The Spin Structure of the Nucleon - University of VirginiaThe Spin Structure of the Nucleon EE.C. Aschenauer.C. Aschenauer SFU, VanCouver, March 2007 11

The Spin Structure of the NucleonThe Spin Structure of the Nucleon

11SFU, VanCouver, March 2007SFU, VanCouver, March 2007EE.C. Aschenauer.C. Aschenauer

Experimental PrerequisitesExperimental Prerequisites

longitudinally polarized lepton beamlongitudinally polarized lepton beam

longitudinally polarized nuclear targetlongitudinally polarized nuclear target

large geometrical acceptancelarge geometrical acceptancesmall anglessmall angleslimited by synchrotron radiationlimited by synchrotron radiation

big anglesbig angles

(E’, p’)

e(E, p)

(E’, p’)

e(E, p)

*γ

(E’, p’)

e

q

(E, p)

*γ

(E’, p’)

e

q

(E, p)


big anglesbig angleslimited by moneylimited by money

good particle identificationgood particle identification

So far only So far only “fixed target”“fixed target” experiments atexperiments at::

*γ

e

q*γ

ud

u

e

q

N

u

*γ

ud

q

Nu

*γ

π+

ud

q

π

p

KN

and polarized ppand polarized pp--collider atcollider at

The The contemporarycontemporary experimentsexperiments

GEM MWPC&Scifi

Target

Trigger Hodoscopes

SM1

ECal1/2 & HCal1/2

−Filterµ

SM2

RICH

MWPC

Two highTwo high--resolution resolution 4 GeV spectrometers4 GeV spectrometers

Hall A

Large acceptance spect. Large acceptance spect. electron/photon beamselectron/photon beams

Hall B

Beam: ≤6 GeV eBeam: ≤6 GeV e--; 85% polarization; 85% polarization

STARSTAR


Beam: 27.5 GeV eBeam: 27.5 GeV e±±; <50>% polarization; <50>% polarizationTarget: (un)Target: (un)--polarized gas targets; <85%> polarizationpolarized gas targets; <85%> polarization

SiliconScifi

beamStraws

Drift chamber

MicroMegas

Beam: 160 GeV Beam: 160 GeV µµµµµµµµ; 75% polarization; 75% polarizationTarget: Target: 66LiD; 50% polarizationLiD; 50% polarization

7 GeV spectrometer, 7 GeV spectrometer, 1.8 GeV spectrometer, 1.8 GeV spectrometer,

large installation experimentslarge installation experiments

Hall CBeam: ≤6 GeV eBeam: ≤6 GeV e--; 85% polarization; 85% polarizationTarget: polarized targets Target: polarized targets 33He, He, 66LiD, NHLiD, NH3 3

Beams: 250 GeV pp; <60>% polarizationBeams: 250 GeV pp; <60>% polarizationLumi: 1.2 10Lumi: 1.2 103131cmcm--22ss--11

HERA @ DESYHERA @ DESYHERMES @ HERAHERMES @ HERA


HERA: eHERA: e++/e/e-- (27GeV) (27GeV) -- proton (920 GeV) colliderproton (920 GeV) collider

The HERMES SpectrometerThe HERMES Spectrometer


Internal Gas Target: He , H , D , H unpol: H2,D2,He,N2,Ne,Kr,Xe

The HERMES polarized gas targetThe HERMES polarized gas target

BRPABS

TGA

1st sexp. magn. syst.

collimator

discharge tube

SFTMFT

2nd sexp. magn. syst.

SFT / WFTQMS

chopper

storage cellSFT

MFT

QMS

choppersexp. magn. syst.

beam blockernozzle

Atomic Beam SourceAtomic Beam Source Breit Rabi PolarimeterBreit Rabi Polarimeter


HERA beam

sample tubeextension tube

beam shutter

SFT

injection tube

ADVANTAGES:ADVANTAGES:no dilution; all the material is polarizedno dilution; all the material is polarizedno radiation damage no radiation damage rapid inversion of polarization direction every 90s in less than 0.5srapid inversion of polarization direction every 90s in less than 0.5s

The HERA PolarimetersThe HERA Polarimeters

20

40

60

850 950 1050

20

40

60

1000 1175 1350

20

40

60

1300 1400 1500

20

40

60

1450 1650 1850

20

40

60

1800 2025 2250

20

40

60

3180 3225 3270

20

40

60

3260 3410 3560

20

40

60

3565 3857.5 4150

20

40

60

4130 4415 4700


HeraHera--e selfe self--polarizing due to Sokolovpolarizing due to Sokolov--Ternov effectTernov effect

20

40

60

850 950 1050

20

40

60

1000 1175 1350

20

40

60

1300 1400 1500

20

40

60

1450 1650 1850

20

40

60

1800 2025 2250

20

40

60

3180 3225 3270

20

40

60

3260 3410 3560

20

40

60

3565 3857.5 4150

20

40

60

4130 4415 4700

The HERMES SpectrometerThe HERMES Spectrometer


Kinematic Range: 0.02 < x < 0.8 at Q2 > 1 GeV2 and W > 2 GeV

Reconstruction:∆∆∆∆p/p < 2%, ∆θ∆θ∆θ∆θ < 1 mrad

Particle ID: TRD, Preshower, Calorimeter

֏1997: Cherenkov, 1998֏: RICH + Muon-ID

Internal Gas Target: unpol: H2,D2,He,N,Ne,Kr, Xe He , H , D , H

hadron/positron separationhadron/positron separationcombining signals from: combining signals from: TRD, calorimeter, preshowerTRD, calorimeter, preshower

hadron separationhadron separationDual radiator RICH forDual radiator RICH for ππππππππ, K, pK, p

Which Hadron (Which Hadron (ππππππππ,K,p) is Which,K,p) is Which


Aerogel; n=1.03

C4F10; n=1.0014

ππππ

K

News on the spin structure of the nucleonNews on the spin structure of the nucleon

Naïve parton modelNaïve parton model

43∆ =∆ =∆ =∆ =vu 1

3∆ = −∆ = −∆ = −∆ = −vd Unpolarised structure fct.Unpolarised structure fct.


1 1( )

2 2 v vu d++++ ∆∆∆∆∆∆∆∆====1 1( )

2 2 v gsv qLd LGqu= + + + += + + + += + + + += + + + +∆∆∆∆∆∆∆∆ ++++∆∆∆∆∆∆∆∆

∆Σ∆Σ∆Σ∆Σ

1 1( )

2 2 v svu q Gd∆∆∆∆ ∆∆∆∆+ ++ ++ ++ +∆∆∆∆ ++++ ∆∆∆∆====

( )∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆s su d u d s s

43∆ =∆ =∆ =∆ =vu 1

3∆ = −∆ = −∆ = −∆ = −vdBUTBUT

1989 EMC measured1989 EMC measuredΣΣΣΣΣΣΣΣ = 0.120 0.094 0.138= 0.120 0.094 0.138± ±

Spin PuzzleSpin Puzzle

Unpolarised structure fct.Unpolarised structure fct.

Gluons are important !Gluons are important !

Sea quarksSea quarks ∆∆∆∆∆∆∆∆qq ss

∆∆∆∆∆∆∆∆GG Full description of JFull description of Jqq and Jand Jggneedsneeds

orbital angular momentumorbital angular momentum

−1Lg ====1f ====

{{{{ }}}}112 ( ) ( ) ( ) ( )1 1 5 1 52

Tw x f x S g x h x S nCorr L T

++++Φ = + γ + γ γΦ = + γ + γ γΦ = + γ + γ γΦ = + γ + γ γ

The quark content of the nucleonThe quark content of the nucleon


HERA F2

0

1

2

3

4

5

1 10 102

103

104

105

F2 em

-log 10

(x)

Q2(GeV2)

ZEUS NLO QCD fit

H1 PDF 2000 fit

H1 94-00

H1 (prel.) 99/00

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102x=0.000161

x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

How to measure Quark PolarizationsHow to measure Quark Polarizations

3/ 2 (~ )q xσσσσ −−−−

* 3/ 2NSSγγγγ + =+ =+ =+ =rrrr rrrr

N qSS ==== −−−−rrrr rrrr

1/ 2 (~ )q xσσσσ ++++

* 1/ 2NSSγγγγ + =+ =+ =+ =rrrr rrrr

N qSS ====rrrr rrrr

Virtual photon Virtual photon γγγγγγγγ** can only couple to quarks of opposite helicitycan only couple to quarks of opposite helicitySelect Select qq++(x)(x) or or qq--(x)(x) by changing the orientation of by changing the orientation of


Select Select qq++(x)(x) or or qq--(x)(x) by changing the orientation of by changing the orientation of target nucleon spin or helicity of incident lepton beamtarget nucleon spin or helicity of incident lepton beam

', ','||

', '

