m. grosse perdekamp, uiuc transverse spin measurements at rhic workshop on transverse spin and the...

M. Grosse Perdekamp, UIUC

Transverse Spin Measurements at RHIC

Workshop on Transverse Spin and the Transverse Structure of the Nucleon

3rd Joint Meeting of the DNP and the JPS in Waikola, Hawaii,

October 13h -17th , 2009 STARSTAR

M. Grosse Perdekamp, UIUC

Transverse Spin Measurements at RHIC

Inclusive Single Spin Asymmetries AN

in Hadron

Introduction RHIC Measurements Interpretation

Measurements to Isolate different Mechanisms Tansversity & Collins Sivers

Future Measurements Drell Yan & Jet-Photon

STARSTAR

Single Spin Asymmetries (SSA) in Hadron Collisions

Introduction

4

Single Spin Asymmetries (SSA) AN in Polarized Proton-Proton Scattering

sp

π

pp

π spp

p

= 0 ? AN =

NL - NR

NL + NR

NL : pions to the left

NR : pions to the right

Xpp Example:Inclusive π productionin polarized p-p

Correlation proton spin Sp vs pπ⊥ π transverse momentum

Single transversespin asymmetries AN

October 13th Transverse Spin Measurements at RHIC

5

Scaling Limit: AN 0 , QCD Test !?

4q 10, 20,3m example, N

qN AGeVsMeV

s

mA


6

Experiment: Sizeable SSA Observed over Large Range of Scales !

Experiment: AN >> 10-4 for 4 GeV < √s < 200 GeV for charged pions !

from Christine Aidala, Spin 2008 andDon Crabb & Alan Krisch in then Spin 2008 Summary, CERN Courier, 6-2009

ZGS √s=4.7 GeV AGS √s=6.5 GeV FNAL √s = 20 GeV RHIC √s = 200 GeV

π+

π-


Soft effects due to QCD dynamics in hadronsremain relevant up to scales where pQCD canbe used to describe the scattering process!

7

NLO pQCD Cross Sections vs RHIC data for Different √s and Rapidity Intervals

√s = 200 GeV

∆ PHENIX π0, η = 0∙ Brahms π+ ,η = 2.95 ⌷ STAR π0 ,η = 0

- - - - - NLO pQCD

√s = 62.4 GeV

See analysis in De Florian, Vogelsang, Wagner PRD 76,094021 (2007) and Bourrely and Soffer Eur.Phys.J.C36:371-374 (2004)

o PHENIX π0, η = 0-------- NLO pQCD

Good agreement between inclusivehadron cross sections from RHIC data and pQCD calculations !

pT [GeV]pT [GeV]


8

Origin of Large SSA Inspect Factorized Cross Section at Hard Scales!

2P

)( 1xqi

)( 2xG

11Px

22PxijLLa

1ps

Jet

proton structure

hard scattering reaction

fragmentationprocess

),(

)(ˆ)(),( ,

21

3

2,121

3

. Thqlkji

Tqi pzFFdxdx

qqqqdxGkxq

dzdxdx

Xppdlk

Final state – hadron fragmentation

pQCD

Initial state – proton structure

Kane, Pumplin, Repko aLL~10-4)

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

-1)


9

Origin of Large SSA for Hard Scattering --Two Solutions: Final State vs Initial State

(I) “Transversity” quark-distributions and Collins fragmentation

Correlation between proton- und quark-spin and spin dependent fragmentation

),()( 221

kzHxq

(II) Sivers quark-distribution+

Correlation between proton-spin and transverse quark momentum

)(),( 21 zDkxf h

qq

T

Collins FFQuark transversespin distribution

Sivers distribution

(III) Initial or final state twist-3+

Qiu/Sterman and Koike

STAR, PRL-92:171801, 2004

+ unified picture: Ji, Qiu, Vogelsang and Yuan in PRL-97:082002, 2006


First measurement atRHIC √s = 200 GeV

RHIC Measurements of AN

for Inclusive Hadrons

11

BRAHMS: AN for Charged Pions vs pT and xF at √s=62.4 GeV and √s=200 GeV

200 GeV

√s=200 GeV

√s=62.4 GeV

0.4<pT<0.6 GeV/c 0.5 pT<0.6 GeV/c 0.6 pT<0.8 GeV/c 0.8 pT<1.0 GeV/c 1.0 pT<1.2 GeV/c

