Jim Stewart DESY Measurement of Quark Polarizations in Transversely and Longitudinally Polarized Nucleons at HERMES for the Hermes collaboration Introduction

Jim StewartDESY

Measurement of Quark Polarizations in Measurement of Quark Polarizations in Transversely and Longitudinally Polarized Transversely and Longitudinally Polarized

Nucleons at HERMESNucleons at HERMES

for the Hermes collaboration

•IntroductionIntroduction•The HERMES ExperimentThe HERMES Experiment•Measurement of the Quark Helicity DistributionsMeasurement of the Quark Helicity Distributions•Transversity Measurements at HERMESTransversity Measurements at HERMES•SummarySummary

August 2004August 2004J. StewartJ. Stewart

Semi-Inclusive Deep Inelastic ScatteringSemi-Inclusive Deep Inelastic Scattering

2

lab

2

lab

22

had

(k k )

E

Q

Qx

2ME

z

E

q

The cross section can be expressed as a convolution of a The cross section can be expressed as a convolution of a

distribution function and a fragmentation function.distribution function and a fragmentation function.

ep eh eq eq

q

p qq h~ D FF F


Distribution FunctionsDistribution Functions

)()()( xqxqxq" )()( xqxqq

"

)()( xqxqq

HERMES 1996-2000HERMES 1996-2000 HERMES >2002HERMES >2002

Leading TwistLeading Twist

3 distribution functions survive the integration over transverse quark momentum3 distribution functions survive the integration over transverse quark momentum

unpolarized DFunpolarized DF Helicity DFHelicity DF Transversity DFTransversity DF

1F (x) 1g (x)

vector charge axial charge tensor charge

SPxqPxqPxqQx 552 )(

21

)(21

)(21

),( SPxqPxqPxqQx 552 )(

21

)(21

)(21

),(

Transversity Transversity

basisbasis


Virtual Photon Asymmetry - Path to Virtual Photon Asymmetry - Path to qq

3/ 2

N

N q

~ q(x)

S S 3/ 2

S S

"1/ 2

N

N q

~ q(x)

S S 1/ 2

S S

•Virtual photon can only couple to quarks of opposite helicityVirtual photon can only couple to quarks of opposite helicity

•Select quark helicity by changing target polarization directionSelect quark helicity by changing target polarization direction

•Different targets give sensitivity to different quark flavors Different targets give sensitivity to different quark flavors

,q (x) (x) (x)

( : , , , , , )

f f fq q

f u d s u d s

."


Quark PolarizationsQuark Polarizations

2 2 2

1/ 2 3/ 2

2 2 21/ 2 3/

2

2

2

21 2 2

( ,Q )A ( ,Q )

( ) ( ,( ,Q ( )

(

) Q )

( ,Q )

( ,

~ ~( ,Q ) ( ,Q ) )

)

hh hf f f f

h h hf f

hq f

hq q q f

hq

f

h

f

e q x dzD z

e q x dzD

e q x dzD z

e dzD z

q

z

x

x

x

z q x

P

1, 1, 1, 1, 1,( ( ), ( ), ( ), ( ), ( ))Kp d p d pA A x A x A x A x A x

, , , ,u d u d s

Qu d u d s

Correlation between detected hadron Correlation between detected hadron and the struck quark allows and the struck quark allows flavor flavor separationseparation

Linear System in Linear System in Q

QA P

Inclusive DIS Inclusive DIS →→Semi-inclusiveSemi-inclusive →→ , , , ,u u d d s


The HERMES ExperimentThe HERMES Experiment

•27.5 GeV polarized positron beam (<P>~53%)

•Longitudinally polarized H

•(<P>~85%)

•Transversely polarized H (<P>~78%)


The Measured Hadron AsymmetriesThe Measured Hadron Asymmetries

DEUTERIUMDEUTERIUM

PROTONPROTON

is an all sea

object and

K us

1,A 0Kd


Polarized Quark DensitiesPolarized Quark Densities

Polarized parallel to the protonPolarized parallel to the proton

q x q x q x ."

u(x) 0

Polarized anti-parallel to the protonPolarized anti-parallel to the proton

d(x)<0

Good agreement with LO-QCD fitGood agreement with LO-QCD fit

u(x) and Δd(x)

u(x) and d(x) ~ 0

s < 0

No indication for No indication for

→0.028 ± 0.033 ± 0.009 0.028 ± 0.033 ± 0.009

Measured rangeMeasured range

Submitted Phys.Rev.DSubmitted Phys.Rev.D


Properties of the Transversity DFsProperties of the Transversity DFs For non-relativistic quarks For non-relativistic quarks q(x)=q(x)=q(x)q(x)

→ q(x) probes the relativistic nature of the q(x) probes the relativistic nature of the quarksquarks