1 e h e he h

B T e h e h

N L N LA

P P N L N L

→ → → →→ → → →→ → → →→ → → →⇐⇐⇐ ⇐ ⇒ ⇒⇒ ⇒⇒ ⇒⇒ ⇒ ⇐⇐⇐ ⇐

→ → → →→ → → →→ → → →→ → → →⇐⇐⇐ ⇐ ⇒ ⇒⇒ ⇒⇒ ⇒⇒ ⇒ ⇐⇐⇐ ⇐

−−−−====

++++

', ',', 1 / 2 3 / 2

|| ', ',1/ 2 3 / 2

~e h e h

e he h e hA

σ − σσ − σσ − σσ − σσ + σσ + σσ + σσ + σ

Asymmetry definition:Asymmetry definition:qq q−−−−++++∆ = −∆ = −∆ = −∆ = −

inclusiveinclusive DIS: only DIS: only e’e’ info usedinfo used semisemi--inclusiveinclusive DIS: DIS: e’+he’+h info usedinfo used

World data on inclusive DISWorld data on inclusive DIS

0

0.5

1

0

0.2

0.4

0.6

0.8

A1p

HERMES (⟨Q2⟩< 1 GeV2)HERMES (⟨Q2⟩> 1 GeV2)E 143E 155

SMCSMC (low x - low Q 2)

CLAS

COMPASSCOMPASS (low x - low Q 2)A

1d

x

⟨Q2 ⟩(

GeV

2 )

10-1

1

10

10-4

10-3

10-2

10-1

1

New data from COMPASS, New data from COMPASS, HERMES & JLab very preciseHERMES & JLab very precisehigh xhigh x--behaviour consistent withbehaviour consistent withAA��1 with x1 with x��11AA11

d d consistent with zero consistent with zero for x < 0.05for x < 0.05

ProtonProton DeuteriumDeuterium(Hall(Hall--A)A)


0

0.2

0.4

0.6

0.8

A1p



CLAS


1d

x

⟨Q2 ⟩(

GeV

2 )

10-1

1

10

10-4

10-3

10-2

10-1

1

CLAS PLB 641, 11 (2006)AA11

nn from from 33HeHe

COMPASS PRD75(2007)012007COMPASS PRD75(2007)012007

World data on inclusive DISWorld data on inclusive DIS

1 1 1

1 3( )(1 )

2 2d p n

Dg g g w= + −= + −= + −= + −Combine p and d to get n:Combine p and d to get n:

or or 33HeHe3

1 1 12He np

pnP Pg g g++++��

0

0.5

1

0

0.2

0.4

0.6

0.8

A1p



CLAS


1d

x

⟨Q2 ⟩(

GeV

2 )

10-1

1

10

10-4

10-3

10-2

10-1

1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

-0.01

0

0.01

0.02

0.03

10-4

10-3

10-2

10-1

1

HERMES (Q2 < 1 GeV2)HERMES (Q2 > 1 GeV2)SMC (low x - low Q 2)SMCE 143E 155

xg1p

x

xg1d

COMPASSCOMPASS (low x - low Q 2)

41 22 2 21 / 2 ( )

22 2( , ) (( , ) , )1

2

2/ 4 8 2

dunpolQ y

y yg x Q g x Qx

dA Q

y dx Qγγγγ

γ παγ παγ παγ πα

σσσσ = += += += +

− −− −− −− −

��

-0.1

-0.05

0

-0.1

-0.05

0

xg1n from p,d:HERMES (Q2< 1 GeV2)HERMES (Q2> 1 GeV2)E155E143SMC

xg1n

E154E142JLABHERMES

xg1n from 3He:

xg1n

x

⟨Q2 ⟩ (

GeV

2 )

1

10

10-2

10-1

1


1 1 12 pnP Pg g g++++��

What can we learn on the PDFsWhat can we learn on the PDFs

21 ~ [ Ge C GCg ΣΣΣΣ ∆∆∆∆ + ∆+ ∆+ ∆+ ∆ΣΣΣΣ⊗ ⊗⊗ ⊗⊗ ⊗⊗ ⊗ ∆∆∆∆∆ +∆ +∆ +∆ +

LO-QCD2 ,1

2p nNSe q∆Σ∆Σ∆Σ∆Σ = + ∆= + ∆= + ∆= + ∆

, ]p nNS NSC q∆ ⊗ ∆∆ ⊗ ∆∆ ⊗ ∆∆ ⊗ ∆

Compass: hepCompass: hep--ex/0609038ex/0609038Hermes: hepHermes: hep--ex/0609039ex/0609039

0

0.2

0.4

0.6

0.8

A1p



CLAS


1d

x

⟨Q2 ⟩(

GeV

2 )

10-1

1

10

10-4

10-3

10-2

10-1

1

-0.01

0

0.01

0.02

0.03

10-4

10-3

10-2

10-1

1

HERMES (Q2 < 1 GeV2)HERMES (Q2 > 1 GeV2)SMC (low x - low Q 2)SMCE 143E 155

xg1p

x

xg1d

COMPASSCOMPASS (low x - low Q 2)

-0.1

-0.05

0

xg1n from p,d:HERMES (Q2< 1 GeV2)HERMES (Q2> 1 GeV2)E155E143SMC

xg1n

E154E142JLABHERMES

xg1n from 3He:

xg1n

x

⟨Q2 ⟩ (

GeV

2 )

1

10

10-2

10-1

1

HERMES: IntegralsHERMES: Integrals

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

x

∫ x g

1dx

0.

9

pdnNS

Q2=5 GeV2 Saturation in deuteron integral is assumedSaturation in deuteron integral is assumeduse only deuteriumuse only deuterium

80191 1

[ ]3 4(1 )2

d

NSS

D

CC w

a a= − ∆= − ∆= − ∆= − ∆∆∆∆∆ −−−−

ΓΓΓΓ

From hyperon beta decayFrom hyperon beta decayaa88=0.586=0.586±±0.0310.031From neutron beta decayFrom neutron beta decay

aa33=1.269=1.269±±0.0030.0031

0.9

10.0210.0436 0.0012( ) 0.0018( ) 0.0008( ) 0.0026( )ddxg stat syst par evol= ± ± ± ±= ± ± ± ±= ± ± ± ±= ± ± ± ±∫∫∫∫


-0.02

0

0.02

10-1

1x

∫ x g

1dx

0.

9

pdnNS

Q2=5 GeV2

QQ22=5 GeV=5 GeV22, NNLO in MS scheme, NNLO in MS scheme

80 3

1[2 3 ]

6au u aa∆ + ∆ = + +∆ + ∆ = + +∆ + ∆ = + +∆ + ∆ = + +

80 3

1[2 3 ]

6ad d aa∆ + ∆ = + −∆ + ∆ = + −∆ + ∆ = + −∆ + ∆ = + −

80

1[ ]

3as s a∆ + ∆ = −∆ + ∆ = −∆ + ∆ = −∆ + ∆ = −

COMPASS: COMPASS:

0.08 0.01 0.02s s = − ± ±= − ± ±= − ± ±= − ± ±∆ + ∆∆ + ∆∆ + ∆∆ + ∆0 0.33 0.03 0.05a = ± ±= ± ±= ± ±= ± ±

CLAS: CLAS: ∆∆∆∆∆∆∆∆qq


Using:Using:

Polarised quark distributionsPolarised quark distributionsCorrelation between detected hadron and struck Correlation between detected hadron and struck qqff

“Flavor “Flavor –– Separation”Separation”

Inclusive DIS:Inclusive DIS:

SemiSemi--inclusive DIS:inclusive DIS:

( )u d u d s s∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆

( , , , , , )u d u d s s∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆In LOIn LO--QCD:QCD:

2 2 2 2( , ) ( , ) ( , )hh h e q x Q D z Q q x Qσ −σ −σ −σ − ∆∆∆∆σσσσ

∑∑∑∑

scattered lepton

u_

d_

u_

u_

u_

ρ−

u_

π0

π0

π+−π

π0

u

ud

u

d

u

ptarget nucleon

incoming lepton

String Breaking

virtual photon

uu

u

uud

ud

ud


2 1/ 2 3 / 21 2 2

1/ 2 3 /2

'2

2 ''

2( , )( , , ) ~

'( , )

( , )

( , )( , )

( , )

h hqh

hq

qh

q qh q

e q x QA x Q z C

e

D z Q

Dq x Q

q Qq Q xzx Q

σ −σ −σ −σ −====

∆∆∆∆σσσσσ + σσ + σσ + σσ + σ ∑∑∑∑ ∑∑∑∑

COMPASS: Valence PDFsCOMPASS: Valence PDFs

/( ) ( )

