CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Transverse Spin...

CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13th 2004

Transverse Spin Physics at RHIC

o Introduction

o Transverse Proton Spin Structure

o Single Transverse Spin Asymmetries

o Avenues to Measure Transversity at RHIC

o Spin Dependent Fragmentation Functions

o Summary

Matthias Grosse Perdekamp, UIUC and RBRC

Proton

averagehelicity quark)Qq(x 2,

differencehelicity quark )Qq(x 2,

fliphelicty )Qq(x 2,

(well known)

(moderately well known)

(unknown)

onDistributi Gluon)QxG 2,(

(moderately well known)

onPolarizati Gluon )QxG 2,((unknown)

Nucleon Structure

Quark and Gluon (parton) Distribution Functions

What is the origin of the Proton Spin? (and it’s mass??)

How Do We Study Proton Sub-Structure?

Hard Scattering!

Deep inelastic lepton nucleon scattering (“DIS”)

High energetic proton-proton collisions

Cross Section, example DIS of e-p:

),(),,(),,(),,(

QxGQxGQxqQxq

Measure: Cross sections/structure functions

Extract: Quark- and Gluon Distribution Functions

protonspectator system

current quark jet

Factorization and Universality?

Cross Section Forward Elastic Scattering AmplitudeOptical Theorem

protonspectator system

current quark jet

q(x,Q2), G(x,Q2)

photon, gluon

proton

pQCD, hard scatteringquark

Process independentquark and gluon distri-butions Universality?

initial state final state

Factorization?

Extracted q(x,Q2) and G(x,Q2):J. Pumplin et.al JEHP 0207:012 (2002)

3.16GeVQ at u

3.16GeVQ at d

10-410-3 10-2 10-1 0.5 x

up-quarks

anti-down

Quark and Gluon Distributions

error on G(x,Q2)

error for u(x,Q2)

+/- 10%

+/- 5% +/- 5%

CTEQ6: use DGLAP Q2-evolution of

quark and gluon distributions to extract q(x,Q2)and G(x,Q2) from global fit to data sets at different scales Q2.

error for d(x,Q2)

10-410-3 10-2 10-1 0.5 x

q(x,Q2) and G(x,Q2) + pQCD beautifully agree with HERA + Tevatron!

J. Pumplin et.al JEHP 0207:012 (2002)

D0 Jet Cross Section ZEUS F2

q(x,Q2), G(x,Q2) and D(z,Q2) + pQCD consistent with experiment at RHIC

o Good agreement between NLO pQCD calculations and experiment can use a NLO pQCD analysis to extract spin dependent quark and gluon distributions from RHIC data!

PHENIX π0 cross section a |η|<0.35 Phys.Rev.Lett.91:241803,2003

STAR π0 cross section a 3.4<η<4.0 Phys.Rev.Lett.92:171801,2004

uncertainty ingluon fragmentation

1P)( 1xfi

)( 2xf j

22Pxij

)()()(

2121,,,

zDdxdx

ffffdxfxfdxdzdx

Xppdkf

lkjiji

Proton Structure

Hard Scattering Process

Fragmentation

Access to Quark and Gluon Distributions in pp at RHIC

pQCD Quark and Gluon distributions from DIS + pp Universality!

Fragmentation Function from e+e- Universality!

measure

Can solve forone unknownparton dstrb.

Observables: spin dependentcross sections, eg. the inclu-sive π0 cross section.

Factorizes: pdf x parton scattering x fragmentation cross section function

Incoming protons Hard scattering

xGqqga

xGqqgaA

sdui ii

Double Spin Asymmetry

qGluon Compton (85% of )

Example: Spin dependent Gluon Distribution ∆G(x,Q2) in Prompt Photon Production I

aLLgggg

Observable:

QCDQCD

prompt photon yields

relative Luminosity

• If projected future PHENIX Prompt Photon Data are included in a Global QCD Analysis the error on ∆G(x,Q2) will be significantly reduced :

AAC Pre

liminary

AAC Pre

liminary

M. Hirai, H.Kobayashi, M. Miyama et al.

Example: Spin dependent Gluon Distribution ∆G(x,Q2) in Prompt Photon Production II

Helicity Amplitudes in Hard Scattering

proton, Hf

Forward Scattering Amplitude

proton, Hi

initial state final state hard probe:gluon, photon

Quark, hfQuark, hi

)δq(x,Q

) (x,QgQxq

)(x,QFQxq ,

h: quark helicity H: proton helicity

In initial andfinal state

Hi hi Hf hf

Helicity isconserved

helicity average

helicity difference

helicity flip

transversity quark distributions

structure functions:

