3; gs = 4παs ; αs =0.25; • Spin precession frequency: • Ωs = Bgs/2vMQ∙(g – 2 + 2MQ/EQ) • Proton resonance energy: ER= 6MQcρ/gsαs(g-2)2ν = 3.76/(g-2)2ГэВ; Предсказание: sR≈2.97/|g-2| ГэВ; Эксперимент: sR = 3.73± 0.13 ГэВ; |g - 2|≈ 0.8 gUem≈2.15; gDem≈2.26

  34. Predictions (23)-(29) for 25 GeV и 40 GeV (FODS-2) pC →π+ pC →π+

  35. Predictions (23)-(29) for 60 GeV (FODS-2) pC →π+ pC →π+ 1012 взаимодействий

  36. Quark counting rules forωAin processes р + р →Λ и р + р →Ξ

  37. Quark counting rules forωAin processes р + π- → π0 и р + р → π+

  38. Comparison quark counting rules with experiment data  = +0[ 3λ - 3τλ]R = +2.553; pp→π+; EXP: +0.9 ± 1.2  = -0[ 3λ - 3τλ]R = -2.553; pp→π-; EXP: -1.6 ± 2.6  = -0[ 3λ + 3τ]R = -0.944; p̃p→π+;  = +0[ 3λ + 3τ]R = +0.944; p̃p→π-; EXP: +1.2 ± 1.8  = +0[ 3λ + 3τ]R = +0.944; p̃p→π0;  = 0[ -6 + 3τ] = +19.91; pp→Λ̃; EXP: +18.5 ± 5.7  = 0[ -6 - 3τλ] = +20.98; pp̃→Λ̃; EXP: +16.2 ± 4.1  = 0[ -6 + 3τ]R = +29.86; pp→p̃; EXP: +24 ± 13 Comparison of predicted and measuredfor pp→π+; • = +0[ 3λ - 3τλ]R =+2.553; pp→π+; experiment: +0.9 ± 1.2 (high energies) experiment:+2.564±0.048ANL, 11.75GeV

  39. Additional figures. Polarization oscillation examples (FNAL) pp →π+ pp→π0

  40. Additional figures. Polarization oscillation examples (FNAL)

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