and the spin of the nucleon selected highlights
DESCRIPTION
and the Spin of the Nucleon Selected Highlights . K. Rith. FAU Erlangen-Nürnberg. Frascati, 29.05.2007. s z = ½ = J q + J g = ½ + L q + ( G + L g ). Overview. Introduction. HERMES. Determination of . The quark helicity distributions q(x). - PowerPoint PPT PresentationTRANSCRIPT
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and the Spin of the Nucleon Selected Highlights
K. Rith
sz = ½ = Jq + Jg = ½ + Lq + (G + Lg)
Frascati, 29.05.2007
FAU Erlangen-Nürnberg
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IntroductionHERMESDetermination of The quark helicity distributions q(x)The gluon helicity distribution g(x)Transverse spin physics: transversity q(x), Collins FF, Sivers DF
Summary and outlook
Overview
Quark orbital angular momenta Lq
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Introduction and Motivation
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Spin-dependent DIS
Quarks
Nucleon
1/2 ~ q+(x)
Quarks
Nucleon
3/2 ~ q-(x)
Helicity DF: q(x):=q+(x) - q-(x) g1(x) := ½ q zq2
q(x) 1/2 - 3/2
g1
Asymmetry: A1= F1(x) :=
1/2 + 3/2
F1
½ q zq2 q(x)
= E - E‘Q2 = -q2
x = Q2/(2M) = fraction of nucleon‘s momentum carried by struck quark
ucleon
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SU(3): 2 relations a3 = u - d = gA/gV = 1,269 Neutron decay a8 = u + d - 2s = 0,586 , decay a0 = = u + d + s =
+36 1p,(n)(Q2)= [ 3a3+ a8 ] CNS(Q2) + 4 CS(Q2) + 8nf G
CG(Q2)-
1 := g1(x)dx; 9 1p,(n)= 4(1)u +1(4)d
+s1
0
? QCD
Ellis-Jaffe S.R.: s = 0 a8 =
1p =(1/12)[a3 + (5/3)a8] C(Q2) 0,175 (for Q2 10 GeV2)
Bjorken sum rule: 6(1p -1
n) a3 = gA/gV
MS scheme: =0
Integrals and sum rules
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1p =0,126 0,010 0,015
Consequence (1987):u 0,78d -0,47s -0,19
QPM: 4/3-1/3 0
2) =u+d+s = 0,12 0,090,14Contribution of Quark Spins toNucleon-Spin very small
Spin-‘crises‘
1
1) Quark-‘Sea‘ is negatively polarised
The EMC result for g1p(x)
J. Ashman et al., PL B 206 (1988) 364 (1337 Cit.)J. Ashman et al. Nucl. Phys. B 328 (1989) 1 (1160 Cit.)
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HERMES
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HERMES history - I
12/87, 1/88: 2 Letters of intent
12/88: Formation of HERMES1/90: HERMES proposal
10/92: Approval (subject to funding)
(11/91), 5/92: Experimental demonstration of e polarisation6/92: LNF joins HERMES
7/93: Final Approval - Technical Design Report 10/5/95: Start data taking (3:40 hrs) 8/93 – 2/95: Detector construction and installation
Idea: longitudinally polarised e- beam of HERA + internal polarised storage cell atomic gas target
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HERMES history - II
1995-2000: Longitudinal target polarisation (1995: 3He, 1996-97 H, 1998-2000 D) + unpolarised targets (H2, D2, 4He, N2, Kr, Xe)
2006-2007: Recoil detector (H2, D2)– exclusive reactions
2002-2005: Transverse target polarisation (H ) + unpolarised targets
2/7/2007: End of HERA
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Electron beam:E = 27,5 GeV, Ie < 50 mA
HERMES @ HERA
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HERA e+/e- beam of 27.6 GeV
tracking: p/p~2%, <0.6 mrad, 40-220 mrad
kinematics: 0.02<x<0.6, 1.0<Q2<15 GeV2
HERMES spectrometer
Aerogel n=1.03
C4F10 n=1.0014
hadron separation
RICH:
Hadron: ~ 98%, K ~ 88% , P ~ 85%
Polarized internal gas target
PID: Calorimeter, Preshower, TRD, RICH
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The polarised atomic gas target
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Longitudinal target polarisation (1995-2000)
Transverse target polarisation (2002-2005)
Num
ber o
f DIS
eve
nts
x106
Data taking with polarised targets
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Determination of
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The Asymmetry A1 g1/F1P. R. D 75 (2007)
012007
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A1 well known for x 10-3
Excellent agreement between all experiments A1 depends only weakly on Q2
<Q2> = f(x)
Knowledge of A1d substantially
improved by HERMES and COMPASS data
?
