Polarized Structure Functions

Gerard van der Steenhoven (NIKHEF)

JLab, Newport News, 4 March 2002

u u

d

9th Int. Conference on the Structure of Baryons

Introduction

� The origin of spin in the baryon octet:

��� �

���q ��G� Lz

� Developing insight:

– EMC (SLAC, SMC and HERMES): ��q � ���� ���– The quark model: ��q � ���� � ���– Relativistic MIT bag model: ��q � ���� ����

� Experimental questions:

– What about flavour dependence?�u�x, �d�x, �s�x

– What about gluons?�G�x

– What about orbital angular momentum?Deeply Virtual Compton Scattering: Lz?

– What about other baryons?n, �,..

– What about lattice QCD?longitudinal spin: ��q � ����� ����

transverse spin: ��q � ���� ����

Outline

� Introduction

� Longitudinal spin:

– Inclusive experiments: gn�p� �x� gn�p� �x– Semi-inclusive experiments: �qf�x– Photo-production of high pT -pairs: �G�x– Deeply-virtual Compton scattering: Lz�x– Hyperon production: -spin

� Transverse spin:

– Single-spin asymmetries in �-production: h��x

1h = -

� Future perspectives:

– HERMES Run-II– COMPASS– RHIC-spin– SLAC– TESLA-N, EIC,...

Introduction

� Polarized Deep Inelastic Lepton Scattering:

θ

E

E'+1

-1/2

+1/2

photon

quark

quark

� Asymmetry w.r.t. to target spin orientation:

A� ��

DPTPB

N�� �N��

N�� �N��

� The spin-dependent structure function g��x :

A� � g��x

F��x� �

F��x

Xf

e�f�qf�x

with the quark polarization:

�qf�x � q�f �x � q�f �x

� General objective:

Spin structure of the nucleon

The HERMES experiment

� The HERMES spectrometer at DESY:

1

0

2

-1

-2

m

LUMINOSITY

CHAMBERSDRIFT

VC 1/2

FC 1/2

VERTEX CHAMBERS

TARGETCELL

DVC

MC 1-3

HODOSCOPE H0

MONITOR

BC 1/2

BC 3/4 TRD

MAGNET

PROP.CHAMBERS

FIELD CLAMPS

PRESHOWER (H2)

STEEL PLATE CALORIMETER

DRIFT CHAMBERS

TRIGGER HODOSCOPE H1

0 1 2 3 4 5 6 7 8 9

IRON

WIDE ANGLEMUON HODOSCOPE

FRONTMUONHODO

RICH

� Internal Target (���H , �

��H , �

��He, �He, ��N, ��Ne, ��Kr) :

gas injection

storage cell

fixed collimator

e-beam

spectrometer

exit window

pumps

suppressors

wake field

target

vacuum chamber

thin walled

beam pipe

Data collected in Run I

� Accumulated polarized DIS events per year:

Hermes Running 1996-2000

0

1000

2000

3000

4000

5000

6000

7000

8000

0 50 100 150 200 250 300Days of Running

Acc

umul

ated

DIS

[·10

3 ]

1996 (e++ p→

)

1997 (e++ p→

)

1998/99 (e-+ d→

)1999 (e++ d

→)

2000 (e++ d→

)

T. L

inde

man

n H

erm

es C

olla

bora

tion

onl

ine

anal

ysis

� Data taking in 2000:

– cell size reduced to 21 X 8.9 mm�

– lower cell temperature: 96 � 62 K

Luminosity increased by factor 2.5 !!