0.5<pT<0.75 GeV/c1.0<pT<1.25 GeV/c 1.25<pT<1.5 GeV/c 1.5<pT<2.0 GeV/c 2.0<pT<2.5 GeV/c

AN increases withxF (valence quarks)

AN increases with pT (?)

Possibly constantfrom pT =1.5 GeV/c ?


PHENIX: AN vs XF for 0’s at √s=62.4 GeV

AN = 0 for xF < 0 no sizeableasymmetries at small x!

Larger forward asymmetries at higher pseudo-rapidity, η ?

Limited by statistics and correlations between xF, pT and η !


13

STAR Run 2006: pT Dependence of AN at √s=200 GeV PRL 101,222001

For given η strong correlation between xF and pT:

AN(pT)integratedover xF

AN(pT, xF)

AN increases with pT up topT ~ 3 GeV/c -- Models: AN ~ 1/pT


Decrease as ~1/pT expected from initial state effects is not observed.AN constant from pT>2.5 GeV. Need more statistics to extend measurement to pT > 4 GeV !

Positive xF Negative xF

Consistent with zero for all pT

STAR Run 2008: pT Dependence of AN at √s=200 GeV Ogawa at CIPANP 2009


K p

Large AN for K- significant Sivers asymmetries for sea quarks ?!

Large AN for anti-Proton unexplained.

BRAHMS: AN for Charged Pions ,Kaons and Protons at √s=200 GeV


Another Surprise: AN for Eta Mesons larger than for Pions !

STARSTAR0.361 0.064NA

0.078 0.018NA

GeV 200

s

Xpp

AN(η) > AN(π0) for 0.55 < xF < 0.75

Does this point to large effectsin the fragmentation?

STAR arXiv:0905.2840 (Heppelmann, DIS08)


17

Understanding of AN in terms of Collins and Sivers Effect:

Work in Progress! Future goal: Extract Sivers and transversity quark distributions from global anlaysis to all SIDIS, pp and e+e- data!

Present work: Extract Sivers + transversity from SIDIS and e+e- and predict AN in pp

Presently: Poor agreement with many problems to solve! Universality, evolution, pdf and fragmentation functions not sufficiently known.

For example, note the impact of un-polarized FFs thick line DSS thin line Kretzer


STAR π0

BRAHMS π+,-

Global analysis of SIDIS & e+e-

Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, TurkPhys. Rev. D75:05032,2007

AN calculation from D’Alesio

18

A RHIC and US-Japan Contribution to Transverse SpinAnalysis: Measurement of the Collins Effect in e+e- Annihilation into Quarks at Belle BNL-Illinois-RBRC-RIKEN

q1

quark-1 spin

electron

positron

q2quark-2

spin

e++e- π+ + π- + X

~ Collins(z1) x Collins (z2)


Belle Collinsasymmetries & global fit

Collins FF extracted from Belle data.

Measurement of the Collinseffect in e+e- at Belle:

SSA in Very Forward Neutron Production

neutron

Large negative SSA observed for xF>0

Diffractive physics Highly useful as local polarimeter at PHENIX


Measurements to Isolate Different Mechanisms o Transversity & Collins o Sivers

21

Ideas for Measurements of Transversity Observables

at RHIC

][

][

Xpp

Xhjetpp

Xpp

Xllpp

hemisphere

hemisphere

Drell Yan:Required luminosity not available at RHIC.

