1. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 1 Outline Motivation Principle of measurement, trigger Model of Sivers asymmetry Measured SSA & DSA Comparison with theory Conclusions Measurement of Sivers Asymmetry for Di-jets in 200 GeV pp Collisions at STAR Jan Balewski, IUCF for STAR Collaboration RHIC Spin Physics, RIKEN, Japan September 29, 2006

2. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 2  Sivers effect:  Sensitive to parton orbital angular momentum  Needs ISI and/or FSI to evade time-reversal violation.  HERMES transverse spin SIDIS asymmetries  non-zero u and d quark Sivers functions of opposite sign, different magnitude.  Sivers effect in pp  spin-dependent sideways boost to di-jets, suggested by Boer & Vogelsang (PRD 69)  Both beams polarized, x a  x b  can distinguish q vs. g Sivers effects.  Do we observe q Sivers consistent with HERMES? Tests universality.  First direct measurement of gluon Sivers effects. Motivation for Di-Jet Sivers Effect Measurement

3. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 3 Sivers Mechanism of SSA y x Spin dependent k T X offset deflects both jets in the same direction reduces average di-jet opening angle can be measured from correlation between di-jet bisector vs. spin direction from accumulated  -spectra (spin) intrinsic  k T unpol proton 2 proton 1 intrinsic  k T p1p1 p2p2 jet 1 jet 2 2  2 partonic scattering p3p3 p4p4  11 22 spin di-jet bisector kTxkTx  > 180  for k T x > 0 spin + spin- dep. k T x Polarized

4. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 4 Is  -distribution narrow enough for precise determination of centroid ? Have we measured di-jets? EMC-based Di-jet Trigger in STAR  =+2  = -1 TPC EMC Barrel EMC Endcap BBC East BBC West Yellow beam Blue   spin bisector  Jet 1 Jet 2 Reco cos(  bisector ) measures sign of net k T x for event Endcap essential for q vs. g Sivers distinction L0 jet patch trigger + L2 EMC-only dijet-finder  2.6M event sample from 1.1 pb –1 of transverse p+p collisions during 2006 run  3 (deg)  4 (deg) |  3-  4| < 60  L2 trigger thresholds: E T EMC > 3.6, 3.3 GeV

5. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 5 How close EMC-only jets resemble full reco jets ? How close full recon jets resemble original scattered partons ?   (rad) Jet finder TPC+EMC jet cone radius 0.6  -resolution, pT of Reconstructed Di-jets Typical x T ~ 0.05 - 0.10;  1 +  2 range  0.01 < x Bj < 0.4 Data: offline di-jet reco for ~2% of all runs PYTHIA+GEANT: full reco jet vs. parton EMC-only  resol’n << k T -induced  width   (full reco) –  (L2) [deg] Full  width ~21 

6. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 6  (+) -  (-) vs. A N ? Toy Model of Sivers Spin Effect Generates AN Throw 1e6 2-parton events in transverse plane Match to p T distribution from full jet reco. Gaussian + exp. tail k T distrib’n reproduces  shape Sivers spin-dep. k T x offset  spin-dep.  distrib’n shift Vary k T x offset, see how pol’n observables change Can introduce  resolution smearing, see its effects A N =measure of L-R asymmetry of k T distribution in L-R symmetric detector Blue beam spin down Blue beam spin up  ( + ) -  (-) Intrinsic k T x,y width = 0.75 GeV/c   (  ) = 6.3  resol’n smear reproduces observed  width  smearing dilutes A N by only 10% of its value  EMC-only analysis OK

7. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 7 Measured Sivers A N for Di-jets A N – L/R asymmetry integrated over STAR detector pseudorapidity STAR EMC   coverage Blue(+z) Yellow(-z) proton +2 Event weights by |cos(  bisector )| account for beam pol’n compo- nent  k T plane. STAR data both jets rotated by 90   rotation samples  k T y , parity-violating  s p k T  correl’n Null Tests

8. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 8  V & Y use these Sivers fcns. (assuming zero gluon Sivers) to predict SSA for pp  dijet + X, integrated over k T distributions within both protons. Note strong y- and weak p T - dependence. Quark Sivers Functions Constrained by SIDIS Results  Sivers sensitivity in depend- ence of SIDIS yield on (  hadron –  proton spin ).  HERMES positive Sivers SSA for  +, but  0 for  –, fitted by Vogelsang & Yuan with u and d quark Sivers fcns. of different sign and magnitude: W. Vogelsang and F. Yuan, PRD 72, 054028 (2005). Jet 1 rapidity Jet p T (GeV/c)

9. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 9 Measured Sivers A N for Di-jets vs. Theory Model w/o hadronization, integrated over STAR , 5<p T <10 GeV/c, includes only quark Sivers -- predicts A N ~ A N HERMES where q Sivers dominates Sign of predictions reversed to adhere to Madison A N sign conventio STAR measured A N all consistent with zero  both quark and gluon Sivers effects much smaller in pp  di-jets than in HERMES SIDIS !! Emphasizes (80%+) gluon Sivers Emphasizes (50%+ ) quark Sivers

10. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 10 Theory - exp’t discrepancy raises questions! Are observed di-jet Sivers SSA much smaller than predictions because:  ISI & FSI both important in pp  jets and tend to cancel?  Need q Sivers or different q Sivers x, k T - shapes in HERMES fits?  If ISI / FSI cancel at mid-rapidity, does their balance change at high  to yield sizable Sivers contribution to observed pp   0 X SSA? SS Initial state interaction p p q q l l  l +  * SIDIS Drell- Yan ISI for Drell-Yan vs. FSI for SIDIS  opposite sign predicted for Sivers SSA

11. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 11 Summary and Conclusions  Large STAR EMC acceptance  large 2006 triggered di-jet data set.  Di-jet A N Sivers all consistent with zero  quark Sivers effects ~ 5-10  smaller than expected from SIDIS. Gluon Sivers comparably small.  Sensitivity of analysis to A N Sivers  0 confirmed by toy model simulations. Beam spin-sorting verified via known non-zero SSA.  Results constrain treatments of Sivers effect and of transverse spin asymmetries in pp collisions.  Extend di-jets in future to higher , where A N meas (pp   0 X) sizable.