Jim StewartDESY

The HERMES ExperimentThe HERMES Experiment

for the Hermes collaboration

•The HERMES ExperimentThe HERMES Experiment•Inclusive Structure FunctionsInclusive Structure Functions•Measurement of the Quark Helicity DistributionsMeasurement of the Quark Helicity Distributions•Transversity Measurements at HERMESTransversity Measurements at HERMES•Fragmentation FunctionsFragmentation Functions•SummarySummary

J Stewart

Hermes at HERAHermes at HERA

Beam Energy: 27.5 GeV

Electrons and positrons

Beam current

~50mA start of fill

~10mA end of fill

Polarized (<P>~53%)

P~45% now

Beam helicity reversable

Can be set at each expt.

Online measurement of beam Online measurement of beam polarization with two Compton polarization with two Compton polarimeters.polarimeters.

1.8 3.4% B

B

ΔP

P

J Stewart

The HERMES ExperimentThe HERMES Experiment

Fixed target experiment.Fixed target experiment. Polarized internal gas target.Polarized internal gas target. Magnetic spectrometer for Magnetic spectrometer for

momentum measurement.momentum measurement. Relatively large acceptance.Relatively large acceptance. Excellent particle identification.Excellent particle identification.

TargetTarget

J Stewart

The HERMES Polarized TargetThe HERMES Polarized Target

Longitudinal polarized H: <P>= 0.85 ± 0.03 =7.6 x 1013 nucl./cm2

Transverse polarized H: <P>= 0.78 ± 0.04 =1.1 x 1014 nucl./cm2

Long. Polarized D: =2.1 x 1014 nucl./cm2

→ <Pz+>=+0.85 ± 0.03 <Pz->= -0.84 ± 0.03

<Pzz+>= +0.89 ± 0.03 <Pzz->= -1.66 ± 0.05

Unpolarized gases used:

→ H2,D2,He,N2,Ne,Xe

J Stewart

The HERMES SpectrometerThe HERMES Spectrometer

21

175

1.0

2

x y

0.02 x 0.8 at Q GeV and W 2GeV

mrad, 4

Reconstruction :

Kinemati

0 mrad 140 mrad

p = 1.0 - 2.0%

c Ran

p

ge :

mrad

Particle Identification: TRD, Preshower, CalorimeterParticle Identification: TRD, Preshower, Calorimeter

1997: Threshold Cherenkov 1998: RICH + Muon-ID 1997: Threshold Cherenkov 1998: RICH + Muon-ID

J Stewart

hadron/positron separationcombining signals from: TRD, calorimeter, preshower, RICHTRD, calorimeter, preshower, RICH

Aerogel; n=1.03

C4F10; n=1.0014

hadron separationDual radiator RICH for , K, p

Particle IdentificationParticle Identification

K

J 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

J Stewart

Virtual Photon Asymmetry and DISVirtual Photon Asymmetry and DIS

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

#$

J Stewart

Cross Section in Deep Inelastic ScatteringCross Section in Deep Inelastic Scattering

L W

2 2

4

d σ E=

dΩdE 2MQ( , , ,) )

E, (

hadronicleptonic

k q s P q S

:L

1 2

1( ) ( )

g

i g

W

g

μ νμν 2 2

Symetric part Spin independent

2 2σ

Asymetric part Spi

1 2

σ σ

n dependent

p p(x,Q ) (x,Q )

qx,Q p q - qp x,QS S

. .

S

+ .

