1

Transverse Spin Measurements at PHENIX

John Kosterfor the PHENIX collaboration

University of Illinois at Urbana-Champaign DIS2009

2009/04/27

2

Xpp

π+

π-

π0

RL

RL

N PA

1

GeV 20s

Experiment:(E704, Fermi National Laboratory, 1991)

Single Transverse Spin Asymmetries in pp Collisions

E704: Left-right asymmetries AN for pions:

AN difference in cross-section between particles produced to the left and right

Theory Expectation: Small asymmetries at high energies (Kane, Pumplin, Repko, PRL 41, 1689–1692 (1978) )

s

mA q

N

Right

Left

AN O(10-1) Measured

AN O(10-4) Theory

s

px L

F

2

AN

xF

3

),(

)(ˆ)(),( ,

21

3

2,121

3

. Thqlkji

Tqi pzFFdxdx

qqqqdxGkxq

dzdxdx

Xppdlk

fragmentationfunction

pQCD Proton Structure

small spindependence

Can initial and/or final state effects generate large transverse spin asymmetries? (AN ~10-1)

Possible Origin of Large Single Spin Asymmetries

h

X’

q

fb

fa

σ

FFq

4

Transverse Spin Effects in p↑p Collisions

(I) Transversity quark distributionsand Collins fragmentation functionCorrelation between proton & quark spin + spin dependant fragmentation function

),()( 221

kzHxqCollins FFQuark transverse

spin distribution

(II) Sivers quark-distribution

Correlation between proton-spin and transverse quark momentum

)(),( 21 zDkxf h

qq

T

Sivers distribution

π+

π-

π0

AN

xF

E704: Left-right asymmetries AN for pions:

D. Sivers, Phys. Rev. D 41, 83 (1990)

J. C. Collins, Nucl. Phys. B396, 161 (1993)

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RHIC Polarized Proton Collider

AGSLINACBOOSTER

Polarized Source

Spin Rotators

200 MeV Polarimeter

AGS Internal Polarimeter

Rf Dipole

RHIC pC Polarimeters Absolute Polarimeter (H jet)

PHENIX

PHOBOS BRAHMS & PP2PP

STAR

AGS pC Polarimeter

Partial Snake

Siberian Snakes

Siberian Snakes

Helical Partial SnakeStrong Snake

Spin Flipper

2009 Run:

Excellent performance during first 500 GeV run at RHIC ~10pb-1

200 GeV run ongoing

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RHIC ∫L* and Polarization

Run Energy Polarization Longitudinal Transverse

[GeV] [%] L [pb-1] LP4 [pb-1] L [pb-1] LP2 [pb-1]

2002 200 15 - - 0.15 3.4 x 10-3

2003 200 27 0.35 1.9 x 10-3 - -

2004 200 40 0.12 9 x 10-3 - -

2005 200 49 (47) 3.4 2 x 10-1 0.16 3.5 x 10-2

2006 200 57 (51) 7.5 7.9 x 10-1 2.7 7.0 x 10-1

2006 62 48 0.08 4.2 x 10-3 0.02 4.6 x 10-3

2008 200 46 - - 5.2 1.1 x 100

2009 500 ~35 ~10

2009 200 In progress

Steadily increasing polarization and luminosity

* integrated luminosity for PHENIX central arm

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0 Cross-Sections at y = 0Experiment vs Theory √s=200 GeV (RHIC) Agreement √s=19.4 GeV (FNAL/E704) Different

Process Contribution to 0, η=0, s=200 GeV

Neutral Pion Cross-Sections Experiment vs pQCD

Guzey et al, PLB 603,173 (2004)

Bourrely et al, Eur.Phys.J.C36:371-374,2004

de Florian et al, PRD:76,0940210 Cross-Sections at y = 0Experiment vs Theory √s=200 GeV (RHIC) Agreement √s=19.4 GeV (FNAL/E704) Different √s=62.4 GeV (RHIC) AgreementMore work needed to understand lower energies