( ) ( )

h h h h

h h h h

A

→ → → →→ → → →→ → → →→ → → →⇐ ⇐⇐ ⇐⇐ ⇐⇐ ⇐ ⇒ ⇒⇒ ⇒⇒ ⇒⇒ ⇒

+ − + −+ − + −+ − + −+ − + −

→ → → →→ → → →→ → → →→ → → →⇐ ⇐⇐ ⇐⇐ ⇐⇐ ⇐ ⇒ ⇒⇒ ⇒⇒ ⇒⇒ ⇒

+ − + −+ − + −+ − + −+ − + −

+ −+ −+ −+ − σ − σ − σ − σσ − σ − σ − σσ − σ − σ − σσ − σ − σ − σ====

σ − σ + σ − σσ − σ + σ − σσ − σ + σ − σσ − σ + σ − σ

( ) ( )( )

( ) ( )K K v v

d dv v

u x d xA x A

u x d xπ ππ ππ ππ π+ − + −+ − + −+ − + −+ − + −− −− −− −− − ∆ + ∆∆ + ∆∆ + ∆∆ + ∆

= == == == =++++ x

-210 -110 1

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

COMPASS

PRELIMINARY

Deuteron data 2002-2004

h+ - h-A

1 1( )N a aΓ = +Γ = +Γ = +Γ = +

For LO:For LO:

Assuming:Assuming:x

-210 -110 1-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

2=10 GeV2SIDIS+DIS, Q

From diff asymmetry d

1From Inclusive gDNS fit (prediction)

)vd∆+vu∆x(

COMPASS

PRELIMINARY


x -210 -110 1

0

0.1

0.2

0.3

0.4

0.5

0.6


s∆s=∆=d∆=u∆

d∆=-u∆

unm

easu

red

0.7

0.006∫ 0.05±0.07±)dx=0.40vd∆+vu∆(

∫x

0.7)dxvd∆+vu∆(

COMPASSPRELIMINARY



1 0 8

1 1( )

9 4N a aΓ = +Γ = +Γ = +Γ = +

1

0( ( ) ( ))v v vu x d x dxΓ = ∆ + ∆Γ = ∆ + ∆Γ = ∆ + ∆Γ = ∆ + ∆∫∫∫∫

1 8

8

1 13

2 121

( ) ( )2

Nv

v

u d a

s s a

∆ + ∆ = Γ − Γ +∆ + ∆ = Γ − Γ +∆ + ∆ = Γ − Γ +∆ + ∆ = Γ − Γ +

= ∆ + ∆ + − Γ= ∆ + ∆ + − Γ= ∆ + ∆ + − Γ= ∆ + ∆ + − Γ x -210 -110 1

0

0.1

0.2

0.3

0.4

0.5

0.6


s∆s=∆=d∆=u∆

d∆=-u∆

unm

easu

red

0.7

0.006∫ 0.05±0.07±)dx=0.40vd∆+vu∆(

∫x

0.7)dxvd∆+vu∆(

COMPASSPRELIMINARY


ΓΓΓΓΓΓΓΓvv is 2.5is 2.5σσσσσσσσstatstat away from flavor away from flavor symmetric sea scenariosymmetric sea scenario

Polarised quark distributionsPolarised quark distributions

Correlation between detected hadron and struck Correlation between detected hadron and struck qqff“Flavor “Flavor –– Separation”Separation”

Inclusive DIS:Inclusive DIS:

SemiSemi--inclusive DIS:inclusive DIS:

( )u d u d s s∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆∆Σ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆

( , , , , , )u d u d s s∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆In LOIn LO--QCD:QCD:

2 2 2 2( , ) ( , ) ( , )hh h e q x Q D z Q q x Qσ −σ −σ −σ − ∆∆∆∆σσσσ

∑∑∑∑

scattered lepton

u_

d_

u_

u_

u_

ρ−

u_

π0

π0

π+−π

π0

u

ud

u

d

u

ptarget nucleon

incoming lepton

String Breaking

virtual photon

uu

u

uud

ud

ud


A PQ====ur urur urur urur ur

Extract Extract ∆∆∆∆∆∆∆∆qq by solving:by solving:

1, 1, 1, 1, 1,( ( ), ( ), ( ), ( ), ( ))Kp p d d dA A x A x A x A x A xπ± π± ±π± π± ±π± π± ±π± π± ±====

urururur

( , , , , , )u d u d s s

Qu d su d s

∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆====urururur

2 1/ 2 3 / 21 2 2

1/ 2 3 /2

'2

2 ''

2( , )( , , ) ~

'( , )

( , )

( , )( , )

( , )

h hqh

hq

qh

q qh q

e q x QA x Q z C

e

D z Q

Dq x Q

q Qq Q xzx Q

σ −σ −σ −σ −====

∆∆∆∆σσσσσ + σσ + σσ + σσ + σ ∑∑∑∑ ∑∑∑∑

2( , , )hqP x Q z MCMC

0.03 0.1

-0.1

0

0.1

0.2

0.3

0.4

0.5A1

A1,d A1,dAh+

SMC

A1,dAπ+ A1,dAK+

0.03 0.1 0.4

-0.1

0

0.1

0.2

0.3

0.4

0.5A1,dAh−

SMC

0.03 0.1 0.4

A1,dAπ−

0.03 0.1 0.4x

A1,dAK−

Measured AsymmetriesMeasured Asymmetries

0

0.2

0.4

0.6

0.8

0.03 0.1

A1

A1,p A1,pAh+

SMC

A1,pAπ+

0

0.2

0.4

0.6

0.8

0.03 0.1 0.4

A1,pAh−

SMC

0.03 0.1 0.4x

A1,pAπ−

ProtonProton

DeuteriumDeuterium


0.03 0.1

-0.1

0

0.1

0.2

0.3

0.4

0.5A1

A1,d A1,dAh+

SMC

A1,dAπ+ A1,dAK+

0.03 0.1 0.4

-0.1

0

0.1

0.2

0.3

0.4

0.5A1,dAh−

SMC

0.03 0.1 0.4

A1,dAπ−

0.03 0.1 0.4x

A1,dAK−

0

0.2

0.4

0.6

0.8

0.03 0.1

A1

A1,p A1,pAh+

SMC

A1,pAπ+

0

0.2

0.4

0.6

0.8

0.03 0.1 0.4

A1,pAh−

SMC

0.03 0.1 0.4x

A1,pAπ−1 ~ 0 ( )KA K us

−−−− −−−− ====⇒⇒⇒⇒

statistics sufficient for statistics sufficient for 5 parameter fit5 parameter fit

( , , , , , 0)u d u d s s

Qu d su d s

∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆∆ ∆ ∆ ∆ ∆ ∆= == == == =urururur

good agreement with NLOgood agreement with NLO--QCDQCDPolarised opposite to proton spinPolarised opposite to proton spin

Polarized Quark DensitiesPolarized Quark Densities

∆∆∆∆u(x) > 0

First complete separation of First complete separation of pol. PDFs without assumption on pol. PDFs without assumption on sea polarizationsea polarization

Polarised parallel to proton spinPolarised parallel to proton spin

∆∆∆∆d(x) < 0

∆∆∆∆u(x), ∆∆∆∆d(x) ~ 0~ 0

No indication forNo indication for ∆∆∆∆s(x) << 00

0

0.2

x⋅∆u

-0.2

0x⋅∆d

-0.1

0

GRSV 2000LO val

BB 01 LOx⋅∆u

–

Q2=2.5GeV2

-0.1

0

x⋅∆d–

-0.1

0

x⋅∆s

0.03 0.1 0.6

x


No indication forNo indication for ∆∆∆∆s(x) << 00

In measured range (0.023 In measured range (0.023 –– 0.6)0.6)

0.002 0.043u∆ = − ±∆ = − ±∆ = − ±∆ = − ±∫∫∫∫0.054 0.035d∆ = − ±∆ = − ±∆ = − ±∆ = − ±∫∫∫∫

0.028 0.034s∆ = + ±∆ = + ±∆ = + ±∆ = + ±∫∫∫∫

0

0.2

x⋅∆u

-0.2

0x⋅∆d

-0.1

0

GRSV 2000LO val

BB 01 LOx⋅∆u

–

Q2=2.5GeV2

-0.1

0

x⋅∆d–

-0.1

0

x⋅∆s

0.03 0.1 0.6

x

-0.2

0

0.2

0.4

-0.2

0

0.2

0.4

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

10-2

10-2

x(∆u+∆u–)

x(∆d+∆d–)

x∆uv

x∆dv

x∆g–

x∆u–

xBj

x∆d–

xBj

x∆s–

xBj

KRE (NLO)KKP (NLO)unpolarizedKRE χ2KRE χmin+1KRE χ2KRE χmin+2%

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

10-2

D. De Florian et al. hepD. De Florian et al. hep--ph/0504155ph/0504155NLO @ Q2=10 GeV2

KretzerKretzer

KKPKKP

χ2DIS χ2

SIDIS ∆uv ∆u∆dv ∆d ∆s ∆g ∆Σ

206206206206206206206206

225225225225231231231231

0.940.940.940.940.700.700.700.70 −−−−0.260.260.260.26

−−−−0.340.340.340.340.0870.0870.0870.087

−−−−−−−−0.0490.0490.0490.0490.0490.0490.0490.049−−−−0.110.110.110.11

−−−−−−−−0.0550.0550.0550.0550.0550.0550.0550.055−−−−0.0450.0450.0450.045−−−−−−−−0.0510.0510.0510.0510.0510.0510.0510.051

