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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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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

sivers effect
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


Two Possibilities:



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


Feng Wei

phenix spin program
PHENIX Spin Program


Prompt Photon

Heavy Flavors

Sivers Effect et al.

Utilizing high energy polarized proton beams of RHIC

Feng Wei

physics observable
Physics Observable

The Sivers di-jet measurement was proposed by Boer-Vogelsang in Phys.Rev.D69:094025 (2004)

Sivers Function




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





Feng Wei

rhic as polarized proton collider
RHIC as polarized proton collider



STAR (p)

Absolute Polarimeter

(H jet)

RHIC pC Polarimeters

Siberian Snakes

Spin Rotators

2  1011 Pol. Protons / Bunch

120 Bunches / Fill

Partial Siberian Snake



Pol. Proton Source

500 mA, 300 ms


AGS Internal Polarimeter

200 MeV Polarimeter

Rf Dipoles

Feng Wei

phenix detector central arm
PHENIX Detector - Central Arm


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)



Tracking and Matching(DC, PC)

charged hadrons

Central Arm: |η| < 0.35

Feng Wei

a n measurements
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

acceptance correction
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

fragmentation dilution
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

preliminary result from phenix in run 6
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

extension work in run 8
Extension work in run-8


Phys. Rev. D 75, 074019 (2007)


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

  • 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

back up
Back Up

Feng Wei

result from star at rhic
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

hermes measurement
Hermes Measurement

PRL. 94, 012002 (2005)

Collins Effect

Sivers Effect

Feng Wei