Review of Polarized lepton-nucleon scattering

sz = = Jq + Jg = + Lq + G + Lg

K. Rith, HERA-III, München, 18.12.2002

Spin-dependent Deep-Inelastic Lepton-Nucleon Scattering

Quarks

Nucleon

1/2 ~ q+

Quarks

Nucleon

3/2 ~ q-

Polarised: qf(x):=qf+(x) - qf

-(x) qf = qf(x) dx1

0 1/2 - 3/2

g1

Asymmetry: A1= g1(x) := f zf2 qf(x)

1/2 + 3/2

F1

Unpolarised: qf(x):=qf+(x) + qf

-(x) F1(x) :=

f zf2 qf(x)

SU(3): 2 relations q3 = u - d = gA/gV = F + D = 1,2573 Neutron-decay q8 = u + d - 2s = 3F - D = 0,579 ,-decay q0 = = u + d + s =

+9 I1p,(n)(Q2)= [ q3+ q8 ] CNS(Q2) + CS(Q2) + 2nf G CG(Q2)

-

Integrals and Sum Rules

I1 := g1(x)dx; 18 I1p,(n)= 4(1)u +1(4)d +s1

0

? QCD

Axial Anomaly

Ellis-Jaffe S.R.: s = 0 q8 =

I1p =(1/12)[q3 + (5/3)q8] C(Q2) 0,175 (at Q2 10 GeV2)

Bjorken Sum Rule: 6(I1p -I1n) q3 = gA/gV

A1 g1/F1 - Proton

g1p/F1

p well known for x 10-3

Excellent agreement between all experiments g1

p/F1p (within errors)

independent of Q2; Q2 dependence of g1 and F1 very similar <Q2> = f(x) Extrapolation to x 0 for

Q2 = Q02 ?

g1(x)/F1(x) - Deuteron

g1(x) - Proton, Deuteron

A1(x), g1(x) - Neutron from 3He

3He: good approximation for polarized n-Target, = 0 QPM18 g1

n(x) ~ u(x) +4d(x) < 0 Expt.

d(x) < 0, d(x) > u(x)

p p

n

3He

Gluons GRest? Orbital angular momenta Lq,g

xg1(x) - world data

Integrals at Q02 = 2,5 GeV2,

QCD analysis of Q2 dependence and SU(3):

=u+d+s 0,20 0,04 ..

?

?

Q2- dependence of g1 (x,Q2)

Q2- dependence in agreement with NLO QCD parameterisation Data still insufficient for reliable QCD analysis and determination of spin-dependent gluon distribution G(x)

NLO QCD (MS) fit Assumptions:- Flavour symmetric spin dependent sea- uv and dv constraint by F and D(SU(3) symmetry)

Results for Q02 = 4 GeV2:

uv 0.73 .....0.86 (0.10) dv -0.40...-0.46 (0.10) qs -0.04 ...-0.09

0.14 ...0.20 G 0.68 ...1.26BB: Blümlein, Böttcher hep/ph 0203155LSS: Leader et al., hep/ph 0111267GRSV: Glück et al., hep/ph 0011215AAC: Goto et. Al., hep/ph 0001046

g2(x)

g2(x,Q2) = - g1(x,Q2) + g1(z,Q2) dz/z + g2(x,Q2) = g2WW(x,Q2) +

g2(x,Q2) ~ ~

Quark-Gluon Correlation (Twist-3 Operator)E155x, hep-ex/0204028

Further improvement by HERMES and COMPASS very unlikely

xng2(x)dx = n/(n+1) (-an +dn)

xng1(x)dx = an

1

x

1

0 1

0

1

0

AT, b1 and b2 - deuteron

Deuteron is spin-1 targetV = Pz = p+ - p- , Pz 1T = Pzz = p+ + p- - 2p0 , -2 Pz z +1