The transversity function h1(x)

quark distrb.

d,su,i

2i1 (unpol.) e F - - )(

1)( xqxxq i

d,su,i

2i1 )(long.pol. e g - - )(

1)( xqxxq i

d,su,i

2i1 .)(trans.pol e h - - )(

1)( xqxxq i

),(),(),( 222 QxqQxqQxq iii

Probability to probe a quark of flavor i and momentum fraction x that contributes to the spin of a transversely polarized proton

Helicity flip!),(),( hHhH

helicity amplitudes

spectators

proton spin

Transversity distributions are the lastunknown leading twist nucleon distribution functions.

Helicity flip amplitude no gluon transversity pure quark observable avoid complicated coupling between gluon- and quark degrees of freedom we observe for longitudinal polarization: Lattice results suggest that the transverse quark spin sum is large. For example,

Interesting properties: chiral odd, does not mix with gluons under evolution

For non-relativistic quarks : Difference provides information on quark dynamics in the nucleon.

Soffer’s bound: not small! Possibly

Some Observations

),(),(),(2 222 QxqQxqQxq iii ii qq

),(),( 22 QxqQxq

09.056.0 sdu S. Aoki, M. Doui, T. Hatsuda and Y. Kuramashi Phys.Rev. D56 (1997)433

),( 2Qxq

Transversity in Inclusive Processes

Does not contribute in leading twist inclusive DIS

q chirality unchangedby strong interactionor electromagnetic

current

1OHigher twist contributions aresuppressed by

Semi-inclusive DIS with chiral odd fragmentation function:

Collins fragmen-tation function

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

The Collins Fragmentation function

z = Eh / Eq

angle between S and kT around quark-jet axis

),()()( 1)(21 TppT kzHxfxqA

AT = q

q)sin(

)(1 zH

, Xppep

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

Scatter hard probe on trans-versely polarized protons andobserve left-right assymmetryAT for pions in the final state!

quark which has absorbedthe hard probe and fragmentsinto a pion. The quark carriesspin Sq.

The Collins Effect in the Artru Fragmentation Model

π+ picks up L=1 tocompensate for thepair S=1 and is emittedto the right.

u-quark absorbsphoton/gluon and flips it’s Spin.

Proton spin is pointing up!

String breaks anda dd-pair with spin-1 is inserted.

A simple model to illustrate that spin-orbital angularmomentum coupling can lead to left right asymmetriesin spin-dependent fragmentation:

First Measurements of AN in E704

ANANAN π+

Theory: Collins only Theory: Sivers only Theory: higher twist Anselmino et al. Anselmino et al. Qiu- Sterman

1 :ObservableGeV 20s

No discriminative power!

What is the Sivers Effect?

Sivers Effect: kT distribution of quarks depends on the transverse proton spin direction.

proton

proton Sivers function:

J. Collins, 1993 : Sivers function is forbidden by symmetry properties (T-odd)Brodsky, Hwang and Schmidt 2002: Sivers function can arise from interference with diagrams with soft final state gluon exchange.

D. Sivers 1990

Sivers Effect and Orbital Angular Momentum(Hide Tanaka at Trento, June 2004)

M. Burkardt

The Sivers Effect in DIS(Hide Tanaka at Trento, June 2004)

M. Burkardt

Collins Asymmetry Sivers Asymmetry

New Hermes Results(A. Miller, Trento June 2004)

π+ appears to be positive!!Relative sign between π+ and π0 requires H1(favored)=-H1(unfavored)

First RHIC Results on AN (I)

o Our ability to distinguish between possible sources of the observed asymmetry is limited by statistics. Run 2005 with P=0.5 and ∫Ldt > 3.0pb-1 will reduce improve errors by factor 10. Brahms!!

PHENIX AN(π0) and AN(π0) at |η|<0.35

C. Aidala, DIS 2004, to be published

STAR AN(π0) at 3.4<η<4.0 Phys.Rev.Lett.92:171801,2004

Run 02, ∫Ldt ~ 0.2pb-1, P~0.15

o First spin results from RHIC AN sizeable in forward XF

AN compatible with 0 at η~0 (as expected from pQCD)

First RHIC Results on AN (II)

STAR AN for leading charged hadrons in the central rapidity region

AN compatible with 0 consistent with pQCD

STAR Prelim

(A) Physics Channels for Low Luminosity (2005/2006)

The Transverse Spin Program at RHIC

GeV 200,pb 101 1 sLdt

)( :A Measure N XhppAN

STAR Phys. Rev. Lett. 92:171801, 2004

Boer and Vogelsang (hep-ph/0312320):azimuthal back to back correlation between hadrons in opposite hemisphere jets:

Separation of intrinsic transverse quark spin (transversity) from trans-verse momentum effects (Sivers)?