Spin dependent Lambda-FF unknown.Measure Λ-FF in e+e- ?

Collins effect in jets:Forward calorimeter upgrade in PHENIX

Di-hadron intereference fragmentation function. IFF data available from e+e- Belle !


22

Interference Fragmentation –IFF- for Di-Hadrons at Mid-Rapidity in

PHENIX

AUT compatible ~0

Dilution from gg processes!

Future:

Update with more statistics Study possibility of forward measurements: enhance qg fraction and higher x.


23

IFF Measurement in e+e- at BELLE

1 2( ) ( )jet jete e X

Artru and Collins,

Z. Phys. C69, 277 (1996)

Boer, Jakob, and Radici,

PRD67, 094003 (2003)

Vossen, Spin Conference in Dubna


q1

quark-1 spin

electron

positron

q2

quark-2 spinzpair-1

zpair-1

z1,2 relative pion-pair momenta

ϕpair-1ϕpair-21

1 2

2 θ

22 2

12 1 1 1 1 2 22

sin~ ( , ) ( , )

1 cos pair pair pair paira H z M H z M

PreliminaryPreliminary

Preliminary

Preliminary


Preliminary

Preliminary

Preliminary

Belle IFF- Asymmetries vs Hadron Pair Momentum Fraction zi

9x9 z1 z2 binning

z1

a12

BNL-Illinois-RBRC-RIKEN


25

Ideas for Measurements of Sivers Observables at RHIC

llpp

Xjetpp

Xpp

Xjetpp

Xflavorheavypp

Xjetjetpp

Xhpp

0

Precision measurement of AN at mid-rapidity.

Back-to-back correlations for jets.

AN for inclusive jets.

AN for heavy flavor.

AN for direct photons.

AN in jet-photon production.

AN in Drell Yan.

significant improve-ments from upgrades: forward calorimeters+ silicon vertex detectors


26

AN from 0 and h+/- at Central Rapidity

PRL 95, 202001 (2005)

Analysis with high statistics 2006+2008 data in progress Statistical uncertainties will reduce by factor 7.

PHENIX AN(η=0), Run 2002 PHENIX AN(η=0), Run 2005Anselmino et al, Phys. Rev. D 74, 094011

Constrain gluon Sivers effect with PHENIX 2002 0 data !


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

27

AN in Di-Jet Production in STAR

zx

y

180º

proton spin

1S

Di-jet pT

Additional kT kick to jet axis from Sivers effect Boer & Vogelsang, PRD 69, 094025 (2004)

parton

kK

Gluon radiation

Di-jet pT

STAR: PRL-99:142003,2007

Di-jet AN consistent with 0 and consistent with DIS


Sivers Effect in Heavy Flavor Production

Heavy flavor production gives sensitivity to gluon Sivers effect . Significant improvement with vertex detector upgrades. Work needed to connect theory and experimental observable.

Anselmino et al, PRD 70, 074025 (2004)

Gluon Sivers=0

Gluon Sivers=Max

Calculations for D mesons

Measurement for -

Future Measurements ofSivers Asymmetries in the

Drell Yan and Jet-Photon Channels

30

Transverse Spin Drell Yan at RHIC vs π-Sivers Asymmetry in Deep Inelastic

Scattering

• Important test at RHIC of the fundamental QCD prediction using gauge link formalism of the non-universality of the Sivers effect!

• Requires very high luminosity (~ 250pb-1)


31

Soft Gluon Interaction in the Initial and Final State of Hard Scattering Processes

...

22/

||)(1

~...

pOpQCQ

...ndtt

Integrate initial state gluon radiation: gauge linkand insert gauge link in hard scattering matrix element

Integrate final state gluon radiation: gauge link and insert gauge link in hard scattering matrix element


Unique predictions forprocess dependence:SIDIS vs Drell Yanor direct photon at RHIC!

