1. Mickey Chiu University of Illinois at Urbana-Champaign JPS/DNP, Maui 2005 September 18, 2005 New Prospects for Transverse Physics with the PHENIX detector

2. Sivers and Why it is Interesting Non-Zero Sivers function means that there is a left/right asymmetry in the k T of the partons in the nucleon Probe of space-time structure of nucleon wave-function Testable k T dependence Sivers and orbital angular momentum? Parton Shadowing causes k T asymmetry? Red Shift/Blue Shift effects in peripheral regions? S T  (P  k T ) is T-odd and naively thought to vanish FSI effects found by Brodsky et.al. that allow T-odd function to be non-zero J=1/2 = ? E704

3. Sivers Fcn from Back2Back Analysis Boer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/0312320 Boer and Vogelsang find that this parton asymmetry will lead to an asymmetry in the  distribution of back-to-back jets There should be more jets to the left (as in picture to the left). Should also be able to see this effect with fragments of jets, and not just with fully reconstructed jets Take some jet trigger particle along S T axis (either aligned or anti-aligned to S T ) Trigger doesn’t have to be a leading particle, but does have to be a good jet proxy Then look at  distribution of away side particles STST j1 j2 00 22  h

4. Unpolarized Results from Run03 p+p anti-aligned aligned Asymmetry numerator is difference between aligned and anti-aligned  dist’s, where aligned means trigger jet and spin in same hemisphere denominator is simply unpolarized  distribution On left are some theoretical guesses on expected magnitude of AN from Siver’s On right are gamma-charged hadron  dist’s from Run03 p+p 2.25 GeV gamma’s as jet trigger, 0.6-4.0 GeV charged hadrons to map out jet shape Dotted lines are schematic effect on away side  dist due to Siver’s Fn (not to scale) Run03  -charged dn/d  Boer and Vogelsang, PRD69:094025,2004 1/Ntrig dN/d  (au)  N g =  N d (E704)

5. Estimated A N from Run03 p+p Parametrized A N with, A=0.08,  =0.8 Used this to calculate A N using unpolarized gamma-charged Run03 p+p dN/d  Put asymmetry into distribution and then calculate A N On right shows statistical significance from Run03 p+p (0.35/pb). Note that area around  =0 can be used as a systematic check (it should be flat) Also note that A N from Boer/Vogelsang paper is idealized, and the real signal will be reduced parametrized A N  -   N g =  N d (E704)

6. A N Reduction 1: Polarization Polarization P < 1 just reduces A N by P Besides that, most of the time the jet is not aligned exactly along the polarization axis, which means A N =A N (  j1,  ) and also the polarization is reduced by cos(  j1 ) We can make a simple (though wrong) estimate for this effect by calculating the average polarization from a jet spread of  /2 around the polarization axis STST j1 j2

7. A N Reduction 2: Di-Hadron vs. Di-Jets up down unpolarized away side parton ANAN di-hadron di-jet Since we don’t reconstruct jets fully, we have to use di-hadron correlations to measure jet . This smears out the di-hadron A N relative to the di-jet A N, with smearing function g (assumed here to be a gaussian, with  jT =0.35). The effect broadens and lowers (by just a little bit) the asymmetry

8. Combined Effects Full di-jet Sivers Reduced by lower, di-hadron smearing Run03 p+p gamma-charged, 0.35/pb Given 0.35/pb of data, we should be able to get 1% statistical significance in A N using gamma-charged measurements of jet dphi Expected raw A N could be 3.5% Could also be as low as 0.5%, or as large as 10% x-dependence of Sivers? Effects from P=0.5, jet angle not aligned with transverse polarization, and fragmentation to dihadrons reduces raw A N to ~1.0% Have not evaluated systematic errors yet (underlying event…) process contribution to  0

9. Run05 Prospects BLUE (A N = 6.24%) YELLOW (A N = 5.27%) (LR) (TB) (LR) (TB) PHYSICS Period Short Transverse Run 0.15/pb, P~50%  FOM = P 2 L = 0.075 Mostly Running Longitudinally in Run05 Transverse component seems to systematically have a radial component 3.8/pb, P Y ~10%, P B ~5%  FOM=0.166 Vertical component seems ~ 0. SLSL STST Commisioning Period Blue : 10.3%  3.9% Yellow : 21.5%  5.3% M. Togawa

10. Prospects (Continued) Full di-jet Sivers Reduced by lower, di-hadron smearing Run03 p+p gamma-charged, 0.35/pb, P=0.5 Run05 expectation, 3.8/pb, P~0.06 Run06, 9.5/pb, P = 0.6 Run05 Run06?

11. Radial vs Vertical Transverse Running Boer and Vogelsang, PRD69:094025,2004 STST STST  1 = 0  1 =  /2  1 = 0 :  1 =  /2 : private communication, Boer and Vogelsang

12. Collins Effect? 00 PHENIX Acceptance edge on view Collins Effect averages to 0 in back-to-back d  di-hadron measurement. distribution of hadrons around away side hadron N(  )/N 0 R. Seidl, Belle Collaboration

13. By Using di-Hadron Correlations at mid-rapidity, the gluon Sivers function can be explored First unambiguous test for gluon Sivers function Inclusive A N could have other contributions No contamination from Collins effect Different effects can smear out the asymmetry Jet fragmentation Normal Intrinsic k T Radiative (e.g., Sudakov) effects In run05, we can approach limits of (and ignoring Sudakov effects) In run06, ~8X better limits if we get 9.5/pb radial transverse run with P~60% Can also look at Muon Arm Correlations… Summary  N g =  N d (E704)

14. Backup Slides

15. Data taken 0.15 pb -1 and 15 % beam polarization Single Spin Asymmetry of  0 and Non- Identified Charged Hadrons at x F ~ 0 vs p T h- A N for both charged hadrons and neutral pions consistent with zero at midrapidity. process contribution to  0 More statistics needed to map out pT  x  g/q dependence

16. A Prediction for Sivers at Mid-Rapidity Umberto D’Alesio, RIKEN BNL SSA Workshop ‘05 LO calculation How valid is the framework? Would be nice to have a measurement that is less reliant on theoretical assumptions

17. process contribution to  0