8

p+p0+X at s=200 GeV/c2

PRL 95, 202001 (2005)

PHENIX Data at Mid-Rapidity Helps Constrain gluon Sivers Function

Experimental Measurement at y~=0 Comparison of Exp. To Theory

Anselmino et al, Phys. Rev. D 74, 094011

•Cyan: Gluon Sivers Function at positivity bound, no sea quark Sivers•Thick Red: Gluon Sivers parameterized to be 1 sigma from PHENIX 0 AN

•Blue: Asymmetry from Sea quark Sivers at positivity bound•Green: Asymmetry from Gluon Sivers for case of sea quark at positivity bound

High statistics 2006+2008 data coming. Smaller statistical errors (factor 23 improvement for 0’s)

Higher pT Possible

AN AN

pT (GeV/c) pT (GeV/c)

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PHENIX Detector at RHIC

Muon Arms 1.2 < | η | < 2.4• J/Psi• Unidentified charged hadrons• Heavy Flavor

Central Arms | η | < 0.35• Identified charged hadrons• Neutral Pions• Direct Photon• J/Psi• Heavy Flavor

MPC 3.1 < | η | < 3.9• Neutral Pion’s• Eta’s

PHENIX strategy:

Measure several observables each sensitive to different transverse spin effects

(i) Forward SSA Sivers & CollinsNeutral Pions

(ii) Transversity-type AsymmetriesInterference Frag. Func. Analysis

(iii) Sivers-type AsymmetriesHeavy FlavorBack to Back HadronsPion AN for y~0

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(i) Forward SSA AN 0 in MPC

Forward asymmetries contain mixture of contributions from

Sivers Transversity x Collins Twist-3PHENIX 0 results available for

√s=62 GeVComing soon from 2008 √s=200 GeV

dataset – 0 and 5.2 pb-1, 46% Polarization

Asymmetries could enter a global analysis on transverse spin asymmetries

Guzey et al, PLB 603,173 (2004)

Process contribution to

0, =3.3, s=200 GeV

• 3.1 < η < 3.7• η > 3.5

• η < 3.5

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(ii) Constraints on Transversity: Dihadron IFF Analysis

Interference Fragmentation Function Analysis

Measure di-hadron asymmetry with hadron pairs in central arm (0,h+) (0,h-), (h+,h-)

Measures δq(x) x H1

Transversity extraction will become possible with Interference Fragmentation Function (H1 ) measurement in progress at BELLE

+

+_

_q

IFF

IFF

21 ,

,

hh

UTA

12

Models for Interference Fragmentation Function

Use partial wave analysis of phase shift data to model IFF

Sign change around mass Jaffe, Jin and Tang, PRL 80 (1998) 1166

( , )q

Breit-Wigner shape for p wave No sign change around mass Trend consistent with HERMES results Bacchetta and Radici, Phys. Rev. D 74, 114007

(2006)

Analysis done in mass bins above and below the ρ mass

13

vs mass of the pair)sin(

UTA

Added statistics from 2008 running NEWNo significant asymmetries seen at mid-rapidity.

14

vs invariant mass of the pairsin

UTA

Added statistics from 2008 running NEWNo significant asymmetries seen at mid-rapidity.

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(iii) Constraints on Sivers Function: Heavy Flavor

D meson AN

• Production dominated by gluon-gluon fusion at RHIC energy

• Gluon transversity zero Asymmetry cannot originate from Transversity x Collins

• Sensitive to gluon Sivers effect

Anselmino et al, Phys. Rev. D 70, 074025 (2004)

p↑pDX

Gluon Sivers=MaxQuark Sivers=0Gluon Sivers=0Quark Sivers=Max

Theoretical prediction:

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(iii) Constraints on Sivers Function: Heavy Flavor