0.570.570.570.570.680.680.680.68

0.310.310.310.310.280.280.280.28

NLO FIT to DIS & SIDIS DataNLO FIT to DIS & SIDIS Data


-0.2

0

0.2

0.4

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

10-2

10-2

x(∆u+∆u–)

x(∆d+∆d–)

x∆uv

x∆dv

x∆g–

x∆u–

xBj

x∆d–

xBj

x∆s–

xBj

KRE (NLO)KKP (NLO)unpolarizedKRE χ2KRE χmin+1KRE χ2KRE χmin+2%

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

10-2

SIDIS data improves description of allSIDIS data improves description of all ∆∆∆∆∆∆∆∆qq, especially light sea, especially light seaKretzer FF favor SU(3) symmetric sea, not so for KKPKretzer FF favor SU(3) symmetric sea, not so for KKP∆Σ ∆Σ ∆Σ ∆Σ ∆Σ ∆Σ ∆Σ ∆Σ ~30%~30% in all casesin all cases

The Gluon PolarizationThe Gluon Polarization


43∆ =∆ =∆ =∆ =vu 1



1 1( )

2 2 v svu q Gd∆∆∆∆ ∆∆∆∆+ ++ ++ ++ +∆∆∆∆ ++++ ∆∆∆∆====

43∆ =∆ =∆ =∆ =vu 1

3∆ = −∆ = −∆ = −∆ = −vdBUTBUT






∆∆∆∆∆∆∆∆GG

1 1( )

2 2 v v su qd= += += += + ∆∆∆∆++++∆∆∆∆∆∆∆∆

( )∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆s su d u d s s

Unpolarized Gluon Distribution Unpolarized Gluon Distribution HERA F2

0

1

2

3

4

5

1 10 102

103

104

105

F2 em

-log 10

(x)

Q2(GeV2)

ZEUS NLO QCD fit

H1 PDF 2000 fit

H1 94-00

H1 (prel.) 99/00

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102x=0.000161

x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

15

20

15

20xg 2 = 20 GeV2Q

2 = 200 GeV2Q15

20 ZEUS-JETS (prel.) 94-00

H1 PDF 2000

total uncert.

exp. uncert.

total uncert.

H1+ZEUS

big Qbig Q22--x lever armx lever armvery accurate G(x)very accurate G(x)


HERA F2

0

1

2

3

4

5

1 10 102

103

104

105

F2 em

-log 10

(x)

Q2(GeV2)

ZEUS NLO QCD fit

H1 PDF 2000 fit

H1 94-00

H1 (prel.) 99/00

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102x=0.000161

x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.650

5

10

15

-410 -310 -210 -110 10

5

10

15

x

2 = 5 GeV2Q

0

5

10

15 total uncert.

How to measure How to measure ∆∆∆∆∆∆∆∆GG

Indirect from scaling violationIndirect from scaling violation

fixed target experimentsfixed target experimentssmall Qsmall Q22--x lever armx lever armeven sign of even sign of ∆∆∆∆∆∆∆∆G unknownG unknown

0

1

2

3

4

5

6

7

8

9

10

E143

HERMES

E155

COMPASS

SMC

g1d(x,Q2) + C(x)

1 10 100Q2 (GeV2)

0

0.1

0.2

0.3AAC06

GRSV

BB

LSS

x∆Σ∆Σ∆Σ∆Σ(x)


0

1

2

3

4

5

6

7

8

9

10

E143

HERMES

E155

COMPASS

SMC

g1d(x,Q2) + C(x)

1 10 100Q2 (GeV2)

-0.10.001 0.01 0.1 1

-0.6-0.4-0.2

00.20.40.60.8

11.21.4

0.001 0.01 0.1 1

x

x∆∆∆∆g(x)

Q2 = 1 GeV2

hephep--ph/0603213ph/0603213

Several more fitsSeveral more fits

using mainly only inclusive data or a combination of inclusive and using mainly only inclusive data or a combination of inclusive and some semisome semi--inclusive datainclusive dataResults for Results for ∆∆∆∆∆∆∆∆G still completely all over the placeG still completely all over the placeNeed a consistent approach for fit and uncertainty determinationNeed a consistent approach for fit and uncertainty determinationwith all world data taken into accountwith all world data taken into account

∆∆∆∆G>0G>0G>0G>0


∆G<0 ∆G<0

∆∆∆∆G>0G>0G>0G>0Lets measure Lets measure ∆∆∆∆∆∆∆∆G more directlyG more directly

The golden channelsThe golden channelsIdea: Direct measurementIdea: Direct measurement ofof ∆∆∆∆∆∆∆∆GG

Isolate the photon gluon fusion process (PGF)Isolate the photon gluon fusion process (PGF)Open Charm productionOpen Charm production

Reaction:Reaction: * 0 0p D D Xγγγγ → + +→ + +→ + +→ + +⇒⇒⇒⇒ * 0reconstruct Dc ,Dcˆ ˆ( , )

ˆ ˆ( , )

PGF

gPGF

N PGF

g

ds G x sA

ds G x sγγγγ

σσσσ

σσσσ

∆ ∆∆ ∆∆ ∆∆ ∆==== ∫∫∫∫∫∫∫∫

PGF

LLa

G

G

∆∆∆∆≈≈≈≈

) 0N(D 604± 14577

Mass 2 1.1 MeV/c± 2.9

Sigma 2 1.2 MeV/c± 26.6

2N

/ 20

MeV

/c

100

310×

candidates in 2002-20040D

=1051 +- 18effS

candidates in 2002-20040D


Sigma 2 1.2 MeV/c± 26.6

]2)[MeV/clit

0)-m(D0m(D-400 -200 0 200 400

N /

20 M

eV/c

20

40

60

80

COMPASS preliminary

) 0N(D 104± 3869

Mass 2 0.8 MeV/c± 4.9 Sigma 2 0.9 MeV/c± 28.6

]2)[MeV/clit

0)-m(D0m(D-400 -200 0 200 400

2N

/ 20

MeV

/c

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

D* candidates in 2002-2004

) 0N(D 104± 3869

Mass 2 0.8 MeV/c± 4.9 Sigma 2 0.9 MeV/c± 28.6

=1966 +/- 51effS

COMPASS preliminary

]2)[MeV/clit

0)-m(D0m(D-400 -200 0 200 400

2N

/ 20

MeV

/c

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

D* candidates in 2002-2004

2002 2003 2004 02-04 0D*+D2002 2003 2004 02-04 0D*+D

G/G

∆

-4

-3

-2

-1

0

1

G/G∆COMPASS Data 2002-2004

preliminaryD*

0D0 D* + D

G/G∆COMPASS Data 2002-2004

(stat.)0.57 0.41 0.17G

G∆∆∆∆ = − ± ±= − ± ±= − ± ±= − ± ±

2 20.15 13Gx µµµµ ====�� GeV

LOLO--MC: AromaMC: Aroma

The golden channelsThe golden channelsIdea: Direct measurement ofIdea: Direct measurement of ∆∆∆∆∆∆∆∆GG

Isolate the photon gluon fusion processIsolate the photon gluon fusion processdetection of hadronic final states with high pdetection of hadronic final states with high pTT

high phigh pTT pairs of hadronspairs of hadronssingle high psingle high pTT hadronshadrons

hh±±hh±±2 1Q >>>>2 0.1Q <<<<

less subless sub--processes contributing processes contributing ☺☺☺☺☺☺☺☺

more submore sub--processes contributing processes contributing ��higher statistics higher statistics ☺☺☺☺☺☺☺☺

Several possible contributions to the measured asymmetrySeveral possible contributions to the measured asymmetry

MC needed to determine R and aMC needed to determine R and aLLLL


hh±±2 0.1Q >>>>2 0.1Q <<<<

higher statistics higher statistics ☺☺☺☺☺☺☺☺



+ + + ..

|||| ||| |( ) ;B SigSig

gmeas i it i i

i tB

tog f AA p f A ff A

σσσσ= = + == = + == = + == = + =σσσσ∑∑∑∑

|| ||ˆ]

1[ meas

Sig

BgBgf

GA

aA

Gf

−−−−∆∆∆∆ ====

q

g

q

g qg

Important Important at Q2<0.1at Q2<0.1




hh±±hh±±2 1Q >>>>2 0.1Q <<<<



Several possible contributions to the measured asymmetrySeveral possible contributions to the measured asymmetry

MC needed to determine R and aMC needed to determine R and aLLLL


hh±±2 0.1Q >>>>2 0.1Q <<<<

higher statistics higher statistics ☺☺☺☺☺☺☺☺



+ + + ..