More structure functions Proton DeuteronF1 zq

2 [q+ + q-] zq2 [q+ + q- +

q0]F2 2xF1 2xF1

g1 zq2 [q+ - q-] zq

2 [q+ - q-]

b1 zq2 [2q0 - (q+ + q-)]

b2 2xb1

meas = u [1 + PbVA + T AT ]

A g1/F1 [ 1 + T AT ]

AT b1/F1

The HERMES polarised internal gas target

AT, b1 and b2 - deuteron

First measurement, only possible with atomic gas target

Model: K. Bora, R.L. Jaffe, PRD 57 (1998) 6906

AT, b1 and b2 - deuteron

Deuteron is spin-1 target AT 10-2

little impact on det. of g1 b1

d is sizeable ! and interesting by itself

related to - nuclear binding - D-state admixture - diffractive nuclear shadowing - nuclear excess pions in D - VMD + double scattering - - -

See e.g.:- P. Hoodboy et al., N.P. B312 (89) 571- R.L. Jaffe & A. Manohar N.P. B321 (89) 343- X. Artru & M. Mekhfi, Z. Phys. C45 (90) 669- N.N. Nikolaec & W. Schäfer, P.L. B398 (97) 245- J. Edelmann et al., Z. Phys. A357 (97) 129, P.R. C57 (98) 3392- K. Bora & R.L. Jaffe, P.R. D57 (98) 6906- -

Spin-dependent quark distributions fromsemi-inclusive asymmetries

Leading hadron originates with large probability from struck quark

D(z):= Fragmentation function

= E - E‘z = Eh/

Semi-inclusive asymmetries-1

zq2q(x) Dq

h(z)A1

h(x,z) = zq2q(x) Dq

h(z)

q

q zq

2q(x) Dqh(z)

q(x)

=

zq‘2q‘(x) Dq‘

h(z) q(x) q 'q

Quark-‘Purity‘ Phq

Different targets and hadrons h: Solve linear system for Q withA = (A1,p, A1,d, A1,p , A1,d , A1,p K )

A = P Q

P.L. B464 (1999) 123

In leading order:

Semi-inclusive asymmetries from Deuteron

,K, p asymmetries identified with RICH

Hadrons Pions Kaons

Statistics sufficient for 5-parameter-fit

Q = (u(x)/u(x), d(x)/d(x), u(x)/u(x), d(x)/d(x), s(x)/s(x) )

Purities

Shaded bands: systematic uncertainties Adequate degree of orthogonality: - u versus d from h+

- valence versus sea from hadron charge - u versus d from h-

Kaons have about 10% sensitivity

to the strange sea

(Probability that observed hadron originates from quark of type f)

Extracted quark-polarisations

Polarisation of sea-quarks small and compatible with 0

No direct evidence for a negative polarisation of strange- quarks

Results for NLO analysis very similar !

Extracted spin-dependent quark distributions

u > d ?

s < 0 ?

The HERMES data are consistent with flavour symmetry of spin-dependent sea Data with much higher statistical accuracy urgently needed

Prospects for spin-dependent quark distributions

COMPASS data will extend to lower x-values Need high statistics data from both LiD and NH3

The gluon polarisation G/GMethod: Photon-Gluon-Fusion

t h/2mq

q

q Charm-production

Pairs of hadrons h+h- with high transverse momenta

c

cc

J/e+, +

e-, - pt

g

*c

c

c

D

D

*

g

*( )

gh1

h2

(Hard scale: mass of c-quark)

(Hard scale: pt )

Gluon polarisation G/G3 main contributions to *p h+h- X :

pq

qq

q qq

V

h2

h1h1

h1

h2

h2

* **

gg

QCDC VMD PGFAVDM 0.5 q/q AVDM = 0

APGF -G/G

?Relative contributions:Monte Carlo simulation - PYTHIA

but: applicable at HERMES energies?

