1. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 1 Outline Motivation Principle of measurement, trigger Toy 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 Jet 1 Jet 2 Vertical Spin Sivers +kT x    spin+ 180 o  (deg)  Jan Balewski, IUCF for STAR Collaboration SPIN2006, Kyoto, Japan z  y x

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 A N 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 beam 1 spin down beam 1 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?  Contributions from Collins fragmentation asymmetries in incompletely reconstructed jets conspire to cancel Sivers asymmetries for quarks, while gluon Sivers functions naturally small?  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.

12. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 12 BACKUP

13. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 13 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. 21 unpol 4 3 Yellow SYSY 12 unpol 3 4 Blue SYSY z y Cross-ratio  forbidden 2-spin correlation  cos(  bisector ) STAR data both jets rotated by 90   rotation samples  k T y , parity-violating  s p k T  correl’n Null Tests

14. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 14 Systematic Corrections, Checks, Errors 1)L2 jet vs. parton  resolution smearing: Systematic uncertainty =  0.05 A N covers model-dependence of toy-model dilution factor already included. 2) Different di-jet yield extraction methods: Syst. Unc. =  0.2  (stat. unc.) covers observed changes when  integration range, baseline subtraction are varied. A N false requires instrumental spin-dependent change in  distribution shape. Cross-ratio extraction, excellent L-R detector symmetry, bunch-to-bunch spin changes, etc., make these very small. 3)Beam polarization calibration: used online RHIC polarimeter results: P B = 0.57, P Y = 0.59. Normalization unc. =  0.15 A N. 4)Other sources: syst. unc. <  0.001, confirmed by null tests & consistency of results for different polarization fill patterns.

15. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 15 STAR Excellent Coverage for Di-Jets +60 deg Jet 1 E T > 3.6 GeV Jet 2 E T > 3.3 GeV -60 deg  =  +   =+2  = -1 TPC EMC Barrel EMC Endcap BBC East BBC West yellow blue EMCal Geometry in L2 trigger 01 2 Endcap EMC  x y Barrel EMC  -units L2 jet

16. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 16   =0 o L2 algo result STAR Triggered on Di-Jet Found On-line Comparison with off-line  similar L2 di-jet logic: 5500 EMC towers sliding jet patches jet size : 0.6x0.6 (  x  ) jet1 Et>3.6, jet 2 Et>3.3 GeV decision : 60 muSec/event event rate ~8 Hz 2005 data event L0 di-jet logic: BBC East.West Etot >14 GeV hardwired jet patches jet size : 1x1 (  x  ) one jet Et>4.0 GeV event rate ~120 Hz L0-L2 logic benefits: large acceptance combined with trigger rejection power full statistics on-line trigger monitoring of EMC compact trig info saved for each event 0 +2  =180 o  =360 o ~180 o back-to-back di-jet Z=Et/GeV Jet  is weighted with EM E T

17. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 17 Toy M-C Matched to Real Data Toy M-C pp200 Real L2 di-jet events Jet 1 Jet 2  (  )=22 0  (  )=21 o Back-to-back di-jet Tails are different

18. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 18 3 Alternative Sivers Spin Observables Sivers kTx leads to displacement of  (other beam unpolarized) 180 o  (deg) eps  N >,+ spin+ spin-  Width of  influenced by DSA Blue + Yell + Z-axis  ++ kTx destructive  Blue + Yell -  +- kTx constructive N <,- N <,+ N >,-  epsR w/ more  -slices  A N (  ) Based on Toy M-C rel. sensitivity of 7  1  7  Sivers Sensitive Observables independent x widens narrows

19. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 19 3M events Fit: A-B*sin(2  ) +/- 1  (A) eps N =0 Unpolarized Yield(  ) eps N (  ) Blue SSA Yellow SSA‘mixed’ DSA Di-jet Results Sivers eps N (  )=A N (  )*P May 2006

20. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 20 2006 pp200 Transverse Run @ RHIC Yellow bXing (uses revTick) STAR event count Yellow Abort gap Blue Abort gap spin8 state STAR spin sorting (uses V124) Imperfections : few ppm Available STAR events: both TPC & EMC active few M 1-jet trig, ET>8.0 GeV 3M di-jet trig, 2xET>3.7 GeV few M di-jet w/o TPC (crude run QA) Example of di-jet events for one of 4 RHIC fill polarization patterns { \\, \\+1, //, //+1 } STAR magnet incident ( ~10 days ) May 9 April 6 WCM intensity No spin Info @ STAR good STAR data good data days in 2006  other value  B –Y – 51  B –Y + 53  B +Y – 83  B +Y + 85

21. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 21 Run QA Pass 1 (results presented in May of 2006) use run Browser: TPC & BTOW & ETOW triggers: BJP0, EJP0 classify runs based on fill pattern 1-4 drop run if mean  -180 o more than: - 1 deg AND it is more than 2 sigma effect, or - 3 deg (no matter what sigma) - in any of the subsamples: bjp0 or ejp0 Pol patt avaliable: #runs, #events accepted: #runs, #events Px073, 725K61, 667K Px1102, 1226K89,1150K Px2113, 1255K90, 1060K Px3114, 1338K92, 1083K Pass 2 (new TrgJetTree in hand) use run Browser: BTOW & ETOW (include no-TPC runs) triggers: BJP0, EJP), minB, zB use official off-line QA (from Jim & Co.) suggestions?

22. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 22 Offline Evaluation of Di-jets Input: 84k BJP1 triggered events from 2005 ( L0 BJP1: ET>4 GeV, only BTOW-W) L2 algo: uses BTOW E+W Offline jet finder : no  cut all BJP1 trig ET2>3 GeV ET2>4 GeV ET2>5 GeV Bias introduced by L2 di-jet 2006 trigger Compare 2006 L2 vs. off-line di-jets - Issam Qattan, IUCF Avoid any  -shape model, fit  ’= a*  +b to match + & - spin state distributions (perhaps it will work?) all BJP1 trig ET2>3 GeV ET2>4 GeV ET2>5 GeV E T EMC / E T TOT 2005 data

23. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 23 Expectation: Sivers Asy Depends on Partonic Process Endcap+Barrel Barrel+Barrel E+E B+E Favors quark jets Available info (trigger level) Eta1,2 ET1,2 Et tot Tower multiplicity Additional info Example: Asymmetric Endcap-Endcap jets  Quark –blue beam  Gluon – yellow beam Favors quark-gluon Z=# of events Selecting regions in  & pT changes probabilities of partonic processes. Justin Stevens

24. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 24 Is the Di-jet Spin Sorting Correct? ( Find MinB BBC SSA) +Z 2 6 West BBC X 6 2 East BBC  Y Blue beam Yellow beam Top view Blue-Left Yellow-Left West-Blue 5.6  West-Yellow 0.3  East-Blue 0.1  East-Yellow 5.8  Pol patt 1,2,3,4 YES ! 12M MinB evens

25. Jan Balewski: Di-jet Sivers in p+p @ 200 GeV 25 An Integrated vs. averaged