|||| ||| |( ) ;B SigSig

gmeas i it i i

i tB

tog f AA p f A ff A

σσσσ= = + == = + == = + == = + =σσσσ∑∑∑∑

|| ||ˆ]

1[ meas

Sig

BgBgf

GA

aA

Gf

−−−−∆∆∆∆ ====

q

g

q

g qg

Important Important at Q2<0.1at Q2<0.1

hh±±hh±± vs. hvs. h±±::hh±± more inclusive more inclusive → → pQCD NLO calculations (easier) possiblepQCD NLO calculations (easier) possible

COMPASS ResultsCOMPASS Results

1 2, 0.7T Tp p GeV>>>> 2 2 2,1 ,2 2.5T Tp p GeV+ >+ >+ >+ >

Channel:Channel:hh±±hh±±

xxFF > 0.1 z > 0.1> 0.1 z > 0.1m(hm(h11,h,h22) > 1.5 GeV) > 1.5 GeV

10% ofstatistics

RRPGFPGF = 0.34 +/= 0.34 +/-- 0.070.07

µµµµµµµµ22((scale) ~ 3 GeVscale) ~ 3 GeV22 <x<xGG> > ~~ 0.130.13

|| 0.015 0.080( ) 0.013( )A

stat systD

= − ± ±= − ± ±= − ± ±= − ± ±

0.06 0.31( ) 0.06( )stg

gat syst==== ±±±±

∆∆∆∆ ±±±±

QQ22 > 1 GeV> 1 GeV22Cuts:Cuts:

QQ22 < 1 GeV< 1 GeV22


used for used for ∆∆∆∆∆∆∆∆g/g extractiong/g extraction

&&

∆∆∆∆∆∆∆∆g/g=g/g=0.0160.016±±0.058(stat.)0.058(stat.)±±0.055(syst.)0.055(syst.)0.070.0350.085gx ++++

−−−−==== µµµµµµµµ22=3.0GeV=3.0GeV22

HERMES ResultsHERMES ResultsChannels:Channels: hh±±hh±±, h, h±±

Subprocess AsymmetriesSubprocess Asymmetries

Subprocess FractionsSubprocess Fractions


Subprocess AsymmetriesSubprocess Asymmetries(using GRSV std.)(using GRSV std.)

World Data on World Data on ∆∆∆∆∆∆∆∆G/GG/G


Long way to go till Long way to go till ∆∆∆∆∆∆∆∆g(x)g(x)

xx

RHIC SPINRHIC SPIN

hadronic final stateshadronic final states

JetsJets

Reaction mechanism:Reaction mechanism:


Hard sub processes:Hard sub processes:

ππππππππ0 0 ProductionProductionunpolarized cross section:unpolarized cross section: sub processes:sub processes:


good agreement with NLO pQCDgood agreement with NLO pQCD

Jet ProductionJet Production

STARSTARunpolarized cross section:unpolarized cross section: Asymmetry:Asymmetry:


good agreement with NLO pQCDgood agreement with NLO pQCD ∆∆∆∆∆∆∆∆G seems smallG seems small

RHIC RESULTSRHIC RESULTS


maybe the way is a bit shorter till maybe the way is a bit shorter till ∆∆∆∆∆∆∆∆g(x)g(x)

Quark Orbital Angular MomentumQuark Orbital Angular Momentum


43∆ =∆ =∆ =∆ =vu 1



1 1( )

2 2 v gsv qLd LGqu= + + + += + + + += + + + += + + + +∆∆∆∆∆∆∆∆ ++++∆∆∆∆∆∆∆∆

∆Σ∆Σ∆Σ∆Σ

1 1( )

2 2 v svu q Gd∆∆∆∆ ∆∆∆∆+ ++ ++ ++ +∆∆∆∆ ++++ ∆∆∆∆====

( )∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆∆ + ∆ + ∆ + ∆ + ∆ + ∆s su d u d s s

43∆ =∆ =∆ =∆ =vu 1

3∆ = −∆ = −∆ = −∆ = −vdBUTBUT






∆∆∆∆∆∆∆∆GG Full description of JFull description of Jqq and Jand Jggneedsneeds


The Hunt for LThe Hunt for Lqq

Study of hard Study of hard exclusive processesexclusive processes leads toleads toa new class of PDFsa new class of PDFs

GGeneralized eneralized PParton arton DDistributionsistributions

, , ,q qq qH H EE % %% %% %% %

possible access topossible access toorbital angular momentumorbital angular momentum



(((( ))))(((( ))))1

1 0

12

qq

q

tHJ Exdx

−−−− →→→→++++==== ∫∫∫∫

12q qLJ ∆∆∆∆ ++++ΣΣΣΣ====

exclusive:exclusive: all products of the reaction are detectedall products of the reaction are detectedmissing energymissing energy ((∆∆∆∆∆∆∆∆E) and missing Mass (ME) and missing Mass (Mxx) = 0) = 0

from DIS:from DIS:HERMES ~0.3HERMES ~0.3

GPDs IntroductionGPDs Introduction

What does GPDs charaterize?What does GPDs charaterize?

unpolarized unpolarized polarizedpolarized

(((( )))), ,qH x tξξξξ (((( )))), ,qH x tξξξξ%%%%

(((( )))), ,qE x tξξξξ%%%%(((( )))), ,qE x tξξξξ

conserve nucleon helicityconserve nucleon helicity��( ,0,0) , ( ,0,0)

qqH x q H x q= = ∆= = ∆= = ∆= = ∆flip nucleon helicityflip nucleon helicitynot accessible in DISnot accessible in DIS

quantum numbers of final state select different GPDquantum numbers of final state select different GPD


DDVVCCSS

∆2

P +∆P -2

x - ξ ξx +

γ∗ γ

GPD

0+

P - ∆2

P + ∆2

π , π

x - ξ ξx +

γ∗

GPD

q 0ρ , Φ , ωq

P + ∆2

P - ∆2

x - ξ ξx +

GPD

γ∗

,q qH E% %% %% %% %pseudopseudo --scaler mesonsscaler mesons

,q qH Evector mesonsvector mesons

AACC,A,A LULU,, AAUTUT, A, AULUL

qE%%%%qH%%%%qEqHAAUTUT,,σσσσσσσσππππππππ++ AAUTUT,,σσσσσσσσρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ωρ,Φ,ω

ee++/e/e--

27.5 GeV27.5 GeV

PPbb=55%=55%

Exclusivity @ HERMESExclusivity @ HERMES


�� missing mass (energy) missing mass (energy) techniquetechnique�� background estimated by MCbackground estimated by MC

(detected)(detected)MC

associated BH

Bethe-Heitler

+ data

no recoil detectionno recoil detection

HERMES / JLAB HERMES / JLAB kinematics: BH >> DVCSkinematics: BH >> DVCS

DVCSDVCStwo experimentally undistinguishable processes:two experimentally undistinguishable processes:

e’e

γ

p + ∆

γ∗

p

ee’

γγ∗

p ∆p +

DVCSDVCS BetheBethe--Heitler (BH)Heitler (BH)

p + p + ∆∆∆∆∆∆∆∆

(((( ))))* 2 2*~ | | | |d τ τ + τ ττ τ + τ ττ τ + τ ττ τ + τ τσ + τ + τσ + τ + τσ + τ + τσ + τ + τ


(((( ))))* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd τ τ + τ ττ τ + τ ττ τ + τ ττ τ + τ τσ + τ + τσ + τ + τσ + τ + τσ + τ + τ

isolate isolate BHBH--DVCS interferenceDVCS interference term nonterm non--zero azimuthal asymmetrieszero azimuthal asymmetries

∆σ∆σ∆σ∆σC ~ cosφφφφ ·Re{ H + ξH +… }~

�polarization observables:polarization observables:

� different charges: edifferent charges: e++ ee-- (only @HERA!):(only @HERA!):

H

DVCS ASYMMETRIESDVCS ASYMMETRIES

(((( ))))* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd τ τ + τ ττ τ + τ ττ τ + τ ττ τ + τ τσ + τ + τσ + τ + τσ + τ + τσ + τ + τ


∆σ∆σ∆σ∆σUT ~ sinφφφφ·Im{k(H - E) + … }

∆σ∆σ∆σ∆σLU ~ sinφφφφ·Im{H + ξH + kE}~

∆σ∆σ∆σ∆σUL ~ sinφφφφ·Im{H + ξH + …}~

�polarization observables:polarization observables:

∆σUT

beam target

kinematically suppressedkinematically suppressed

H

H

H, E

~

ξ = xB/(2-xB ),k = t/4M2

CLAS: DVCS CLAS: DVCS -- BSABSA

<-t> = 0.18 GeV2 <-t> = 0.30 GeV2 <-t> = 0.49 GeV2 <-t> = 0.76 GeV2


Integrated over tIntegrated over t

Accurate data in a Accurate data in a large kinematical large kinematical domaindomain