Unpolarized data taking

� End-of-Fill running:

– Last hour of every fill: high-density targets– Loss of normal data taking: few �– Targets used: �H, �H, �He, ��Ne– Positron beam life time: 0.5 – 2 hours– Data collected: 13.6 Million DIS events

0

20

40

60

80

100

120

12 14 16 18 20 22 0 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 0

10

20

30

40

50

60

HERA

Current-p [mA] Lifetime-e [h] Current-e [mA]

Time [h]

Fri Jul 14 12:00 2000 Sun Jul 16 12:00 2000

p: 103.6 [mA] -1.0 [h] 920 [GeV/c] e+: 41.0 [mA] 6.9 [h] 27.6 [GeV/c]

luminosity run

Tau(e)ProtonsLeptons

Maximum luminosity: 4 10�� N/cm�/s

� Dedicated HERA run at E = 12 GeV:

– HERMES spectrometer operated well– Collected: 1 Million DIS ev. on �H, �H, ��N, ��Kr.

Inclusive measurements - 1

� New deuterium data on gd��x�Fd� �x:

gd�F d�

��

� � �

�Ad��

D� �� � �Ad

�

�

0

0.1

0.2

0.3

0.4

10-2

10-1

x

g1d

F1d

HERMES PRELIMINARY(’00 data, no smearing correction)

exp. systematic uncertainty

uncertainty due to R

� Observation:

HERMES probes down to x � � ����

Inclusive measurements - 2

� Compare to existing data:

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

10-4

10-3

10-2

10-1

g1d

F1d

HERMES PRELIMINARY

SMC

E143

E155(averaged by HERMES)

(’00 data, no smearing correction)

10-2

10-1

1

10

10-4

10-3

10-2

10-1

x

<Q2>

GeV2

� Conclusion:

gd��x: no strong Q� dependence

Polarized Structure Functions

� Overview of existing xg��x data:

0

0.02

0.04

0.06xg1

proton

HERMESHERMES prel.HERMES prel. rev.

E143E155

SMC

0

0.02

0.04 deuteron

-0.04

-0.02

0

0.02

E142E154

x

neutron (3He)

0.0001 0.001 0.01 0.1 1

The structure function g��x

� Preliminary data from SLAC E143 and E155x:

[g��x� is sensitive to qg-correlations and higher twist]

gWW�

�x� exp.:� solid;M. Stratmann (93):

� dot-dash;Gamberg-Weigel (97):

� short-dash;Song (96):

� dotted;Wakamatsu (96):

� long-dash;

� Wandzura - Wilczek interpretation:

gWW� �x�Q� � �g��x�Q� �

Z �

x

g��y�Q�

ydy

g��x�Q� dominated by twist-2 part

Semi-Inclusive Asymmetries

� Asymmetry for semi-inclusive hadron (h) production:

Ah��x �

RdzP

f e�f �qf�xD

hf �zR

dzP

f e�f qf�xD

hf �z

Nh�� �Nh

��

Nh�� �Nh

��

� Define purity Phf �x:

Phf �x �

e�fqf�xRDhf �zdzP

f e�fqf�x

RDhf �zdz

[probability that hadron h is produced when quark f is hit]

� Measure asymmetries on various targets:

�A�x � P�x �Q�x

with �A�x� = (A�p,Ah�

�p , Ah�

�p , A�d, ...)and �Q�x� = (�u�x�, �d�x�, ��u�x�, ...)

� Polarized quark distributions: �u�x, �d�x, ...

Polarized quark distributions - 1

� Measured semi-inclusive asymmetries Ah��x:

-0.2

0

0.2

0.4

0.6

0.8

1

0.02 0.1

A1,d

HERMES prelim.(spring '99 data)

E143

0.02 0.1

A1,d

h+

HERMES prelim.(spring '99 data)

SMC

x0.02 0.1 0.7

A1,d

h−

� Extracted quarkspin distributions:

0

0.25

0.5

0.75 HERMES preliminary (1995 - Spring 1999)

(∆u+∆u–)/(u+u

–)

-1

-0.5

0

0.5(∆d+∆d

–)/(d+d

–)

-2

-1

0

∆qs/qs

0.02 0.1 0.6x

Spin - flavourseparation.