F F

Purely electromagnetic Purely electromagnetic →→ Calculable in QED Calculable in QED

:1 2, F FUnpolarized Structure FunctionsUnpolarized Structure Functions Polarized Structure FunctionsPolarized Structure Functions

1 2, :g gbb11,b,b22,b,b33,b,b4 4 for spin 1 nucleon “Tensor structure functions”for spin 1 nucleon “Tensor structure functions”

Momentum distributionMomentum distribution Helicity distributionHelicity distribution

1 2

1( ) ( )

1

61

2

g

g

W

i g

μ νμν 2 2

2 2σ σ σ

2 2μν μν μν

2 2μν μν μν μ4

1

ν

1 2

3

2

p p(x,Q ) (x,Q )

qS x,Q p qS -S qp x,Q

x,Q r x,Q s + t +u

1x,Q s -u +

b

x,Q s

F

b

b2

F

b - t

J Stewart

Structure Functions and Measured AsymmetriesStructure Functions and Measured Asymmetries

2 2e e 1 f f ff f

1 1F = q x q x q x

2 2 2 2g e e 1 f f ff f

1 1(x) = q x - q x q x

2 2

Momentum distribution of the QuarksMomentum distribution of the Quarks Helicity distribution of the QuarksHelicity distribution of the Quarks

A =

1 2A = D A + A

A =

2 1A = d A A

With D,d,R,With D,d,R, being being kinematic factorskinematic factors

Measurable AsymmetriesMeasurable Asymmetries

21 32 2 1 2

1 32 2

g g

11

AF

1 2g g

2 TL

1T

AF

Virtual Photon AsymmetriesVirtual Photon Asymmetries

J Stewart

World Data on World Data on

b t

1 N L -N LA =

P P N L -N L 1

21

g

2

A1A

F 1+ D

ProtonProton DeuteronDeuteron

Data shown at measured <QData shown at measured <Q22>:0.02-58 GeV>:0.02-58 GeV22

1 1g F

August 2005 J Stewart

Model-independent unfolding detector smearing QED radiative effects

)(

born

)(

born

meas

born

meas

ij

)(N

),(N

N

N

σ

σS

j

ji

radiative effects detector smearing

smearing within acceptance

kinematic migration insideacceptance for each spin state

systematic correlations between bins fully unfolded resulting (small) statistical correlations known

j=0 bin: kinematic migration into the acceptance

J Stewart

World Data on World Data on

Very precise proton dataVery precise proton data The most precise deuteron dataThe most precise deuteron data

The most precise neutron dataThe most precise neutron data

0.021-0.9 measured range:0.021-0.9 measured range:

1g2x (x,Q )

1 1 1p dg g g

3He

1 1 131 12 2

d p ndg g g w

1

1

0.1246 0.0032 0.0074

0.0452 0.0015 0.0017

p

d

g

g

J Stewart

The Structure Function bThe Structure Function b11(x,Q(x,Q22))

2 012

2 1b q

q

e q q q

0

1

1

02 3

2

dzzA

b

F

andand

J Stewart

First measurement of and First measurement of and at small xat small x In measured range (0.002-0.85)In measured range (0.002-0.85)

Qualitative agreement with Qualitative agreement with coherent double-scattering coherent double-scattering modelsmodels

The structure function bThe structure function b11(x,Q(x,Q22))

dzzA d

1bdzzA 0

dzzA 1%d1b 0

2d1 (1.05 0.34 0.35) 10b

hep-ex/0506018

3.2 M DIS events3.2 M DIS events<Pzz+>= +0.89 ± 0.03 <Pzz+>= +0.89 ± 0.03 <Pzz->= -1.66 ± 0.05<Pzz->= -1.66 ± 0.05

J Stewart

Quark PolarizationsQuark Polarizations

2 2 2

1/ 2 3/ 2

2 2

21 2

1/ 2 3/ 2

2 2

2 2

( ,Q ) ( ,Q )~ ~

( ,Q ) ( ,Q

( ) ( ,QA ( ,

)

)

(Q )

( )

) ( ,Q )

( , )