AA way to E and Jway to E and Juu--JJdd

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0 0.5

-0.2

-0.4

-0.6

0

0.2

-0.2

-0.4

-0.6

0

0.2

0 0.25 0.5

-t (GeV2)

AU

Tsi

n(φ-

φ s)cos

(φ) HERMES

PRELIMINARY(in HERMES acceptance)

0 0.2 0.4

e+ p ⇑ → e+ γ X(Mx < 1.7 GeV)

0 0.1 0.2 0.3

xB

0 5 10

Ju=0.2Ju=0.4

Ju=0

(hep-ph/0506264)

0 2.5 5 7.5 10

Q2 (GeV2)

2 1Im( )F H F E−−−−

sin( )cos( ) ~sUTA φ−φ φφ−φ φφ−φ φφ−φ φ

Hermes DVCSHermes DVCS--TTSA:TTSA:


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0 0.5

-0.2

-0.4

-0.6

0

0.2

-0.2

-0.4

-0.6

0

0.2

0 0.25 0.5

-t (GeV2)

AU

Tsi

n(φ-

φ s)cos

(φ) HERMES

PRELIMINARY(in HERMES acceptance)

0 0.2 0.4

e+ p ⇑ → e+ γ X(Mx < 1.7 GeV)

0 0.1 0.2 0.3

xB

0 5 10

Ju=0.2Ju=0.4

Ju=0

(hep-ph/0506264)

0 2.5 5 7.5 10

Q2 (GeV2)

Hall A nDVCSHall A nDVCS--BSA:BSA:

x=0.36 and Qx=0.36 and Q22=1.9GeV=1.9GeV22

Neutron obtained combining Neutron obtained combining deuterium and protondeuterium and proton

FF11 small u & d cancel in small u & d cancel in H%%%%1 1 2 22~ ( )

4LU

tF H x F F H F E

MA + + −+ + −+ + −+ + −%%%%

Can we constrain (JCan we constrain (Juu -- JJdd))


first model dependent extraction of first model dependent extraction of JJuu -- JJdd possiblepossibleVGGVGG--Code: GPDCode: GPD--model: LO/Regge/Dmodel: LO/Regge/D--term=0term=0

The end of polarized targets at HERMESThe end of polarized targets at HERMESDVCS exclusivity by missing mass MDVCS exclusivity by missing mass Mxx

Improve ExclusivityImprove ExclusivityDetect recoiling protonDetect recoiling proton

modify target regionmodify target region


The HERMES Recoil Detector The HERMES Recoil Detector

detection of the recoiling protondetection of the recoiling protonp; 135 p; 135 --1200 MeV/c1200 MeV/c76% 76% φφφφφφφφ acceptanceacceptanceππππππππ/p PID via dE/dx/p PID via dE/dx

improved timproved t--resolutionresolutionstudy kinematical study kinematical dependencesdependences

−−−−background suppressionbackground suppression

SciFiSciFi


Build by DESY, Erlangen, Ferrara, Frascati,Build by DESY, Erlangen, Ferrara, Frascati,Gent, Giessen and GlasgowGent, Giessen and Glasgow

~pp t−−−−~ xt M−−−−

background suppressionbackground suppressionsemisemi--incl.: 5% incl.: 5% ֏ ֏ <<1%<<1%associated: 11% associated: 11% ֏ ֏ ~1%~1%

SiliconSilicon

Access to LAccess to Lqq in semiin semi--inclusive scatteringinclusive scatteringNew structure function accessible with SSANew structure function accessible with SSA

2

11

φ φφ φφ φφ φ−−−−

⊥⊥⊥ ⊥

⊥⊥⊥ ⊥⋅⋅⋅⋅= −= −= −= −

sin( )

,( , , )h s

T

T

UU T h

h pF x z P f D

M

$

C�

std. FFstd. FFSivers DFFSivers DFFSide viewSide view Front viewFront viewleftleftleft

quarks


right

photon

NOTE: QCD tells us that the FSI has to be attractive, since NOTE: QCD tells us that the FSI has to be attractive, since quark and remnants form a color antisymmetric statequark and remnants form a color antisymmetric state

right

photon

rightproton

��

A distortion in the distribution of quarks in transverse A distortion in the distribution of quarks in transverse space can give rise to a nonzero Sivers functionspace can give rise to a nonzero Sivers function

The presence of spin can distort the distribution of quarks in The presence of spin can distort the distribution of quarks in transverse space (orbital angular momentum of quarks is required)transverse space (orbital angular momentum of quarks is required)

HERMES & COMPASS MeasurementsHERMES & COMPASS Measurements

0

0.05

0.1

0.15

0.2

0.25

2 ⟨s

in(φ

-φS)⟩

h U

T

K+

π+

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.1 0.2 0.3

2 ⟨s

in(φ

-φS)⟩

h U

T

K-

π-

x0.2 0.3 0.4 0.5 0.6

z0.2 0.4 0.6 0.8 1

Ph⊥ [GeV]

IIIHERMES PRELIMINARY 2002-2005lepton beam asymmetry, Sivers amplitudes8.1% scale uncertainty

Proton:Proton:Sivers moment:Sivers moment:ππππππππ++ > 0 > 0 ππππππππ-- ~ 0~ 0

KK+ + > 0 K> 0 K-- ~ 0~ 0KK++ >> ππππππππ++

sea quarks importantsea quarks importantDeuterium ~ 0 Deuterium ~ 0


0

0.05

0.1

0.15

0.2

0.25

2 ⟨s

in(φ

-φS)⟩

h U

T

K+

π+

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.1 0.2 0.3

2 ⟨s

in(φ

-φS)⟩

h U

T

K-

π-

x0.2 0.3 0.4 0.5 0.6

z0.2 0.4 0.6 0.8 1

Ph⊥ [GeV]

IIIHERMES PRELIMINARY 2002-2005lepton beam asymmetry, Sivers amplitudes8.1% scale uncertainty

DeuteriumDeuteriumProtonProton

sea quarks importantsea quarks importantDeuterium ~ 0 Deuterium ~ 0

u and d quark cancelu and d quark cancel

Results from theoryResults from theoryLattice QCD: SiversLattice QCD: Sivers

negative negative for up quarksfor up quarks

Pheno. analysis from data:Pheno. analysis from data:


QCDSF/UKQCD Collab. (hepQCDSF/UKQCD Collab. (hep--ph/05110032) ph/05110032)

positive positive for down quarksfor down quarks

Anselmino et al., hepAnselmino et al., hep--ph/0511017ph/0511017

[20] Anselmino et al., PRD72 (05)[20] Anselmino et al., PRD72 (05)

[21] Vogelsang, Yuan, PRD72 (05)[21] Vogelsang, Yuan, PRD72 (05)

[23] Collins et al., hep[23] Collins et al., hep--ph/0510342ph/0510342

SummarySummary

∆∆∆∆∆∆∆∆qq

∆∆∆∆∆∆∆∆GGLLqq

∆∆∆∆∆∆∆∆qq δδδδδδδδqq1Tf⊥⊥⊥ ⊥

0

0.2

x⋅∆u

-0.2

0x⋅∆d

-0.1

0

GRSV 2000LO val

BB 01 LOx⋅∆u

–

Q2=2.5GeV2

-0.1

0

x⋅∆d–

-0.1

0

x⋅∆s

0.03 0.1 0.6

x


∆∆∆∆∆∆∆∆qq

LLggδδδδδδδδqq1Tf⊥⊥⊥ ⊥

∆∆∆∆∆∆∆∆GGLLgg

LLqq

Spin is fascinatingSpin is fascinating

W. PauliN.Bohr


Thank you for your attentionThank you for your attention

BACKUP SLIDESBACKUP SLIDES


Results for Results for ∆∆∆∆∆∆∆∆Q and Q and ∆∆∆∆∆∆∆∆SS

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

x

A1d

Inclusive Asym

metry

Inclusive Asym

metry

Kaon A

symm

etryK

aon Asym

metry

xbj

A1K(x

)

HERMES PRELIMINARY

e + d → K± + X→ →

-0.2

0

0.2

0.4

0.6

0.8

1

10-1

'e d e K X±±±±+ →+ →+ →+ →r urr urr urr ur

Need a longitudinal polarized deuterium targetNeed a longitudinal polarized deuterium targetstrange quark sea in proton and neutron identicalstrange quark sea in proton and neutron identicalfragmentation simplifiesfragmentation simplifies

All needed information can be extracted from HERMES data aloneAll needed information can be extracted from HERMES data aloneinclusive Ainclusive A1,d1,d(x,Q(x,Q22)and kaon A)and kaon AKK

1,d1,d (x,Q(x,Q22) double spin asym.) double spin asym.Kaon multiplicitiesKaon multiplicities


-0.110

-1

x

A1d

xbj

A1K(x

)