Polarized quark distributions - 2

� Expected data quality with ’00 data included:

HERMES ∆q extraction MC projection

0

0.25

0.5

x (∆

u +

∆u–

)

MC: 96/97 H→

+ 98-00 D→

HERMES publ. PLB 464 (1999) 123

-0.25

0

0.25

x (∆

d +

∆d–

)

CTEQ4LQ / (1+R)GRSV 2000 / (1+R)

0

0.05

x ∆u

–

0

0.05

x ∆d

–

-0.05

0

0.05

x ∆s

= x

∆s–

0.02 0.1 0.7x

M. B

eckm

ann,

J. W

endl

and,

H

ER

ME

S 2

001

High-pT hadron pairs from �H

� pQCD Compton graph and Photon-Gluon Fusion:

������

��

��

�

����

���

�� �� ��

�����

q

��

g

q

����

���

������

��

��

��

g

��

q

�q

� Asymmetry for high-pT pions (R � PGF�Com) :

AeN�h�h�LL � �aQCDC

�q

q

�

� �R� �aPGF

�G

G

R

� �R

� Target spin-asymmetry on long. polarized �H:

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.6 0.8 1 1.2 1.4 1.6 1.8 2

GSA (<∆G/G> ~ 0.4)GSB (<∆G/G> ~ 0.3)GSC (<∆G/G> ~ -0.1)

pTh2 (GeV/c)

A||(

pTh

1 ,pTh

2 )

pTh1>1.5 GeV/c ∆G/G=-1

∆G/G=0

∆G/G=+1

∆G/G=0.41

HERMES CollaborationPRL 84 (2000) 2584

High-pT hadron pairs on �H

� Require oppositely charged hadron pairs:

– PGF produces only (+ –) pairs: favored– pQCD on �H � more + hadrons: disfavored

� Preliminary results on �H:

pTh+ (GeV/c)

A||(

p Th-

,pT

h+)

pTh- (GeV/c)

A||(

p Th+

,pT

h-)

pTh2 (GeV/c)

A||(

p Th1

,pT

h2)

pTπ2 (GeV/c)

A||(

p Tπ1

,pT

π2)

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.5 1 1.5 2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.5 1 1.5 2

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.5 1 1.5 2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.5 1 1.5 2

High-pT kaon pairs

� Strangeness production suppressed in pQCD....

� High-pT kaon pairs on �H and �H:

pTK2 (GeV/c)

A||(

p TK

1 ,p T

K2 )

pTK2 (GeV/c)

A||(

p TK

1 ,p T

K2 )

pTK2 (GeV/c)

A||(

p TK

1 ,p T

K2 )

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.5 1 1.5 2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.5 1 1.5 2

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.5 1 1.5 2

� More statistics needed (+ MC studies)

Deep Virtual Compton Scattering

� Off-shell photon�-quark scattering:

– Detect e� and �, and require: Emiss = 0

� Ji’s sumrule [Phys. Rev. Lett. 78 (1997) 610]:Zxdx�H�x���� �E�x���� � � Aq��

� �Bq���

with �� � �t and

lim����

�Aq��� �Bq��

�� � �Jquark � �q � �Lq

� DVCS: total quark angular momentum

� Experimental considerations:

– Interference with Bethe-Heitler process:

DVCSN

BH makes DVCS measurable

– Detect scattered photon, but suppress � �’s– Observe azim. asymmetry: A BetheHeitler

LU � �

First observations of DVCS

� Missing mass spectrum and Asin�LU � �N

PNi�

sin�iPl�i

:

0

1000

2000

3000

4000

5000

-5 0 5 10 15 20 25 30 35 40 45

Co

un

ts

0

200

400

600

800

1000

-4 -2 0 2 4 6 8

Mx2 (GeV2)

Co

un

ts

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-1 0 1 2 3 4 5 6 7

e→+p → e+γ X

Mx (GeV)

AL

Usi

n φ

� Azimuthal (�) distributions from HERMES & JLab:

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-3 -2 -1 0 1 2 3

φ (rad)

AL

U

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 50 100 150 200 250 300 350φ (deg)

A

HERMES, PRL 87(’01)182001 CLAS Collab., PRL 87(’01)182002

DVCS: helicity dependence

� Exclusive leptoproduction of photon:

d�

d�dtdQ�dx�

xy�

�� ����Q�

j�BH� �DVCSj��� � �x�m��Q�

���

� Leading order interference term:

���BH�DVCS � ��DVCS�BHpol ��p� me�

tQx� �p

�� x

el Pl

�� sin� �r� �

Im �M���

�� Extract sin��-moment, Asin��

LU � �N�

PN�

i�sin�ijPlji

:

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-1 0 1 2 3 4 5 6 7

λBeam = +1

λBeam = -1

Average

Mx (GeV)

AL

Usi

n φ±

e→+p → e+γ X

Data showexpectedhelicitydependence!

DVCS: formalism

� Beam-charge asymmetry with unpolarised leptons:

d��e�p� � d��e

�p� � cos�� �

Re

�F�H� �

xB

�� xB�F� � F�� eH� �

��

�M�F�E�

�

� Beam-spin asymmetry with polarised positrons:

d����e�p� � d��

��e�p� � sin�� �

Im

�F�H� �

xB

�� xB�F� � F�� eH� �

��

�M�F�E�

�

� Relate DVCS amplitudes H�� eH�,.. to GPDs:

ImH� � ��Xq

e�

q�H��� ������H���� ������

Im eH� � ��Xq

e�

q�eH��� ���

�� � eH���� ���

���

ReH� �Xq

e�

qP

Z ��

��

H�x� ����� �

x� ��

x � ��dx �

Re eH� �Xq

e�

qP

Z ��

��

eH�x� ����� �

x� ��

x � ��dx �

New DVCS results

� Dependence of Asin�LU on x and �t:

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.05 0.1 0.15 0.2 0.25 0.3

xBj

AL

Usi

n φ

e→+p → e+γ X Mx < 1.7 GeV

⟨-t⟩ = 0.25 GeV2 ⟨Q2⟩ = 2.46 GeV2

HERMES 96/97 PRELIMINARY

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-0.2 0 0.2 0.4 0.6 0.8 1

-t (GeV2)

AL

Usi

n φ

e→+p → e+γ X Mx < 1.7 GeV

⟨xBj⟩ = 0.11 ⟨Q2⟩ = 2.46 GeV2

HERMES 96/97 PRELIMINARY

� Q�-dependence and new 2000 data for Asin�LU :

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

1 2 3 4 5 6 7 8 9 10

Q2 (GeV2)

AL

Usi

n φ

e→+p → e+γ X Mx < 1.7 GeV

⟨xBj⟩ = 0.11 ⟨-t⟩ = 0.25 GeV2

HERMES 96/97 PRELIMINARY

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-3 -2 -1 0 1 2 3

φ (rad)

AL

U

e→ + p → e+γ X (Mx< 1.7 GeV)

HERMES 2000PRELIMINARY

P1 + P2 sin φ

P1 = -0.01 ± 0.03 (stat)

P2 = -0.21 ± 0.04 (stat)

No Q�-dependence: hard scattering regime!

DVCS: beam-charge asymmetry

� First data for AC � Ne��Ne�

Ne��Ne�on �H:

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-3 -2 -1 0 1 2 3

φ (rad)

AC

e± p → e±γ X (Mx< 1.7 GeV)

HERMES PRELIMINARY

P1 + P2 cos φ

P1 = -0.05 ± 0.03 (stat)

P2 = 0.11 ± 0.04 (stat) -0.2

-0.1

0

0.1

0.2

0.3

0.4

-1 0 1 2 3 4 5 6

M x (GeV)