Clean channel for Sivers effect!

STAR, PHENIX and BRAHMS STAR and PHENIX

(I) (II)

(B) Physics Channels for high L

:ionFragmentat ceInterferen

Transverse Spin at RHIC

: Jets in EffectCollins

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

R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920

J. Collins, S. Heppelmann, G. Ladinsky, Nucl.Phys. B420 (1994)565

GeV 200,pb 100-03 1 sLdt

Statistical sensitivity for AT with 32pb-1 Brahms AN measurements from 2004and 2005 polarized proton runs!

Brief PHENIX and STAR runs on AN and back-to-backcorrelations as ∫ Ldt/week>1pb-1/week (2006?)

STAR and PHENIX

: gmentationLambda Fra

XppAT M. Anselmino

qqllppATT )( : YanDrell

34 103105 TTA

production jet Inclusive

J.Ralston and D.E. Soper, Nucl. Phys. B152, 109(1979)

qqllppATT )( : YanDrell

O.Martin, A. Schafer, M. Stratmann, W. VogelsangPhys.Rev. D60, 117502(1999)

Drell Yan

func.) dis. func. dis. O (

Observable

qq J.Ralston and D.E. Soper, Nucl. Phys. B152, 109(1979)

][GeV masspair lepton

PHENIX at pb ,320 1 Ldt

upgrade RHIC fb ,8 1 Ldt

Luminosity limited!

The PHENIX Detector

• 2 central arms: electrons, photons, hadrons– charmonium J/, ’ ee

– vector meson ee – high pT

– direct photons– open charm – hadron physics

• 2 muon arms: muons– “onium” J/, ’, – vector meson – open charm

• combined central and muon arms: charm production DD e

• global detectors

forward energy and multiplicity– event characterization

designed to measure rare probes: + high rate capability & granularity+ good mass resolution and particle ID- limited acceptance

Au-Au & p-p spin

The PHENIX Detector: Central Arms

Two Collisions seen by the PHENIX Central Arms

Au-Au d-Au

RHIC Schedule for Future Runs

2004 2005 2006 2007 2008 2009 ….

pp 5+1 5+10 5+11 0 5+9 156pb-1

√s= ……………………….. 200 GeV ………………….........|

P= 0.45 0.5 0.7 ………………………………………….

Inclusive hadrons + Jets Transverse Physics Charm Physics direct photons Bottom physics W-physics

ALL(hadrons, Jets) ALL(charm)

ALL(γ) AL(W)

L= 6x1030cm-2s-1 8x1031cm-2s-1

Polarized pp, SIDIS, e+e-: Global Analysis

q̂ q Measure

datafactory -b using ee in ,q̂ Measure

global analysis for best results…

1HqSingle transverse spin asymmetries in SIDISHERMES COMPASSJLAB

in polarized pp: AN, AT, ATT

BRAHMS PHENIX STAR

IV Lattice calculation of the tensor charge RBRC and elsewhere

Spin Fragmentation Functions from Belle

Raw charged pion Fragmentation (no corrections!) scanning about 0.3% of total sample

“World Data” for charged hadrons

NLO QCD parametrizations:(Kretzer and Kniehl Kraemer, Poetter)

Belle FFs consistent with LEP

*VERY* large sample:

Goal: measure Collins and interference fragmentation functions

Event Structure at Belle

e- , 8 GeV

e+ , 3.5 GeV

Jet axis: Thrust

<Nh+,-> = 6.4

Near-side Hemisphere: hi , i=1,Nn with zi

Far-side: hj , j=1,Nf with zj

Correlation Analysis: Collins Interference Fragmentation

zi vs zj zi1, zi2

vs zj1, zj2

GeV 5.10 ,2

• e+e- +jet1-

• Reaction plane defined withbeam (z-axis) and jet axis

• Hadron plane defined with and jet axis on each side:

i angle between the planes

A (z1)

(z2)cos()

Example: Collins Fragmentation Function in e+e-

Schedule: Measure spin dependent fragmentation function by the end of 2005 as input for future transversity measurements.

Summary

First evidence from HERMES that Transversity and Sivers functions may be different from zero.

