Victor AbramovSPIN-2005, XI International Workshop, Dubna, September 27 - October 1, 2005

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 measured for reactions

p + А с X, where с = , , K, K, p and p, in central

and forward regions using 40 GeV/c IHEP polarized proton beam.

Victor AbramovSPIN-2005, XI International Workshop, Dubna, September 27 - October 1, 2005

Outline

Beam & FODS-2 experimental setup

Measurements

Results

Summary

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.

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.

FODS-2 – Rotating Double Arm Spectrometer

T1 – Target H – HodoscopeČ – cherenkov counterS – Trigger counter DC – Drift chamberPC – Prop. chamber SCOCH – Ring imagingcherenkov spectrometer HCAL – Hadron calorimeter STEEL – Muon detector MAGNET absorbs beam

Two arms allowed to cancel some apparatus biases.

SCOCH – cherenkov Ring Imaging Spectrometer

HPM – Hodoscopephotomultipliers

Identification:

π+, π–, K+, K–, p, p̃

24 HPMs

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).

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

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 performed at 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.

Difference in mean coordinates for Up and Down beam polarizations

Beam coordinates are measured in each event by X and Y hodoscope 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.

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 than 0.002.

The remaining systematic uncertainty 0.04 is estimated from run to run AN variation and is added in quadrature to the statistical error.

Analyzing Power for p + A π+ X

There is no significantA-dependence of AN.

There is a breakdownin pT-dependence withmaximum 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.

Analyzing Power for p + A π– X

AN ≈ 0 for θcm ≈ 85o.

First π– data for pT ≥ 2.2 GeV/c.

There is no significantA-dependence of AN.

The measurements at other angles are required in order to disentangle the PT and xF dependences. We plan to do these measurements in future.

Analyzing Power for p + A K+ X

There is breakdownin pT-dependence near 2.2 GeV/c.

First K+ data for pT ≥ 1 GeV/c.

There is no significantA-dependence of AN.

There is similarity with π+ asymmetry. In both cases valence u-quark contributes to the hadron production.

Analyzing Power for p + A K– X

There is no significantA-dependence of AN.

First K– data for pT ≥ 1 GeV/c.

AN for K– data ≈ 0, as expected due to small sea quark polarization.

Analyzing Power for p + A p X

AN ≈ 0 for θcm ≈ 88o.

AN oscillates as a function of pT with minimum at 1.3 GeV/c and maximum near 2.2 GeV/c for θcm ≈ 50o.

First proton data for pT ≥ 1 GeV/c.

Data are consistent with other experiments, all of which have pT < 1 GeV/c and AN 0.

Analyzing Power for p + A p X

There is no significantA-dependence of AN.

First p data.

AN for p data ≈ 0, as expected due to small sea quark polarization.

AN for p + A π+ X at 104.4o

There is no significantA-dependence of AN.

There is no pT-dependence of AN.

AN 0.05 for pC and pCu.

First π+ data for θcm > 90o.

AN for p + A π─ X at 104.4o

There is no significantA-dependence of AN.

There is no pT-dependence of AN.

AN 0 for pC and pCu.

First π─ data for θcm > 90o.

AN for p + A p X at 108.2o

There is no significantA-dependence of AN.

AN 0 for pC and pCu.

First p data for θcm > 90o.

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.

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.

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.

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.

xF -dependence of AN for π+ and π─ production

AN energy dependence for protons

Dimensional SSA analysis and scaling

Scaling for large of s, -t и –u:AN = AN (PT/PT

h, PT/PTQ, MQ/s, xA, xB) (4)

PT < PTh 1/Rh 0.35 GeV (quarks are not seen inside

hadrons)PT

h < PT < PTQ (constituent quarks revealed)

PT > PTQ 3/RQ 2.7 ГэВ (transition to current quarks)

Scaling variables: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)

Threshold energy (ETh) of hadron С in c.m.: ETh NQ[MQ + XMINs/2], (7)where NQ – number of quarks in С; XMIN – minimal momentum fraction carried by constituent quark Q.

Energy dependence of hadron C threshold energy (ETh) in c.m.

ETh NQ[MQ + XMINs/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]

Quark interaction with color flux tube in QCD

В dependence on distance r from tube axes:B = -2αsν r/ρ3 exp(-r2/ρ2) (12) where ν – number of quarks, ρ 1.25RC 2.08 GeV-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)

Longitudinal chromoelectric and circular chromomagnetic fields in the color flux tube.

μ = sggs/2MQ – chromomagnetic moment of constituent quark.

Polarization effects in color flux tube field

S ~ lf ~ p ~ PAXA (if formation length is less than S )

AN ~ δPx ~ μ sin(kS)/a ~ sin(kS)/(g – 2) (20)

kS ~ XAν/MQ ~ ωAXA (21) G(XA) ~ sin[ωA(XA - XTh)], (22)

where XTh takes into account threshold energy ETh.

Quark path length (S) in color flux tube at fixed pT

S ~ RT/sin(θLab) ~ p/pT ~PAXA/pT

Experimental data and dependence on kinematical variables (A + B → C + X)

AN and PN dependence:

AN = F(PT)[G(A, xA) - ()G(B, xB )] (23)

G(A, xA) = C(s ) sin[ωA(xA - xTh)] (24)

() = χ sin() + 1 – χ (for A ≡ 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)

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?

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)2 ГэВ;

Предсказание:

sR ≈ 2.97/|g-2| ГэВ;

Эксперимент:

sR = 3.73 ± 0.13 ГэВ;

|g - 2| ≈ 0.8

gUem ≈2.15; gD

em ≈2.26

Predictions (23)-(29) for 25 GeV и 40 GeV (FODS-2)

pC →π+ pC →π+

Predictions (23)-(29) for 60 GeV (FODS-2)

1012 взаимодействий

pC →π+ pC →π+

Quark counting rules for ωA

in processes р + р →Λ и р + р →Ξ

Quark counting rules for ωA

in processes р + π- → π0 и р + р → π+

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 ± 0.048 ANL, 11.75 GeV

Additional figures. Polarization oscillation examples (FNAL)

pp→π0

pp →π+

Additional figures. Polarization oscillation examples (FNAL)