feng wei phenix collaboration iowa state university

Spin 2008 - Sivers Effect Feng Wei 1

Measuring the Sivers Effect via Back-to-Back Di-Hadron Correlations in the PHENIX

Experiment at RHIC Feng WeiPHENIX CollaborationIowa State University

Feng Wei 2Spin 2008 - Sivers Effect

Sivers effect

||||||

)(),(),(),,( 2

10

TpT

TpTT

NTTT

kPS

kPSkxfkxfSkxf

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 3Spin 2008 - Sivers Effect 3

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:


PHENIX Spin Program

Prompt Photon LLA (gq X)

Transverse Spinu u d d , , ,

u u d d

Flavor decomposition

GGluon Polarization

L lA (u d W ) T

,

A p p ( , ) X

I nterference fragmentation:

:Transversity q

NSingle Asymmetries A

Production LLA (gg,gq X) W Production

L lA (u d W )

Heavy Flavors LLA (gg cc,bb X)

TTDrell Yan A

Utilizing high energy polarized proton beams of RHIC

Sivers Effect et al.


Physics Observable

||||||

)(),(),(),,( 2

10

TpT

TpTT

NTTT

kPS

kPSkxfkxfSkxf

TkPS

kPS

N kATpT

TpT

||||||

)(

Sivers Function

X

Y

pT

(h)

pT (π0)

qTqT┴

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)


RHIC as polarized proton collider

BRAHMS & PP2PP (p)

STAR (p)

PHENIX (p)

AGS

LINACBOOSTER

Pol. Proton Source500 A, 300 s

1-2

-1

nb607L)FOM(P

onPolarizati Average%53

pb 2.7 Luminosity ,200

GeVs

Spin Rotators

Partial Siberian Snake

Siberian Snakes

200 MeV Polarimeter AGS Internal PolarimeterRf Dipoles

RHIC pC PolarimetersAbsolute Polarimeter (H jet)

2 1011 Pol. Protons / Bunch120 Bunches / Fill


PHENIX Detector - Central Arm

h-

0

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


AN Measurements

NNNN

NNNN

PA

L

LR

RNN

RNN

PA

N

N

1

,1

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


Acceptance Correction

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

kT┴ kT||

Factor 0.83 1.24

Full 2π Acceptance

PHENIX Acceptance

Input Asymmetry

Output

Asym

metry

)acceptance 2 Full(

)acceptance PHENIX(

DHN

DHN

A

Af

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

cGeVkk TT /5.12//

2


Fragmentation DilutionToy 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

Input Asymmetry

Output

Asym

metry

PHENIX Acceptance

Full 2π Acceptance

]1,2[]1,2[])1(1[)1(

0 ),(

iiiiii

ii

iiai

BBzzzNH

i zD

PRD 76, 074033 (2007)

Where DiH for quarks and anti-quarks of

all flavors i as well as for gluons

cGeVjT /587.02


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.

TzNzNTpTN qPAPAkPSA for )()( )(If an asymmetry is

measured


Extension work in run-8

Central arms: ||<0.35, =290o

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

hadron

π0Phys. Rev. D 75, 074019 (2007)

By C.J. Bomhof et al.


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 rapidityCentral-Muon arm di-hadron correlationDi-hadron measurement with the MPC (See

M.Chiu’s Talk)


Back Up


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)


Hermes Measurement

Yan-Drell2

1SIDIS2

1 |),(|),( TTTT kxfkxf

PRL. 94, 012002 (2005)

Collins Effect

Sivers Effect

feng wei phenix collaboration iowa state university

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dilutedasymmetry of

acceptanceasymmetry

proton spin

qtthe sivers

sivers effectparametrizes

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