PHENIX: no reconstruction of D meson

Exploratory measurements of AN for single muons

Dominated by charm production in current kinematic range

Predicted asymmetry smeared by decay kinematics

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(iii) Constraints on Sivers Function: J/Psi

Exploratory measurement of AN J/Psi

J/Psi production mechanism not well understood

Single spin asymmetries may shed light on production mechanism

Constraints on gluon Sivers functionYuan, PRD78:014024,2008

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(iii) Constraints on Sivers Function: DiJet Production

Azimuthal distribution of Di-Jet production in ppSuggested in: Boer, Vogelsang, Phys. Rev. D 69, 094025

δφ

Counts

Beam is in and out of pageLook at back-to-back jet opening angles

δφ

Proton SpinkT

Sensitive to Sivers function only!

No Collins-type effects

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(iii) Constraints on Sivers Function: DiHadron Production

PHENIX Result from 2006 data:

Done with di-hadrons at y1=y2~=0

Asymmetry consistent with zero

Large 2008 data set available!

ηmin

ηmax

-3.7-3.1

-2.0-1.4

-0.35+0.35

1.42.0

3.13.9

Similar analysis possible in different combinations of rapidity

Works in progress…

pi0

h+/-

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Near Term Outlook -- Large 2008 Dataset

Initial constraints on gluon Sivers function Dedicated transversity channels:

– IFF Analysis– Future analysis with Collins asymmetry (See next slide)

Sivers function constraints possible with more data– Connection to orbital angular momentum?

Summary

(i) Forward SSA AN

0 at √s=200 GeV soon. Exploring η, K0short, Direct γ

(ii) Transversity-type measurements IFF results already preliminary Exploration Forward IFF

(iii) Sivers-type measurementsAN for y~0 smaller errors and higher pT

AN Heavy Flavor -- Forward open heavy flavor, J/Psi -- Mid-rapidity open heavy flavor

Di-Jet analyses will expand to rapidity-separated hadron pairs

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Long Term Outlook -- Upgrades

Vertex Detectors (2011-2012)

Large acceptance precision tracking– Heavy flavor tagging– Jets– Drell-Yan– Electrons from charm decays and

beauty decays separately– c,b-Jet Correlations

Forward Calorimetery (2012-2013)

Proposed PHENIX Upgrade ( 1 < eta < 3 )

– AN 0, Direct γ, γ-Jet

– Collins-type analyses

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Backup

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IFF: Definition of Vectors and Angles

1 2

1 2

1 2

, : momenta of protons

, : momenta of hadrons

( ) / 2

: proton spin orientation

A B

h h

C h h

C h h

B

P P

P P

P P P

R P P

S

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pp hhX

1 2hadron plane: ,

scattering plane: ,

h h

C B

P P

P P

����������������������������

���������������������������� : from scattering plane

to hadron planeR : from polarization vector

to scattering plane S

Bacchetta and Radici, PRD70, 094032 (2004)

2 CR��������������

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IFF: Transversity from di-hadron SSA

UTUT

UU

A

Physics asymmetry

IFF + Di-hadron FFto be measured in e+e-

Transversityto be extracted

Hard scatteringcross sectionfrom pQCD

Unpolarized quark distribution Known from DIS

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Ongoing IFF measurement at BELLE (RBRC/Illinois)

2

1

1hP

2hP

2h1h PP

e+

e-

thrust

axis

1 2

1 1 1 1 2 2 1 2

( ) ( )

( , ) ( , ) cos( )

jet jete e X

A H z m H z m

Artru and Collins, Z. Phys. C69, 277 (1996)

Boer, Jakob, and Radici, PRD67, 094003 (2003)

IFF sensitivity projection from data

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Use partial wave analysis of phase shift data to model IFF

Sign change around mass Jaffe, Jin and Tang, PRL 80 (1998) 1166

Models for IFF

( , )q

Breit-Wigner shape for p wave No sign change around mass Trend consistent with HERMES results Bacchetta and Radici, Phys. Rev. D 74, 114007

(2006)