( )

hh hf f

hf f f f f

hq

hf f f f

h h hf f f f

he q x dzD z

e q

e q x dzD z

e q x x dzD z

x

dzD z

q x

q

z

xx

P

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

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

Qu d u d s 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

J Stewart

The Measured Hadron AsymmetriesThe Measured Hadron Asymmetries

DEUTERIUMDEUTERIUM

PROTONPROTON

is an all sea

object and

K us

1,A 0Kd

J Stewart

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 In 0.028 ± 0.033 ± 0.009 In

the measured rangethe measured range

A. Airapetian et al, Phys. Rev D 71 A. Airapetian et al, Phys. Rev D 71 (2005) 012003(2005) 012003

J Stewart

Polarized SeaPolarized Sea

d u 0 Unpolarized data on sea shows the Gottfried sum rule is broken Unpolarized data on sea shows the Gottfried sum rule is broken

Reanalyze polarized data: Reanalyze polarized data:

Polarized data favor a symmetric sea ,but large uncertaintiesPolarized data favor a symmetric sea ,but large uncertaintiesd u

u d u- d s= , ,Fit ,

u d u-d for

s Q

J Stewart

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

5 5

1 1 1( ) ( ) ( ) ( )

2 2 2x q x P q x P q x P S 5 5

1 1 1( ) ( ) ( ) ( )

2 2 2x q x P q x P q x P S

Transversity Transversity

basisbasis

J Stewart

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

J Stewart

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 momentum Observed asymmetry in azimuthal angle about lepton scattering Observed asymmetry in azimuthal angle about lepton scattering

plane plane

2 (1/ 2)1

( , ) ( , )1,

( , ) ( , )

~ ( )si )( (n )

h S h S

UT ST h S h S

qqS

N NA

S N N

e q x H z

J Stewart

Sivers Function Sivers Function

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

2 (1/ 2)UT 1 1A ~ (sin( ) ) ( )q

q TS qe f x D z

(1/ 2)1Tf

August 2005 J Stewart

Single target-spin asymmetry

angle of hadron relative to final quark spin

angle of hadron relative to initial quark spin

h S h SS

T h S h S

Collins SiversUT S UT S

N ( , ) N ( , )1( , )

| | N ( , ) N ( , )

A sin( ) A sin( )

S

hUTA

amplitudes fit simultaneously (prevents mixing effects due to acceptance)

J Stewart

Collins MomentCollins Moment Result is consistent with the Result is consistent with the

published Collins moment.published Collins moment.

Large negative Large negative -- moment moment unexpectedunexpected

One possibility One possibility

Additional information on the Collins Additional information on the Collins fragmentation function needed to fragmentation function needed to extract the transversity distribution. extract the transversity distribution. → BelleBelle

u 0

usin( ) 0s

sin( ) 0s

(1/ 2) (1/ 2)1 1( ) ( )unfavored favoredH z H z

J Stewart

Sivers MomentSivers Moment

++ sivers moment > 0! sivers moment > 0!→ Clear sign for non-zero Clear sign for non-zero

orbital angular orbital angular momentum!momentum!

Sivers moment for Sivers moment for -- is is consistent with zero.consistent with zero.→ Unfavored frag.?Unfavored frag.?

Unpolarized fragmentation Unpolarized fragmentation functions are known functions are known → Sivers function can be Sivers function can be

extracted.extracted.

ff1T1T

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

(x) DY(x) DY→ UNIVERSALITYUNIVERSALITY

J Stewart

Why are Fragmentation functions important?Why are Fragmentation functions important?

In Semi-inclusive DIS:In Semi-inclusive DIS:

Important for Important for q,q,q, and q, and Test factorizationTest factorization Test universalityTest universality

DF FF

1Tf

12 2 h 2h 2 f f f0

f1DIS 2 2

f f0f

e dxq x,Q D z,QdN z,Q1

N dz e dxq x,Q

Extract Extract , K, and p multiplicities:, K, and p multiplicities:

J Stewart

Multiplicity ExtractionMultiplicity Extraction

Born Level Born Level

multiplicitiesmultiplicities

ExperimentalExperimental

Multiplicities Multiplicities

in acceptancein acceptance

MCMC

Excl. VM Corr.Excl. VM Corr.

