# Presentation: 883484

## 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

- Spin 2008 - Sivers Effect

## Sivers effect

- It is sensitive to **proton spin** and related to **parton orbital angular momentum**

- Sivers Function

- D.W. Sivers, Phys. Rev D41, 83 (1990), Phys. Rev. D 43, 261 (1991)

- In arbitrary scale, schematic to show shape

- kT ┴

- kT ┴

- Perturbative LO Twist-3 Calculations (Qiu-Sterman, Efremov, Koike) is related

- Feng Wei

- Spin 2008 - Sivers Effect

## Interpretation

-  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

- P1

- P2

- 1. Nuclear Shadowing (angular momentum)

- 2. Impact Parameter Space Changes with polarization

**Two Possibilities:**

- Feng Wei

- Spin 2008 - Sivers Effect

## PHENIX Spin Program

- Prompt Photon

**** Production

- Heavy Flavors

- Utilizing high energy polarized proton beams of RHIC

**Sivers Effect et al.**

- Feng Wei

- Spin 2008 - Sivers Effect

## Physics Observable

- Sivers Function

- X

- Y

- pT (h)

- pT (π0)

- qT

- qT┴

- qT||

- ST

- Pp

-  PHENIX central arms cover only half of the azimuthal angle
-  Measure the vector sum of trigger π0 and away-side leading hadrons' transverse momentum as qT

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

- Feng Wei

- Spin 2008 - Sivers Effect

## RHIC as polarized proton collider

**AGS**

**LINAC**

**BOOSTER**

- Pol. Proton Source
- 500 A, 300 s

**Spin Rotators**

- Partial Siberian Snake

- Siberian Snakes

- 200 MeV Polarimeter

- AGS Internal Polarimeter

- Rf Dipoles

- RHIC pC Polarimeters

- Absolute Polarimeter
-              (H jet)

- 2  1011 Pol. Protons / Bunch
- 120 Bunches / Fill

- Feng Wei

- Spin 2008 - Sivers Effect

## PHENIX Detector - Central Arm

- h-

- EMCAL — measure energy deposit of particles — e,γ, h
- DC — obtain momentum of charged particles

- PC — measure hit position of charged particles

- Tracking and Matching (DC, PC)
- charged hadrons
- Central Arm: |η| < 0.35

- EMCAL (PbSc + PbGl)
- 0

- Feng Wei

- Spin 2008 - Sivers Effect

## 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

- Spin 2008 - Sivers Effect

## Acceptance Correction

**Toy MC simulation:**
- A simple “Gaussian” model
- kT┴ and kT|| are Gaussian distributions
- 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

|  | kT┴ | kT||  |
| --- | --- | --- |
| Factor | 0.83 | 1.24 |

- Full 2π Acceptance

- PHENIX Acceptance

- Input Asymmetry

- Output Asymmetry

- Fragmentation is not included, kT┴, kT||  were studied

- Feng Wei

- Spin 2008 - Sivers Effect

## 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
- Use the same cuts for real data analysis to select the hadron pair
- Calculate output asymmetry respect to input asymmetry to extract dilution factor

- Input Asymmetry

- Output Asymmetry

- PHENIX Acceptance

- Full 2π Acceptance

- arXiv:0707.1506v1

- Where DiH for quarks and anti-quarks of all flavors i as well as for gluons, into protons or antiproton (H = p or p-bar)

- Feng Wei

- Spin 2008 - Sivers Effect

## 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

- Spin 2008 - Sivers Effect

## Extension work in run-8

-  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 Mickey’s talk)
-  Higher luminosity — more than twice recorded luminosity  in  run6

- hadron

**π****0**

- Phys. Rev. D 75, 074019 (2007)

- By C.J. Bomhof et al.

- Feng Wei

- Spin 2008 - Sivers Effect

## 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 Mickey’s Talk)

- Feng Wei

- Spin 2008 - Sivers Effect

## Back Up

- Feng Wei

- Spin 2008 - Sivers Effect

## 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

- Spin 2008 - Sivers Effect

## Hermes Measurement

- PRL*. *94, 012002 (2005)

- Collins Effect

- Sivers Effect

- Feng Wei

- Spin 2008 - Sivers Effect