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Mickey Chiu University of Illinois at Urbana-Champaign RBRC SSA Workshop 2005

New Prospects for SSA Measurements in PHENIX: How can we separate out the various contributions to SSA at RHIC?. Mickey Chiu University of Illinois at Urbana-Champaign RBRC SSA Workshop 2005. 2.  0. . h. Sivers Fcn from Back2Back Analysis.

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Mickey Chiu University of Illinois at Urbana-Champaign RBRC SSA Workshop 2005

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  1. New Prospects for SSA Measurements in PHENIX:How can we separate out the various contributions to SSA at RHIC? Mickey Chiu University of Illinois at Urbana-Champaign RBRC SSA Workshop 2005

  2. 2 0  h Sivers Fcn from Back2Back Analysis Boer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/0312320 • Non-Zero Sivers function means that there is a left/right asymmetry in the kT of the partons in the nucleon • For a positive Siver’s function, there will be net parton kT to the left (relative to direction of proton, assuming spin direction is up). • 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

  3. Unpolarized Results from Run03 p+p Boer and Vogelsang, PRD69:094025,2004 Run03 -charged dn/d anti-aligned aligned • Asymmetry • numerator is difference between aligned and anti-aligned  dist’s, where aligned means trigger jet and spin in same direction • 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)

  4. Estimated AN from Run03 p+p 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). • Assumed Poisson statistics • 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

  5. 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

  6. 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

  7. Combined Effects Full di-jet Sivers Reduced by lower <P>, di-hadron smearing Run03 p+p gamma-charged, 0.35/pb

  8. process contribution to 0 x, pT coverage Vogelsang et al • Boer-Vogelsang paper considers pT ~ 10 GeV jets • x coverage here slightly lower • gluon dominated region

  9. “Radial” Running Modes ST ST SL • Could run in “radially” transverse mode • Preferred mode for this analysis • There could be a transverse component during longitudinal running • Coexist with longitudinal running • Have to worry about longitudinal asymmetry contribution

  10. Measuring Collins in p+p? Belle cos(2h) method Seidl ~ h e+e- p+p • Important test of Universality and Scale Evolution • Collins needs to be known in p+p to get transversity from SSA • p+p is much more complicated • Intrinsic kT as well as radiative effects • Many other diagrams • t-channel “dominates” over s-channel • At LO, this is a dilution of 10-3 • ~5% cos(2h) modulation at Belle becomes 0.5x10-4 modulation at RHIC • unpolarized beam required: ~ 300/pb (200 GeV), 980/pb (500 GeV)

  11. Summary & Observations • It could already be that transversity and Collins are not important in p+p, and that gluon Sivers = 0. • Would be important to verify this independently with techniques that are a priori theoretically unambiguous • Given 0.35/pb of data, we should be able to get 1% statistical significance in AN using gamma-charged measurements of jet  • Expected raw AN could be 3.5% • Could also be as low as 0.5%, or as large as 10% • Effects from P=0.5, jet angle not aligned with transverse polarization, and fragmentation to dihadrons reduces raw AN to ~1.0% • Can Collins be directly measured at RHIC? • Contribution is whatever remains? Sivers Collins Higher Twist

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