PID with the RICHPID with the RICH

UnpolarizedUnpolarized

H&D dataH&D data

AcceptanceAcceptance

Radiative effectsRadiative effects

J Stewart

MC tuningMC tuning

Monti Carlo:Monti Carlo:→ Lepto in combination with Lepto in combination with

JETSET; JETSET; → PDF: CTEQ-6LPDF: CTEQ-6L→ Fragmentation Fragmentation

parameters tuned to parameters tuned to HERMES multiplicities in HERMES multiplicities in the acceptancethe acceptance

Data: Data: → QQ22>1GeV>1GeV22, W, W22>10GeV>10GeV22, ,

z>0.2, 2GeV <p< 15GeV z>0.2, 2GeV <p< 15GeV ((, K, and P), K, and P)

Excellent Agreement even Excellent Agreement even at the cross section levelat the cross section level

→ DATA/MC <10%!DATA/MC <10%!

++ --

++ --

PP++ PP--

J Stewart

± ± Multiplicities vs zMultiplicities vs z

Systematic uncertainties mainly from hadron PID correctionSystematic uncertainties mainly from hadron PID correctionQQ22>1GeV>1GeV22, W, W22>10GeV>10GeV22

Comparison with EMC FF, Nucl. Phys. B321 (1989) 541Comparison with EMC FF, Nucl. Phys. B321 (1989) 541Reasonable agreement with FF from S. KretzerReasonable agreement with FF from S. Kretzer

J Stewart

KK±± Multiplicity vs z Multiplicity vs z

Charge separated Kaon multiplicitiesCharge separated Kaon multiplicities Systematic uncertainty mainly from hadron PIDSystematic uncertainty mainly from hadron PID Low KLow K-- statistics at high z statistics at high z will collect more data will collect more data

J Stewart

Agreement with existing Frag. Fns.Agreement with existing Frag. Fns.

J Stewart

Summary Summary

Longitudinally Polarized Target DataLongitudinally Polarized Target Data The structure functions have been measured.The structure functions have been measured.

→ First measurement of bFirst measurement of b11..

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

Transversely Polarized Target DataTransversely Polarized Target Data Collins:Collins:

→ Non-Zero asymmetries measured.Non-Zero asymmetries measured.→ Disfavored fragmentation functions appear to be Disfavored fragmentation functions appear to be

important and have opposite sign to the favored.important and have opposite sign to the favored. Sivers: Sivers:

→ ++ Amplitude is greater than zero. Amplitude is greater than zero.→ Orbital angular momentum must be non-zero!Orbital angular momentum must be non-zero!

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

1 1 1, ,g gp d dand b

J Stewart

Outlook Outlook

Data taking with transverse polarized target will continue Data taking with transverse polarized target will continue till November.till November.

Expect about 5M DIS events in the final data set. Expect about 5M DIS events in the final data set. New multiplicities New multiplicities

→ New millennium extraction of New millennium extraction of q (purity free).q (purity free).→ New extraction using isoscalor methodNew extraction using isoscalor methodΔs+ Δs

J Stewart

Backup SlidesBackup Slides

J Stewart

q

q

J Stewart

Purities Purities -- -- --

J Stewart

J Stewart

J Stewart

Distribution and Fragmentation FunctionsDistribution and Fragmentation Functions

hqeqeqq

qHehXeH Df

J Stewart

Exclusive VM ContaminationExclusive VM Contamination

Exclusive vector meson (VM) Exclusive vector meson (VM) contribution estimated using Pythia-6contribution estimated using Pythia-6

Correct data set for VM contamination.Correct data set for VM contamination.→ Different process than SIDISDifferent process than SIDIS

Evaluate ratio:Evaluate ratio:

Large contamination for Large contamination for at high z at high z Contribution for K moderate vs zContribution for K moderate vs z Contribution grows for small x for both Contribution grows for small x for both

and K and K

h hexcl.VM excl.VMN (z)/N (z)