Due to Angular Momentum ConservationDue to Angular Momentum Conservation→ Different QCD evolutionDifferent QCD evolution→ No gluon componentNo gluon component

→ Predominately sensitive to valence quarksPredominately sensitive to valence quarks

BoundsBounds Soffer Bound: Soffer Bound:

T-evenT-even Chiral oddChiral odd

→ Not measurable in inclusive DISNot measurable in inclusive DIS

( ) ( ) ( )q

x q x q x

( ) ( )q x q x ( ) ( ) ( )q x q x q x


Measuring TransversityMeasuring Transversityep eh eq eq

q

p hq q~ D FF F Need a chiral odd fragmentation function: ‘Collins FF’Need a chiral odd fragmentation function: ‘Collins FF’

•ForbiddenForbidden •Need chiral odd Need chiral odd fragmentation functionfragmentation function

Transverse quark polarization affects transverse hadron momentumTransverse quark polarization affects transverse hadron momentumObserved asymmetry in azimuthal angle about lepton scattering Observed asymmetry in azimuthal angle about lepton scattering

plane plane Collins EffectCollins Effect

Artru string fragmentation modelArtru string fragmentation model String break produces quark- String break produces quark-

antiquark pairantiquark pair pair must preserve vacuum quantum pair must preserve vacuum quantum

numbersnumbers angular momentum conservation angular momentum conservation

gives the produced hadron gives the produced hadron transverse momentumtransverse momentum


Sivers Function fSivers Function f1T1T

(x)(x)

Distribution functionDistribution function→ Naïve T-ODDNaïve T-ODD→ Chiral evenChiral even

a remnant of the quark transverse momentum a remnant of the quark transverse momentum can survive the photo-absorption and the can survive the photo-absorption and the fragmentation processfragmentation process

Can be inherited in the transverse momentum Can be inherited in the transverse momentum component component → influence azimuthal distributioninfluence azimuthal distribution

Non-vanishing Sivers function requires quark Non-vanishing Sivers function requires quark orbital angular momentumorbital angular momentum

Cross section depends on the angle between Cross section depends on the angle between the target spin direction and the hadron the target spin direction and the hadron production planeproduction plane


How to Measure TransversityHow to Measure Transversity

2 (1/ 2)1

2 (1/ 2)1 1

sin(

( , )

sin( )

( , )1,

( , ) ( , )

~ ( ) ( )

( ) ( )

)S

h S h S

UT ST h S h S

qq

qq TqS

N NA

S N N

e q x H z

e f x D z

Collins azimuthal momentCollins azimuthal moment

Sivers azimuthal momentSivers azimuthal moment

sin( )h

TS U

sin( )h

TS U Assuming gaussian distributions for initial Assuming gaussian distributions for initial

an final quark momentuman final quark momentum


RESULTSRESULTSCollinsCollins

SiversSivers

u 0

usin( ) 0s

and ssin( ) 0 in( ) 0s s

Unexpected result:Unexpected result:

sin( ) sin( ) ss

- Possible interpretation:Possible interpretation:

1, 1,disf favH H

usin( ) 0 L 0s

Sivers MomentSivers Moment

More theoretical input needed to More theoretical input needed to clarify interpretationclarify interpretation

ff1T1T

(x) DIS = - f(x) DIS = - f1T1T

(x) DY (x) DY

UNIVERSALITYUNIVERSALITY

Collins MomentCollins Moment

- Same SizeSame Size

Submitted to Phys.Rev.Lett.Submitted to Phys.Rev.Lett.


Summary and ConclusionsSummary and ConclusionsLongitudinally Polarized Target DataLongitudinally Polarized Target Data

First direct measurement of the helicity distributionsFirst direct measurement of the helicity distributions

Transversely Polarized Target DataTransversely Polarized Target Data Collins: Disfavored fragmentation functions appear to be Collins: Disfavored fragmentation functions appear to be

important and have opposite sign to the favoredimportant and have opposite sign to the favored Sivers: Amplitude is greater than zeroSivers: Amplitude is greater than zero

0, 0, , , 0u d u d s


Polarized SeaPolarized Sea

Unpolarized data on sea shows Unpolarized data on sea shows the Gottfried sum rule is broken the Gottfried sum rule is broken

d u 0

QSM expectation: Eur.Phys.J.QSM expectation: Eur.Phys.J.C14C14,147(2000),147(2000)Meson cloud model: Phys.Rev.DMeson cloud model: Phys.Rev.D6868,074002(2003),074002(2003)

Data favor symmertic ,but large uncertaintiesData favor symmertic ,but large uncertaintiesd u u d u- d s

Fit for , , ,u d u-d s


Purities Purities -- -- --


q

q

Documents

Jim Stewart DESY Measurement of Quark Polarizations in Transversely and Longitudinally Polarized Nucleons at HERMES for the Hermes collaboration Introduction