Exciting connections to orbital angular momentumand quark dynamics in the nucleon.

Many complementary channels to explore transversespin phenomena at RHIC. Unique Sivers signature!

All experimental tools required are in place in STAR,PHENIX and BRAHMS.

AGSLINACBOOSTER

Polarized Source

Spin RotatorsPartial Snake

Siberian Snakes

200 MeV Polarimeter

AGS Internal Polarimeter

Rf Dipole

RHIC pC Polarimeters Absolute Polarimeter (H jet)

PHENIX

PHOBOS BRAHMS & PP2PP

Siberian Snakes

Run 04 achieved:1

106~GeV 200

peakLs ,

Pb~45% , 55 bunchesNew working point with long beam and polarization lifetimes

Run 05 planned:Time to tune accelerator complexMeasure: ALL(jets), ALL(π0)Commission strong supercon-ducting AGS snake (see M. Bai’s talk)

AGS pC Polarimeter

The successful Development of a novel Experimental Method:

Polarized Proton Collisions!

Helical Partial SnakeStrong Snake

Spin Flipper

source: Thomas Roser, BNL

)( 1xqi

)( 2xqi

22Pxij

dddzdm

dtdxdx

qqqqdxqxq

dddtdzdmdxdx

Xppd H

)()()(

Proton Structure

Hard Scattering Process

InterferenceFragmentation

Jian Tang , Thesis MIT, June 1999

R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920

X. Ji, Phys. Rev. D49 (1994)114J. Collins, S. Heppelmann, G. Ladinsky, Nucl.Phys. B420 (1994)565

Nucleon transversity through Interference Fragmentation

Currently unknown: Model Calculations LEP Measurement(s)

Model Calculations

(RBRC Workshop on Future Transversity:Delphi, Jakob et.al., Polyakov, Weiss et.al.Leader et.al )

measured parton dis.

1 :Experiment

Interference fragmentation

s-p wave interference fragmentation:

Parton emits followed by absorption of a forming a parton

200 GeV

500 GeV

qqqqqq

2,3/ˆˆ4ˆ

1cos83.0,0

Transverse Single Spin Asymmetry (Jian Tang, Thesis, MIT)

)(ˆsin)(ˆsin...ˆ)()(

...ˆ)(ˆ)()(

)cos()sin(sinsin4

zqzqxGxG

zqxGxq

Maximum Asymmetry

][GeVp jetT

Func. ionFragmentat Pol. :

DFs quarkity Transvers:

Shifts Phase Pion Two: sin

Pair Yield Pion

...sin)(ˆ)(ˆsin 10102

i ezqzqedzdm

Strong interaction phase shifts ,

s-wavep-wave

Non-vanishing “support” only in the mass region!

Sufficient mass Resolution?

Great for systematics!

,0IWhere:

P. Estabrooks and A.D. Martin, Nucl. Phys. B79 (1974)301

functions ionfragmentat ference

-dif and average spin :)(ˆ),(ˆ zqzq II

Interference Fragmentation

CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Transverse Spin...

Documents

Transverse spin results from PHENIX

RHIC SPIN: Experimental Issues

(longitudinal) Spin Program at RHIC-PHENIX

Xiaodong Jiang Gluon spin with longitudinal asymmetries at RHIC. Parton angular motion - transverse spin asymmetries. Spin at RHIC : p+p. Spin at JLab:

Future Perspectives on Transverse Single Spin Asymmetries at RHIC

Transverse Spin and RHIC Probing Transverse Spin in p+p Collisions

P-25 RHIC-SPIN research program

Single-Spin Asymmetries and Transverse-Momentum-Dependent Distributions at RHIC

Transverse Spin Asymmetries at RHIC Access to transverse momentum dependent distributions L.C. Bland Brookhaven National Laboratory 11 June 2007

Transverse Spin Physics: Recent Developments

RHIC Spin Physics

TRANSVERSE SPIN MEASUREMENTS IN

Transverse and Longitudinal Dynamics at RHIC

Spin Physics Results from RHIC

RHIC Spin and Collider

Carl Gagliardi – WWND – Trans Spin at RHIC 1 Transverse Spin Physics in pp Collisions at RHIC Carl A. Gagliardi Texas A&M University Outline Introduction

Transverse Single Spin Asymmetries in p+p Collisons at RHIC L.C. Bland Brookhaven National Laboratory Transverse Partonic Structure Workshop Yerevan, 21

Single Transverse Spin Asymmetries

RHIC Spin Flipper

Transverse Spin Physics at PHENIX