Kein Folientitel

1
Review of Polarized lepton-nucleon scattering
K. Rith, HERA-III, München, 18.12.2002
sz ? Jq Jg ??? Lq ?G Lg
2
Spin-dependent Deep-Inelastic Lepton-Nucleon
Scattering
Nucleon
Nucleon
?
?
?
?
Quarks
Quarks
?1/2 q
?
?
?3/2 q-
Polarised ?qf(x)qf(x) - qf-(x) ?qf
?qf(x) dx
?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)
3
Integrals and Sum Rules
? I1 g1(x)dx ? 18 I1p,(n) 4(1)?u
1(4)?d ?s
SU(3) 2 relations ? ?q3 ?u - ?d gA/gV
F D 1,2573 Neutron-decay ? ?q8 ?u
?d - 2?s 3F - D 0,579
?,?-decay ? ?q0 ?? ?u ?d ?s
?
QCD

9 I1p,(n)(Q2) ? ?q3? ?q8 ? CNS(Q2) ?? ?
CS(Q2) 2nf ?G ? CG(Q2)
-
Axial Anomaly
? Bjorken Sum Rule 6(I1p -I1n) ? ?q3
gA/gV
? Ellis-Jaffe S.R. ?s 0 ? ?q8
?? I1p (1/12)?q3 (5/3)?q8 ? C(Q2) ?
0,175 (at Q2 ? 10 GeV2)
4
A1 ? g1/F1 - Proton
? g1p/F1p well known for x ? 10-3 ? Excellent
agreement between all
experiments ? g1p/F1p (within errors)
independent of Q2 Q2 dependence of g1 and
F1 very similar ? ltQ2gt f(x) ? Extrapolation
to x ? 0 for Q2 Q02 ?
5
g1(x)/F1(x) - Deuteron
?
6
g1(x) - Proton, Deuteron
7
A1(x), g1(x) - Neutron from 3He
?
3He
p
p
n
3He good approximation for polarized n-Target,
0
QPM 18 g1n(x) ?u(x) 4?d(x)
lt 0 Expt.
??d(x) lt 0, ??d(x)? gt ???u(x)
8
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 ?..
?
Gluons ?G Rest? Orbital
angular momenta Lq,g
9
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)
10
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 ...1.26
BB Blümlein, Böttcher hep/ph 0203155 LSS Leader
et al., hep/ph 0111267 GRSV Glück et al., hep/ph
0011215 AAC Goto et. Al., hep/ph 0001046
11
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
xng2(x)dx ? n/(n1) (-an dn)
xng1(x)dx ? an
? Further improvement by HERMES and COMPASS
very unlikely
12
AT, b1 and b2 - deuteron
? Deuteron is spin-1 target V Pz p - p- ,
?Pz ? ?1 T Pzz p p- - 2p0 , -2 ? Pz z ?
1 ? More structure functions
?meas ?u 1 PbVA?? ? T AT A?? ? g1/F1
1 ? T AT AT ? ? b1/F1
Proton Deuteron F1 ??
zq2 q q- ? ? zq2 q q- q0 F2
2xF1 2xF1 g1 ?? zq2 q -
q- ?? zq2 q - q- b1
?? zq2 2q0 - (q q-) b2
2xb1
13
The HERMES polarised internal gas target
14
AT, b1 and b2 - deuteron
? First measurement, only possible with atomic
gas target
Model K. Bora, R.L. Jaffe, PRD 57 (1998) 6906
15
AT, b1 and b2 - deuteron
? Deuteron is spin-1 target ? AT ? 10-2
little impact on det. of g1 ? b1d 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 -
-
16
Spin-dependent quark distributions
from semi-inclusive asymmetries
? E - E z Eh/?
Leading hadron originates with large probability
from struck quark D(z) Fragmentation function
17
Semi-inclusive asymmetries-1
In leading order
P.L. B464 (1999) 123
zq2?q(x) Dqh(z) A1h(x,z)
zq2q(x) Dqh(z)

