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Feng Wei PHENIX Collaboration Iowa State University

Measuring the Sivers Effect via Back-to-Back Di-Hadron Correlations in the PHENIX Experiment at RHIC. Feng Wei PHENIX Collaboration Iowa State University. Sivers effect. It is sensitive to proton spin and related to parton orbital angular momentum. Sivers Function.

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Feng Wei PHENIX Collaboration Iowa State University

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  1. Measuring the Sivers Effect via Back-to-Back Di-Hadron Correlations in the PHENIX Experiment at RHIC Feng Wei PHENIX Collaboration Iowa State University Feng Wei

  2. Sivers effect It is sensitive to proton spin and related to parton orbital angular momentum Sivers Function Perturbative LO Twist-3 Calculations (Qiu-Sterman, Efremov, Koike) is related D.W. Sivers, Phys. Rev D41, 83 (1990), Phys. Rev. D 43, 261 (1991) In arbitrary scale, schematic to show shape kT ┴ kT ┴ Feng Wei

  3. Interpretation Two Possibilities: P1 P2 1. Nuclear Shadowing (angular momentum) 2. Impact Parameter Space Changes with polarization • Attractive rescattering of hit quark by gluon creates transverse momentum • M.Burkardt [hep-ph0309269] – impact parameter formalism • Orbital angular momentum at finite impact parameter • Observed and true x differ • Observable left/right asymmetry 3 Feng Wei

  4. PHENIX Spin Program Production Prompt Photon Heavy Flavors Sivers Effect et al. Utilizing high energy polarized proton beams of RHIC Feng Wei

  5. Physics Observable The Sivers di-jet measurement was proposed by Boer-Vogelsang in Phys.Rev.D69:094025 (2004) Sivers Function Y qT qT┴ pT (π0) pT (h) • PHENIX central arms cover only half of the azimuthal angle • Measure the vector sum of trigger π0and away-side leading hadrons' transverse momentum as qT qT|| X ST Pp Feng Wei

  6. RHIC as polarized proton collider BRAHMS & PP2PP (p) PHENIX (p) STAR (p) Absolute Polarimeter (H jet) RHIC pC Polarimeters Siberian Snakes Spin Rotators 2  1011 Pol. Protons / Bunch 120 Bunches / Fill Partial Siberian Snake LINAC BOOSTER Pol. Proton Source 500 mA, 300 ms AGS AGS Internal Polarimeter 200 MeV Polarimeter Rf Dipoles Feng Wei

  7. PHENIX Detector - Central Arm   0 EMCAL — measure energy deposit of particles — e,γ, h DC —obtain momentum of charged particles PC —measure hit position of charged particles EMCAL (PbSc + PbGl) 0 h- Tracking and Matching(DC, PC) charged hadrons Central Arm: |η| < 0.35 Feng Wei

  8. AN Measurements N: Di-Hadron Yield ↑(↓): Spin Up (Down) + (-) : qT┴>0 (<0) R: Relative Luminosity (BBC) P: Beam Polarization Bunch spin configuration alternates every crossing Possibility for false asymmetries are greatly reduced Feng Wei

  9. Acceptance Correction Fragmentation is not included, kT┴, kT|| were studied Toy MC simulation: • A simple “Gaussian” model • kT┴ and kT|| are Gaussian distributions PRD 74, 072002 (2006) • The kT┴ distribution “shift” due to the Sivers effect • Parametrizes the pythia output to inject an asymmetry • Calculate the output asymmetry in acceptance • Asymmetry of kT┴ is diluted • Asymmetry of kT|| is enhanced Output Asymmetry Full 2πAcceptance PHENIX Acceptance Input Asymmetry Feng Wei

  10. Fragmentation Dilution Toy MC simulation: • A recent global analysis of fragmentation functions for charged hadrons was Included • The parameterization for light quarks only • The transverse momentum of each “hadron” is smeared using a Gaussian jT, PRD 74, 072002 (2006) • Use the same cuts for real data analysis to select the hadron pair • Calculate output asymmetry respect to input asymmetry to extract dilution factor Output Asymmetry Full 2πAcceptance PHENIX Acceptance Input Asymmetry PRD 76, 074033 (2007) Where DiH for quarks and anti-quarks of all flavors i as well as for gluons Feng Wei

  11. Preliminary Result from PHENIX in run-6 • qT┴ should show an asymmetry due to Sivers function. • qT|| should show no asymmetry, only for cross check. • Measurement result: the asymmetry for qT┴ due to Sivers effect is consistent with zero. • Fragmentation dilution factor is not included. If an asymmetry is measured Feng Wei

  12. Extension work in run-8 hadron Phys. Rev. D 75, 074019 (2007) π0 By C.J. Bomhof et al. • Central arms: ||<0.35, =290o • Muon arms: 1.2<||<2.4, =360o • New muon arm hadron trigger was used • MPC: 3.1<||<3.7, =360o (See M.Chiu’s talk) • Higher luminosity — more than twice recorded luminosity in run6 Feng Wei

  13. Summary • PHENIX measured the asymmetry due to the Sivers effect consistent with zero in di-hadron correlation at mid-rapidity. More data would produce a better constraint. • Theory suggests that the asymmetry may be larger at forward rapidity than that at mid-rapidity • Exciting results can be expected from run8 at forward rapidity • Central-Muon arm di-hadron correlation • Di-hadron measurement with the MPC (See M.Chiu’s Talk) Feng Wei

  14. Back Up Feng Wei

  15. Result from STAR at RHIC PRL 99, 142003 (2007) - VY 1, VY 2 are calculations by Vogelsang & Yuan, PRD 72 054028 (2005) - Bomhof et al PRD 074019 75, (2007) Feng Wei

  16. Hermes Measurement PRL. 94, 012002 (2005) Collins Effect Sivers Effect Feng Wei

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