Gluon polarisation G/G

Asymmetry is negativeFrom this: G/G = 0.41 0.18 0.08

(G/G) G(x) dx 0,6 .....28.0

06.0

1

28.0...... small,

06.0

0..... COMPASS

RHIC

<x> = 0.17

2006

P.R.L. 84 (2000) 2584

Gluon polarisation G/G

COMPASS : N D0 X ( h+h- X) A 0.04

SLAC-E161: p D X Acc 0.006

Orbital angular momentum contributions Lq,g to nucleon spin ?

= + Lzq + G + Lz

g

0,10 > 0,6

‘No one knows how to measure it‘ (R. Jaffe)one hope: Exclusive processes, Generalised parton distributions (GPDs)

p pp p

?

* *

DVCS

, K, ,,

X.Ji: Jq = + Lzq = lim dx x [H(x,,t) + E(x,,t)]

t 0 1

1

Orbital angular momentum contributions Lq,g ?Example: DVCS (Interference of DVCS and Bethe-Heitler)Azimuthal asymmetries: beam polarisation, beam charge, target polarisation

P.R.L. 87 (2001) 182001 P.R.L. 87 (2001) 182002

Hermes CLAS

DVCS

HERMES Recoil-DetectorExpected accuracies for 2 years of data taking

g1 = - longitudinal quark spin, , q 5q

Transverse quark polarisation , ‘Transversity‘ h1Complete description of nucleon in leading order QCD: 3 distribution functionsf1 = Quark momenta, q q

h1 = - transverse quark spin, , q 5 q

Importance of h1 measurement: coupling to gluons smaller than in longitudinal case

Q2 evolution is weaker QCD test Redistribution of ang. moment. between quarks and gluons is smaller: < < 1 Lattice QCD: = 0,18(10) and = 0,56(9)

h1 is chiral odd, can only be measured in conjunction with other chiral odd distribution (pol. Drell-Yan) or fragmentation function (SIDIS)

P.R. D64 (2001) 097101

Transverse quark polarisation , ‘Transversity‘ h1

‘Transversity‘ h1 - Model calculationsAUL

sin SL(M/Q) za2 x [hL

a(x) H1a(z) - x h1L

a(x) Ha(z)/z + ....] - ST za2 x h1

a(x) H1a(z)

SL >> ST Collins fragmentation function0.33 z

Example: Quark Soliton ModelEfremov et al., Eur. Phys. J. C24 (2002) 407

Need measurements with transverse target polarisation

Azimuthal asymmetries: Collins vs Sivers effect

2 different possible sources for azimuthal asymmetry: product of chiral-odd transversity distribution h1(x) and chiral-odd fragmentation function H1

(z) (Collins) product of T-odd distribution function f1T

and familiar unpolarised fragmentation function D1(z) (Sivers)

Longitudinally polarised target: Collins and Sivers effect indistinguishableTransversely polarised target: Collins andSivers distinguishableLepton

TargetspinHadron

ls

lh

<sin(lh - l

s)> moment; <sin(lh + l

s)> moment

Prospects for h1 measurements, HERMES & COMPASS

Deuteron (LiD) COMPASS: Projectionfor 12 days LiD , (h1 = g1)SMC magnet L = 4.3 1037 cm-2 per dayE = 160 GeVx

x ea2 h1

a (x)

HERMES: Expected accurayfor 2 years of data taking withtransversely polarised proton target

V.A. Korotkov et al., Eur. Phys. J. C18 (01) 639

ProspectsHERMES (2002-2006): Transversaly polarised target - h1, g2

unpolarised high density target: DVCS - Lq

COMPASS (2002 - ? ): Full polarisation program, especially G

RHIC (2002 - ?) [p p WX, jets]: u(x), d(x), u(x), d(x), G

SLAC-E161 (2003 - ?) [ p D X]: G Detailed investigation of h1 and GPDs via exclusive processes requires a new generation of polarised lepton nucleon scattering experiments with high luminosity and high resolution like ELFE, TESLA-N, EVELIN, JLAB-12GeV