Mickey Chiu University of Illinois at Urbana-Champaign

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

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

3. 2 0  h 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 ST axis (either aligned or anti-aligned to ST) • 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 j1 ST j2

4. Ng = Nd (E704) anti-aligned aligned Unpolarized Results from Run03 p+p Boer and Vogelsang, PRD69:094025,2004 Run03 -charged dn/d 1/Ntrig dN/d (au) • 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)

5. Estimated AN from Run03 p+p Ng = Nd (E704) parametrized AN - • Parametrized AN with , A=0.08, =0.8 • Used this to calculate AN using unpolarized gamma-charged Run03 p+p dN/d • Put asymmetry into distribution and then calculate AN • 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 AN from Boer/Vogelsang paper is idealized, and the real signal will be reduced

6. AN Reduction 1: Polarization • Polarization P < 1 just reduces AN by P • Besides that, most of the time the jet is not aligned exactly along the polarization axis, which means AN=AN(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 j1 ST j2

7. AN Reduction 2: Di-Hadron vs. Di-Jets AN away side parton up down unpolarized 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 AN relative to the di-jet AN, 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. process contribution to 0 Combined Effects Full di-jet Sivers Reduced by lower <P>, 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 AN using gamma-charged measurements of jet dphi • Expected raw AN 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 AN to ~1.0% • Have not evaluated systematic errors yet (underlying event…)

9. ST SL Run05 Prospects BLUE (AN = 6.24%) (LR) (LR) YELLOW (AN = 5.27%) Commisioning Period PHYSICS Period M. Togawa (TB) (TB) • Blue : 10.3%  3.9%Yellow : 21.5%  5.3% • Short Transverse Run • 0.15/pb, P~50%  FOM = P2L = 0.075 • Mostly Running Longitudinally in Run05 • Transverse component seems to systematically have a radial component • 3.8/pb, PY~10%, PB~5%  FOM=0.166 • Vertical component seems ~ 0.

10. Run05 Run06? Prospects (Continued) Full di-jet Sivers Reduced by lower <P>, 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

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

12. N(f)/N0 Collins Effect? PHENIX Acceptance R. Seidl, Belle Collaboration 0 edge on view distribution of hadrons around away side hadron Collins Effect averages to 0 in back-to-back d di-hadron measurement.

13. Summary • By Using di-Hadron Correlations at mid-rapidity, the gluon Sivers function can be explored • First unambiguous test for gluon Sivers function • Inclusive AN could have other contributions • No contamination from Collins effect • Different effects can smear out the asymmetry • Jet fragmentation • Normal Intrinsic kT • 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… Ng = Nd (E704)

14. Backup Slides

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

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

17. process contribution to 0