HERMES PRELIMINARY

e + d → K± + X→ →

-0.2

0

0.2

0.4

0.6

0.8

1

10-1

.( ) 4 ( ) ( )K K K K Kds un trD z dz D z dz D z dz

+ − + −+ − + −+ − + −+ − + −+ ++ ++ ++ +−−−− = += += += +∫ ∫ ∫∫ ∫ ∫∫ ∫ ∫∫ ∫ ∫

( ) 2 ( )strangK K K

seD z dz D z dz+ −+ −+ −+ −++++====∫ ∫∫ ∫∫ ∫∫ ∫

.( ) ( ) ( ) ( )( ) /( ) / 5 ( ) 2 ( )

nK

str strangKK

Dis

eQ x D z dz S x D z dzdN x dxdN x dx Q x S x

−−−− ++++====

++++∫ ∫∫ ∫∫ ∫∫ ∫

Fit xFit x--dependence of multiplicitiesdependence of multiplicitiesusing PDFs from CTEQusing PDFs from CTEQ--66

x

(dN

K(x

)/dx

)/(d

ND

IS(x

)/dx

)

0.5

HERMES PRELIMINARY (Evolved to Q 2=2.5 GeV2)

Q(x)∫DQ(z)dz+S(x) ∫DS(z)dz

5Q(x)+2S(x)

Non Strange contribution

Strange contribution

10-2

10-1

1

10-1

( )trgKsD z dz∫∫∫∫

( )KnstrgD z dz∫∫∫∫

This Work Kretzer KKPThis Work Kretzer KKP

0.410.41±±0.02 1.103 1.1110.02 1.103 1.111

1.411.41±±0.29 0.783 0.2960.29 0.783 0.296

Only assumptions used:Only assumptions used:isospin symmetry between proton and neutronisospin symmetry between proton and neutronchargecharge--conjugation invariance in fragmentationconjugation invariance in fragmentation

Results for Results for ∆∆∆∆∆∆∆∆Q and Q and ∆∆∆∆∆∆∆∆SS-2

-1

0

10-1

XBj

XBj

x.∆S

(x)

HERMES PRELIMINARY

-0.1

0

0.1

10-1

0

0.1

10-1

XBj

XBj

x.∆Q

(x)

HERMES PRELIMINARY

0

0.1

0.2

10-1

( ) ( ) ( ) ( ) ( )Q x u x u x d x d x= + + += + + += + + += + + + ( ) ( ) ( )S x s x s x= += += += +

1

0.020.286 0.026 0.011Q∆ = ± ±∆ = ± ±∆ = ± ±∆ = ± ±∫∫∫∫

1

0.020.006 0.029 0.007S∆ = ± ±∆ = ± ±∆ = ± ±∆ = ± ±∫∫∫∫


Earlier HERMES conclusions of Earlier HERMES conclusions of unpolarized strange sea confirmedunpolarized strange sea confirmed

factor 2 smaller error barsfactor 2 smaller error barsErrors very sensitive to FF inputErrors very sensitive to FF input




COMPASSCOMPASS HERMESHERMES

------


hh±±hh±± vs. hvs. h±±::

hh±±hh±± ------

hh±± ------

2 1Q >>>>2 1Q <<<< 2 0.1Q <<<<

2 0.1Q >>>>2 0.1Q <<<<





------

hh±± more inclusive more inclusive → → pQCD NLO calculations (easier) possiblepQCD NLO calculations (easier) possible

The Model in PYTHIAThe Model in PYTHIA--66

VMD VMD directdirect anomalous photonanomalous photon

„Soft“ VMD:„Soft“ VMD: QCDQCD-- Splitting of Splitting of

p a) p b) p )Model:Model: Mix processes with different photon characteristicsMix processes with different photon characteristics


„Soft“ VMD:„Soft“ VMD:Elastic, diffractive, Elastic, diffractive, nonnon--diffractive diffractive („minimum bias“,(„minimum bias“,„low„low--pp TT““ ) ) processesprocessesHard VMD:Hard VMD:QCD 2QCD 2→→2 2 processesprocesses

QCDQCD--ComptonComptonPGFPGFLO DIS LO DIS (virtual (virtual photonsphotons))

Splitting of Splitting of γγγγγγγγ→→qqqqQCD 2QCD 2→→2 2 processesprocesses

Small QSmall Q 22: VMD+anomalous (=„resolved“) photon dominate: VMD+anomalous (=„resolved“) photon dominateLarge QLarge Q 22: LO DIS dominates: LO DIS dominatesChoice of hard process according to hardest scale i nvolved:Choice of hard process according to hardest scale i nvolved:If all scales are too small: „soft“ VMD (diffractiv e or „lowIf all scales are too small: „soft“ VMD (diffractiv e or „low--pT“)pT“)The „resolved“ part is modeled to match the world d ata on The „resolved“ part is modeled to match the world d ata on σσσσσσσσ((γγγγγγγγp) p)

k⊥⊥⊥ ⊥

p⊥⊥⊥ ⊥

Q

The MethodThe Method

Measured asymmetry is an incoherent superposition of Measured asymmetry is an incoherent superposition of different subdifferent sub--process asymmetries:process asymmetries:

Signal: Gluon of the nucleon in the initial stateSignal: Gluon of the nucleon in the initial state

|||| ||| |( ) ;B SigSig

gmeas i it i i

i tB

tog f AA p f A ff A

σσσσ= = + == = + == = + == = + =σσσσ∑∑∑∑

Asymmetry of the Asymmetry of the hard subhard sub--processprocess|| ˆ ˆ( ) ; :Sig

t Sig Sig

GA p a a

∆∆∆∆====


Background: all other subBackground: all other sub--processesprocesses

The gluon polarization is then:The gluon polarization is then:

hard subhard sub--processprocess|| ˆ ˆ( ) ; :t Sig SigA p a aG

====

|| ||ˆ]

1[ meas

Sig

BgBgf

GA

aA

Gf

−−−−∆∆∆∆ ====

HERMES ResultsHERMES Results

1 2, 0.5T Tp p GeV>>>> 2 2 2,1 ,2 2.0T Tp p GeV+ >+ >+ >+ >

Channels:Channels:

hh±±hh±± with Qwith Q22<<0.1GeV0.1GeV22;;hh±± with Qwith Q22>>0.1GeV0.1GeV22; P; PTT>1GeV>1GeVhh±± with Qwith Q22<<0.1GeV0.1GeV22; ; ppTT>1GeV>1GeV

-0.1

0

0.1

0.2

0.3

MC, ∆G/G= 0MC, ∆G/G= -1

MC, ∆G/G= +1

ep→h+XHERMES Preliminary

A||

Hermes Data (e± not in acc.)

ep→h-X

-0.1

0

0.1

0.2

0.3

0 1 2

ed→h+X

0 1 2

ed→h-X

pT(beam)(GeV)

Considered subConsidered sub--processes:processes:LOLO--MC: PYTHIA 6.2MC: PYTHIA 6.2

0

0.2

0.4

0.6

0.8

1

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25

low pTQCD 2→2(q)

ela./diff. VMDLO DISQCDC

PGFQCD 2→2(g)

pT(beam) (GeV)

Sub

proc

ess

Fra

ctio

ns-0.4-0.2

00.20.40.60.8

11.21.4

1.2 1.4 1.6 1.8 2

h+ antitagged (e± not in acc.)h- antitagged (e± not in acc.)

Proton

<∆g/

g>

1.2 1.4 1.6 1.8 2

h+ taggedh- taggedpairs

Deuteron

HERMES Preliminary

pT (GeV)


-0.1

0

0.1

0.2

0.3

MC, ∆G/G= 0MC, ∆G/G= -1

MC, ∆G/G= +1

ep→h+XHERMES Preliminary

A||

Hermes Data (e± not in acc.)

ep→h-X

-0.1

0

0.1

0.2

0.3

0 1 2

ed→h+X

0 1 2

ed→h-X

pT(beam)(GeV)

0

0.2

0.4

0.6

0.8

1

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25

low pTQCD 2→2(q)

ela./diff. VMDLO DISQCDC

PGFQCD 2→2(g)

pT(beam) (GeV)

Sub

proc

ess

Fra

ctio

ns-0.4-0.2

00.20.40.60.8

11.21.4

1.2 1.4 1.6 1.8 2

h+ antitagged (e± not in acc.)h- antitagged (e± not in acc.)