32

Drell Yan at RHIC

ϒ-states

J/Ψ

Drell Yan

Ψ’

charm

bottom

FVTX enables DY measurement byrejecting heavy flavor background:Measurement: 4 GeV < Q < 10 GeV

yie

ld in

arb

itra

ry

un

its


Bland et al. “Transverse Spin Drell-Yan Physics at RHIC”http://thy.phy.bnl.gov/~vogelsan/drellyan1/dy_final.pdf

33

0.1 0.2 0.3 x

Siv

ers

Am

plitu

de

0

Experiment SIDIS vs Drell Yan: Sivers|DIS= − Sivers|DY

Test Unique Prediction of Gauge Theory

HERMES Sivers Results

Markus DiefenthalerDIS WorkshopMűnchen, April 2007

0

RHIC Drell Yan Projections


Bland et al. “Transverse Spin Drell-Yan Physics at RHIC”http://thy.phy.bnl.gov/~vogelsan/drellyan1/dy_final.pdf

34

ANphoton+Jet : An Alternative Test of the

Process Dependence of the Sivers Effect at RHIC

Bachhetta, Bomhof, D’Alesio, Mulders, MurgiaPhys.Rev.Lett.99:212002,2007.

Weig

hte

d m

om

en

t of

AN

ph

oto

n+

Jet

no process dependence

Correct process dependence

Measurement: AN in jet-photon productionforward photon η > 2jet -1 < η < 0

Much less luminosity hungry …

NSAC milestone for transverse spin (HP-13, 2015) ! Reachable at STAR. Requires FOCAL upgrade in PHENIX.


35

Summary

Single spin asymmetries found in the past at low center of massenergies persist at the highest center of mass energies at RHIC.

Precise AN data for inclusive hadrons are available from RHIC. Morestatistics is still needed to characterize the kinematic dependence ofAN at high pT. The theoretical analysis of AN into Collins and Sivers contributions continues to be challenging.

SSA in forward neutron production discovered at RHIC, are sizeable at all center of mass energies and used for local polarimetery at RHIC.

Several observables exist that will permit to isolate Sivers and Collins effects at RHIC. These measurement will benefit from detector and luminosity upgrades in progress at RHIC.

The newly developed gauge link formalism makes uniquepredictions for the process dependence of Sivers asymmetries that can be tested at RHIC in Drell Yan or Jet-Photon production.


36

Backup


37

Simple QEDexample:

DIS: attractive Drell-Yan: repulsiveSame in QCD:

As a result:

Non-universality of Sivers Asymmetries:Unique Prediction of Gauge Theory !


38

Collins Effect in Quark FragmentationJ.C. Collins, Nucl. Phys. B396, 161(1993)

q

momentum hadron relative : 2

z

momentum hadron e transvers:

momentum hadron :

spinquark :

momentumquark :

h

sE

EE

p

p

s

k

h

qh

h

h

q

qs

k

hph

,

Collins Effect:Fragmentation of a transversely polarizedquark q into spin-less hadron h carries anazimuthal dependence:

hp

sin

qh spk


39

General Form of Fragmentation Functions

h

qhh

hqhqh

h

q zM

spkpzHzDpzD

ˆ ),()(),( 2,

1,

1

Number density for finding hadron h from a transversely polarized quark, q:

unpolarized FF Collins FF


IFF- a12 vs Invariant Mass8x8 m1 m2 binning

40


Preliminary

Preliminary

Preliminary Preliminary

Preliminary

PreliminarySystematic errors shown.a12 increases with m1 and m2

reaches |a12 | ~ 0.1 at large mi.

m1 [GeV/c2]

a12

41

The Sivers Effect

proton

Sp

Sp

proton

Sivers function:D. Sivers 1990

Sivers:

Correlation between the transverse spin of theproton and the transverse momentum kT of quarks and gluons in the proton (link to orbitalangular momentum?)

M

SkPkxfxqA PTq

TN

)ˆ(

),()( 2211Observed asymmetry:


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