zq2q(x) Dqh(z) ?q(x)
zq2q(x)
Dqh(z) q(x)
Quark-Purity Phq
Different targets and hadrons h Solve linear
system for Q with A (A1,p, A1,d, A1,p ??, A1,d
??, A1,p K? ) A P Q
18
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) )
19
Purities
(Probability that observed hadron originates from
quark of type f)
? 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
20
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 !
21
Extracted spin-dependent quark distributions
?u gt ?d ?
?The HERMES data are consistent with
flavour symmetry of spin-dependent sea ? Data
with much higher statistical accuracy
urgently needed
?s lt 0 ?
22
Prospects for spin-dependent quark distributions
? COMPASS data will extend to lower x-values
? Need high statistics data from both LiD
and NH3
23
The gluon polarisation ?G/G
Method Photon-Gluon-Fusion
q q
?t ? h/2mq
? Charm-production
(Hard scale mass of c-quark)
e, ?
e-, ?-
D
J/?
?
?
c
pt
c
c
c
c
g
g
c
D
? Pairs of hadrons hh- with high transverse
momenta
(Hard scale pt )
h2
?
g
( )
h1
24
Gluon polarisation ?G/G
3 main contributions to ?p ? hh- X
h2
?
q
h2
h2
?
?
q
?
?
q
V
q
?
g
?
p
?
q
g
q
h1
?
h1
QCDC
VMD
PGF
h1
AVDM ? 0.5 ?q/q
AVDM 0
APGF ? -?G/G
Relative contributions Monte Carlo simulation -
PYTHIA but applicable at HERMES energies?
?
25
Gluon polarisation ?G/G
P.R.L. 84 (2000) 2584
2006
?
ltxgt 0.17
Asymmetry is negative From this ?G/G 0.41 ?
0.18? 0.08
(?G/G) G(x) dx ? 0,6 ?.....
COMPASS RHIC
small,
26
Gluon polarisation ?G/G
COMPASS ?N ? D0 X (? hh- X)
?A 0.04 SLAC-E161 ? p ? D X
?Acc 0.006
27
Orbital angular momentum contributions Lq,g to
nucleon spin ?
? ??? Lzq ?G Lzg
0,10 gt 0,6
?
No one knows how to measure it (R. Jaffe) one
hope Exclusive processes,
Generalised parton distributions (GPDs)
X.Ji Jq ??? Lzq lim ? dx x H(x,?,t)
E(x,?,t)
t ? 0
?
?
?
?, K, ?
?,?, ?
?
?
?
?
p
p
p
p
DVCS
28
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
29
DVCS
Expected accuracies for 2 years of data taking
HERMES Recoil-Detector
30
Transverse quark polarisation , Transversity h1
Complete description of nucleon in leading order
QCD 3 distribution functions
?
f1 Quark
momenta, ? q?? q
?
?
g1 - longitudinal
quark spin, ??, ? q? ? ? 5q
?
h1 - transverse
quark spin, ??, ? q??? ?5 q
?
h1 is chiral odd, can only be measured in
conjunction with other chiral odd distribution
(pol. Drell-Yan) or fragmentation function (SIDIS)
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 ?? lt ?? lt 1 ? Lattice QCD ??
0,18(10) and ?? 0,56(9)
31
Transverse quark polarisation , Transversity h1
P.R. D64 (2001) 097101
32
Transversity h1 - Model calculations
AULsin? ? SL(M/Q) ?za2 x hLa(x) H1?a(z) - x
h1L?a(x) Ha(z)/z .... - ST ? za2 x h1a(x)
H1?a(z) SL gtgt ST
Collins fragmentation function
?0.33 z
Example ? Quark Soliton Model Efremov et al.,
Eur. Phys. J. C24 (2002) 407
Need measurements with transverse target
polarisation
33
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 indistinguishable Transv
ersely polarised target Collins andSivers
distinguishable
Targetspin
Hadron
ltsin(?lh - ?ls)gt moment ltsin(?lh ?ls)gt moment
?lh
Lepton

?ls
34
Prospects for h1 measurements, HERMES COMPASS
HERMES Expected accuray for 2 years of data
taking with transversely polarised proton
target
V.A. Korotkov et al., Eur. Phys. J. C18 (01) 639
Deuteron (LiD)
COMPASS Projection for 12 days LiD , (h1
g1) SMC magnet L 4.3 1037 cm-2 per day E?
160 GeV
x ?ea2 h1a (x)
x
35
Prospects
HERMES (2002-2006) Transversaly polarised target
- h1, g2
unpolarised high density target DVCS -
Lq COMPASS (2002 - ? ) Full polarisation
program, especially ?G RHIC (2002 - ?) p p ?
W?X, 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