Proton

<∆g/

g>

1.2 1.4 1.6 1.8 2

h+ taggedh- taggedpairs

Deuteron

HERMES Preliminary

pT (GeV)

COMPASS ResultsCOMPASS Results

1 2, 0.7T Tp p GeV>>>> 2 2 2,1 ,2 2.5T Tp p GeV+ >+ >+ >+ >

Channel:Channel:Cuts:Cuts:

hh±±hh±± with Qwith Q22<<1GeV1GeV22

Considered subConsidered sub--processes:processes:LOLO--MC: PYTHIA 6.2MC: PYTHIA 6.2

0

0.1

0.2

0.3


(PGF)qq→g*γqg→q*γ

q→q*γ

qq’→qq’qg→qggg→gg

Tlow p

(PGF)qq→g*γqg→q*γ

q→q*γ

qq’→qq’qg→qggg→gg

Tlow p

0

0.1

0.2

0.3

used for used for ∆∆∆∆∆∆∆∆g/g extractiong/g extraction

∆∆∆∆∆∆∆∆g/g=0.016g/g=0.016±±0.058(stat.)0.058(stat.)±±0.055(syst.)0.055(syst.)0.070.0350.085gx ++++

−−−−==== µµµµµµµµ22=3.0GeV=3.0GeV22

10-510-410-310-210-11

ed→h+Xdσh /d

p T (

µb/G

eV)

HERMES Preliminary

PYTHIADeuteron Data, e± not in acc.

ed→h-X

0.20.40.60.8

11.2

0 0.5 1 1.5 2

LO MC

σMC/σ

Dat

a

0 0.5 1 1.5 2

pT(beam) (GeV)

10-510-410-310-210-11

ed→h+Xdσh /d

p T (

µb/G

eV)

HERMES Preliminary


ed→h-X

0.20.40.60.8

11.2

0 0.5 1 1.5 2

LO MC

LO MC×k-Factor

σMC/σ

Dat

a

0 0.5 1 1.5 2

pT(beam) (GeV)

Cross Section DataCross Section Data--MCMCHERMES cross section:HERMES cross section:kkTT, p, pT T standard values:standard values:

, 0.40pTk GeVγγγγ ==== 0.40frag

Tp GeV====M.Anselmino et al. Phys. Rev. D71,074006M.Anselmino et al. Phys. Rev. D71,074006

2 20.25 20%tk GeV= ±= ±= ±= ± 2 20.20 20%tp GeV= ±= ±= ±= ±


10-510-410-310-210-11

ed→h+Xdσh /d

p T (

µb/G

eV)

HERMES Preliminary


ed→h-X

0.20.40.60.8

11.2

0 0.5 1 1.5 2

LO MC

σMC/σ

Dat

a

0 0.5 1 1.5 2

pT(beam) (GeV)

10-510-410-310-210-11

ed→h+Xdσh /d

p T (

µb/G

eV)

HERMES Preliminary


ed→h-X

0.20.40.60.8

11.2

0 0.5 1 1.5 2

LO MC

LO MC×k-Factor

σMC/σ

Dat

a

0 0.5 1 1.5 2

pT(beam) (GeV)hephep--ph/0505157ph/0505157

2000

4000

COMPASS standard values:COMPASS standard values:

0.50Tk GeVγγγγ ====

0.36fragTp GeV====

1.00pTk GeV====

Cross Section Data Cross Section Data -- MCMC


2000

[GeV/c]T

p0 1 2 3

1

2

hephep--ph/0505157ph/0505157

=q1h −=q

1g −=q1f

{ } +++=Φ nxhxgxfx T1

5151L1Tw2Corr Sγγ)(γ)(S)(

2

1)(

The 3The 3rdrd TwistTwist--2 structure function 2 structure function


longitudinally polarizedlongitudinally polarizedquarks and nucleonsquarks and nucleons

∆∆∆∆∆∆∆∆q(x): helicity differenceq(x): helicity difference

�� axial chargeaxial charge

knownknown

unpolarised quarksunpolarised quarksand nucleonsand nucleons

q(x): spin averagedq(x): spin averaged

�� vector chargevector charge

well knownwell known

transversely polarizedtransversely polarizedquarks and nucleonsquarks and nucleons

δδδδδδδδq(x): q(x): helicity fliphelicity flip

�� tensor chargetensor charge

measuring!measuring!

=q1h −

{ } +++=Φ nxhxgxfx T1

5151L1Tw2Corr Sγγ)(γ)(S)(

2

1)(

Peculiarities of transversityPeculiarities of transversity

chiral odd chiral odd FFFF

relativistic nature of quarkrelativistic nature of quark : : in absence of relativistic effects hin absence of relativistic effects h 11(x)=g(x)=g11(x)(x)

QQ22 ––evolutionevolution : unlike for g: unlike for g 11pp(x), (x),

the gluon doesn’t mix with quark inhthe gluon doesn’t mix with quark inh 11pp(x)(x)


transversely polarizedtransversely polarizedquarks and nucleonsquarks and nucleons

δδδδδδδδq(x): q(x): helicity flip helicity flip

�� tensor chargetensor charge

measuring !measuring !single helicity

flip

CHIRAL ODD CHIRAL ODD NOT ALLOWED IN NOT ALLOWED IN

E.M. E.M. INTERACTIONSINTERACTIONS

doubledoublehelicity fliphelicity flip

the gluon doesn’t mix with quark inhthe gluon doesn’t mix with quark inh 11 (x)(x)(no gluon analog for spin(no gluon analog for spin--½ nucleon)½ nucleon)

sensitive to the sensitive to the valence quark polarisationvalence quark polarisationq and q have opposite sign.q and q have opposite sign.

_

tensor charge:tensor charge: first moment of hfirst moment of h 11(large from lattice QCD)(large from lattice QCD)

first data for Collins FF first data for Collins FF available from Belleavailable from Belle

extraction of hextraction of h 11 fromfrom

1 ( )H z⊥

Collins momentsCollins moments

Collins moment:Collins moment:ππππππππ++ > 0 > 0 ππππππππ-- < 0< 0

ππππππππ-- unexpected largeunexpected largerole of unfavoured FFrole of unfavoured FF

[PRL94(2005),012002; hep-ex0507013]

-0.02

0

0.02

0.04

0.06

0.08

0.1

2 ⟨s

in(φ

+φS)⟩

π U

T

π+

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.1 0.2 0.3

2 ⟨s

in(φ

+φS)⟩

π U

T

π-

x0.2 0.3 0.4 0.5 0.6

z0.2 0.4 0.6 0.8 1

Ph⊥ [GeV]

IIIIIIHERMES PRELIMINARY 2002-2004virtual photon asymmetry amplitudes6.6% scale uncertainty

-0.1

0

0.1

0.2

0.3

0.4

2 ⟨s

in(φ

+φS)⟩

h U

T

K+

-0.4

-0.2

0

0.2

0.4

0.6

0.1 0.2 0.3

2 ⟨s

in(φ

+φS)⟩

h U

T

K-

x0.2 0.3 0.4 0.5 0.6

z0.2 0.4 0.6 0.8 1

Ph⊥ [GeV]



extraction of hextraction of h 11 fromfromHermes asymmetriesHermes asymmetries

2005 data:2005 data:2 dimensional binning2 dimensional binning

disentangle x (PDF) and disentangle x (PDF) and zz (FF) dependence(FF) dependence

-0.02

0

0.02

0.04

0.06

0.08

0.1

2 ⟨s

in(φ

+φS)⟩

π U

T

π+

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.1 0.2 0.3

2 ⟨s

in(φ

+φS)⟩

π U

T

π-

x0.2 0.3 0.4 0.5 0.6

z0.2 0.4 0.6 0.8 1

Ph⊥ [GeV]


-0.1

0

0.1

0.2

0.3

0.4

2 ⟨s

in(φ

+φS)⟩

h U

T

K+

-0.4

-0.2

0

0.2

0.4

0.6

0.1 0.2 0.3

2 ⟨s

in(φ

+φS)⟩

h U

T

K-

x0.2 0.3 0.4 0.5 0.6

z0.2 0.4 0.6 0.8 1

Ph⊥ [GeV]


KK++ > 0 K> 0 K-- > 0> 0KK++ in agreement with in agreement with ππππππππ++

)( Sφφ− angle of hadron relative to angle of hadron relative to initialinitial quark spin (Sivers)quark spin (Sivers)

)( Sφφ+ angle of hadron relative to angle of hadron relative to finalfinal quark spin (Collins)quark spin (Collins)

⊥⊗ 11 Hh (Collins)(Collins)

Azimuthal angles and asymmetriesAzimuthal angles and asymmetries


)( Sφφ− initialinitial quark spin (Sivers)quark spin (Sivers)

1T1 Df ⊗⊥(Sivers)(Sivers) chiralchiral--even naïve Teven naïve T--odd DFodd DF

related to parton orbital related to parton orbital momentummomentum

violates naïve universality of PDFviolates naïve universality of PDF

peculiarity of fpeculiarity of f ⊥⊥⊥ ⊥⊥ ⊥⊥ ⊥1T1T

different sign of fdifferent sign of f ⊥⊥⊥ ⊥⊥ ⊥⊥ ⊥1T1T in DYin DY

Documents

The Spin Structure of the Nucleon - University of VirginiaThe Spin Structure of the Nucleon EE.C. Aschenauer.C. Aschenauer SFU, VanCouver, March 2007 11