review of polarized lepton-nucleon scattering s z = = j q + j g = + l q + g + l g k. rith,...
DESCRIPTION
SU(3): 2 relations q 3 = u - d = g A /g V = F + D = 1,2573 Neutron-decay q 8 = u + d - 2 s = 3F - D = 0,579 , -decay q 0 = = u + d + s = + 9 I 1 p,(n) (Q 2 )= [ q 3 + q 8 ] C NS (Q 2 ) + C S (Q 2 ) + 2n f G C G (Q 2 ) - Integrals and Sum Rules I 1 := g 1 (x)dx; 18 I 1 p,(n) = 4(1) u +1(4) d + s ? QCDQCD Axial Anomaly Ellis-Jaffe S.R.: s = 0 q 8 = I 1 p =(1/12)[ q 3 + (5/3) q 8 ] C(Q 2 ) 0,175 (at Q 2 10 GeV 2 ) Bjorken Sum Rule: 6(I 1 p - I 1 n ) q 3 = g A /g VTRANSCRIPT
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
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