AC

co

s φ

e± p → e±γ X

HERMES PRELIMINARY

AC cos φ |M < 1.7 GeV = 0.11 ± 0.04 (stat) ± 0.03 (sys)

x

� Calculation by Kivel et al. [hep-ph/0012136]:

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 20 40 60 80 100 120 140 160 180

e-/e+ + p → e-/e+ + p + γEe = 27 GeV, Q2 = 2.5 GeV2, xB = 0.3, t = -0.25 GeV2

d

σ e- /

(dQ

2 dx B

dt d

Φ)

(nb

/GeV

4 )

Φ (deg)

(σe+

- σ

e-)

/ (σ e+

+ σ

e-)

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100 120 140 160 180

BH + twist 2 + D-termBH + tw 2 + tw 3 + D-termBH onlyBH + twist 2 - D-term

The spin structure - 1

� Two schemes for the spin content:

– Quark parton model: �s = 1.00– SU(3) flavour symm.: �s = 0.6, �u = �d = -0.2

� Measure the polarization from � p��:

�

N

dN

d��

�

���� � ��� �P � �p

� Determine u� spin transfer D LL�:

D LL� �

�P � �L�PBD�y

�

Pf e

�f q

Nf �x �D

f �zP

f e�f q

Nf �xD

f �z

� �D u �z

D u �z

� Electroproduction of hyperons at HERMES:

0

100

200

300

400

500

600

700

1.08 1.1 1.12 1.14 1.16 1.18 1.2

Invariant mass (GeV/c2)Invariant mass (GeV/c2)Invariant mass (GeV/c2)

EV

EN

TS

DΛu ≈ nΛ(z), no Monte-Carlo correction

HERMES PRELIMINARY

z*=(EΛ-mΛ)/ν

DΛ u

Kaidalov, Piskunovade Florian, Stratmann, Vogelsang (LO)de Florian, Stratmann, Vogelsang (NLO)

10-5

10-4

10-3

10-2

10-1

1

0 0.2 0.4 0.6 0.8

The spin structure - 2

� Data for u� spin transfer:

Diquark, u+d (Boros)

Diquark (Ma)pQCD (Ma)

z

Lo

ng

itu

din

al s

pin

fra

nsf

er D

Λ

SU(3)f( BJ)

u+d+s

naive CQM

HERMES 1996-2000 PRELIMINARY

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

� D�

LL�� = 0.04(9)

consistent with�u� � 0(CQM prediction).

� Negative polarisation for xF (= �pLW � 0:

xF

Lo

ng

idu

din

al s

pin

tra

nsf

er D

LΛ a

lon

g W

/γ

HERMES PRELIMINARY Ee=27.5 GeVNOMAD <Eν> =43.8 GeVWA59 <Eν

_> =44.2 GeVE665 Eµ =470 GeV

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

NOMAD Collab.NPB 588 (2000) 3

Contributions from:��� �

���

��� ��

Transverse polarization

� Three leading order distribution functions:

1f = momentum carried by quarks

g1 -= longitudinal quark spin, ��

1h = - transverse quark spin, ��

� Importance of h��x measurements:

– HERMES data: �� = 0.30 � 0.04 � 0.09– �� is so small because of axial anomaly:

� Redistribution of angular momentum in nucleon:

�

��� � ���, �G � ��, Lz � ����

� Redistribution is less in transverse case:

�� � �� � 1 (Quark Parton Model)

� Lattice QCD calculation (Phys. Rev. D 56 (1997) 433):

�� = 0.18(10) and �� = 0.56(9)

Measurements of h��x

� The structure function h��x is chirally odd :

– Not accessible in inclusive DIS– Use semi-inclusive DIS with chirally-oddH

���u� �z

– Assume u-quark dominance– Asymmetry for Collins process:

A��

T �x� y� z � PT �Dnn � �u�xu�x

� H���u� �z

Du��z

�

– H���u� depends on �c � �h � �s � �

� Evidence for transversity from HERMES �H data:

0.2 0.4 0.6

-0.05

0

0.05

0.1 0.2

z

AU

L

sin

φ

π0

π+

π-

x P⊥ (GeV)

0.25 0.5 0.75 1

[HERMES, PRL 84 (2000) 4047 and PRD 64 (2001) 097101]

Single-Spin Asymmetries on �H

� z, x, p�-dependences of Asin�UL for ���� and K�:

-0.1

-0.05

0

0.05

0.1

0.15

0.2 0.4 0.6 0.8 1

z

AU

L

sin

φ

HERMES PRELIMINARY

deuteron

π+

π-

-0.1

-0.05

0

0.05

0.2 0.4 0.6 0.8 1

z

AU

L

sin

φ

HERMES PRELIMINARY

deuteron

K+

-0.02

0

0.02

0.04

0 0.1 0.2 0.3

xB

AU

L

sin

φ

HERMES PRELIMINARY

deuteron

π+

0.2<z<0.7

π-

0

0.025

0.05

0.075

0.1

0 0.1 0.2 0.3

xB

AU

L

sin

φ

HERMES PRELIMINARY

deuteron

K+

0.2<z<0.7

-0.02

0

0.02

0.04

0 0.25 0.5 0.75 1

pt / GeV

AU

L

sin

φ

HERMES PRELIMINARY

deuteron

π+

0.2<z<0.7

π-

-0.02

0

0.02

0.04

0.06

0 0.25 0.5 0.75 1

pt / GeV

AU

L

sin

φ

HERMES PRELIMINARY

deuteron

K+

0.2<z<0.7

Future: HERMES

� HERMES - Run II: 2001 – 2006

– Transverse spin 2001 - 2003– Longitudinal spin 2003 - 2004– Excl. react. w. Recoil Detector : 2004 - 2006– Unpolarized end-of-fill runs 2001 - 2006

Simulated DVCS data with Recoil Detector (1 yr run):

φγ, rad

Ach

e p → e p γ

-0.1

-0.05

0

0.05

0.1

-3 -2 -1 0 1 2 3φγ, rad

AL

U

e p → e p γ

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-3 -2 -1 0 1 2 3

� HERMES - Run III(beyond 2006 ?)

detectorphoton

boardssilicon &

LambdaWheels pumping cross

flange tochamber1mm alu

space forconnectors

magnet

C2 collimator

C2 flangefibers

Future: COMPASS

� The Compass experiment at CERN:

� Successful commissioning in 2001:

– Most detectors commissioned at 2 10� �/s.– Tracking: half of the channels– �LiD target hosted in SMC magnet: P � ����– 2 weeks smooth data taking

� Prospects for 2002:

– Complete tracking and finish commissioning– First measurement of �G�G in 3 month run– Other objectives: �q�x, h��x, �D , spectroscopy

Future: RHIC

� RHIC at BNL as seen by LANDSAT:

� Experimental break-through at RHIC:

Colliding polarized protons atps = 200 GeV

– Pproton = 70� at injection and 25 � at 100 GeV– Luminosity: 1.5 10�� cm��s��

– Physics: transverse spin asymmetries AN

� Longitudinal polarization: spin rotators in 2002

– Measure �G�G from jets, c�c, ...– Measure �qf from W� production

� The PHENIX experiment:

Outlook

� End-station A at SLAC:

– E160: single spin-asymm. for inelastic J��– E161: open charm photoproduction � �G�G

� What to expect in coming years?

– Polarized quark distributions– Polarized gluon distribution

� The big challenges in spin physics:

– The role of orbital angular momentum:

Analysis and interpretation of DVCS � Jq?

– The role of transverse spin:

Measure the (x�Q�)-dependence of h��x

� The more distant future (� 2010):

– Electron-Ion Collider at BNL: 10 250 GeV�

– TESLA-N at DESY: 250 GeV e� on fixed target