A1p(x=1) 1
A1d(x=1) = ?
A1 g1/F1
P. R. D 75 (2007) 012007
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g1
P. R. D 75 (2007) 012007
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Integrals,
x
[Q2>1 GeV2 data only]
Assumption: 1d saturates for x<0.05
a0= (exp) (theory) (evol) = 0,330 ± 0,025 ± 0,011 ± 0,028
MS
ωD=0,05±0.05
1d = 0,042 0,001(stat)
0,003(sys)
QCD QCD
a8=0,586measured
SMC: = 0,12 0,090,14
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Quark helicity distributions q(x)
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q(x) from SIDIS
Leading hadron originates with large probability from struck quark Dq
h(z):= Fragmentation function (FF)z = Eh/
zq2q(x)
Dqh(z)
A1h(x,z) = zq
2 q(x) Dqh(z)
q
q
Measure hadron asymmetries
Targets: H, D ; h = ±, K±, p (identified with RICH)
Measure hadron asymmetries
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PRL 92 (2004) 012005, PRD 71 (2005) 012003
u quarks: large positive polarisation
d quarks: negative polarisationd(x) - 0.4 u(x) (!?)
x
Sea quarks (u, d, s): polarisation compatible with 0.
s < 0 ?
u > d ?
u(x) dx = +0.601 0.063d(x) dx = -0.226 0.063u(x) dx = -0.002 0.043d(x) dx = -0.054 0.035s(x) dx = +0.028 0.034
In measured range (0,023 – 0.6):
Quark helicity distributions
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Gluon helicity distribution g(x)
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])Q,(g)Qq(x,[e21)Qx,( g
2qq
22q
2LO1
2NLO1 CxCegg
q and g from (N)NLO-QCD Fits
uv and dv (rather) well determined g and q very badly determined g 0,5 1,1
Note: From g1d
(0,01<x<1)exp 0,330,03
From NLO fits (0<x<0.01)fit -0,13 0,11
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Method: Photon-Gluon-Fusion
t h/2mq
q
q Charm-production
(Pairs) of hadrons with high transverse momenta
c
cc
J/e+, +
e-, - pt
g
*c
c
c
D
D
*
g
*( )
gh1
h2
(Hard scale: mass of c-Quarks)
(Hard scale: pt )
Direct determination of g/g
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Data: Deuteron target Single hadron with high transverse momentum No scattered electron in acceptanceMC: PYTHIA 6.2 Simulation of total ep cross section Determination of relative contributions R of sub-processes - Vector mesons - anomalous (* qq ) processes - direct photon processes (PGF, QCDC) - LO DIS (* q q ) and their asymmetries
Direct determination of g/g
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Comparison of measured asymmetries with those from MC for:
g/g = 0 (middle curve)(contribution of quarks)g/g = -1 (upper curve)g/g = +1 (lower curve)
Determination of g/g:
Measured asymmetries
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Direct determination of g/g
<2>=1.35 GeV2
x
g/g
HERMES, PRL 84 (2000) 2584
g/g(x,2) = 0.071 ± 0.034(stat) ± 0.010 (sys-exp) (sys-model)
-0.105+0.127
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Transverse spin physics
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The 3 leading twist distribution functionsAll equally important for a complete description of momentum and spin distribution of the nucleon at
leading-twist. Unpolarised
DFHelicity DF Transversity DF
q(x), f1q(x)
q(x), g1q (x)
q(x), h1
q (x)
well known
‚unknown‘
known
HERMES 1995-2000 HERMES 2002-2005
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q(x,Q2)Helicity basis: |+, |-
q(x,Q2)Transverse Spin basis: | , |
q in helicity basis:
|| 2
1 i| ,
q is chiral-oddassociated with helicity flip of struck quark
Hard EM and strong interactions cannot flip the chirality of the probed quark
q is not accessible in inclusive DIS
The transversity distribution
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one hadron in the initial state and at least one in the final state
(semi-inclusive leptoproduction)
Need another chiral-odd object! Semi-Inclusive DIS
How can one measure transversity?How to measure transversity
DF
FFchiral – odd
DFchiral – odd
FFchiral-odd
DFchiral-odd
FF
FF q h
FF
q
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h
h
q q
Chiral – odd & naïve T – odd
produces left-right asymmetry in the direction of the outgoing hadron
The Collins fragmentation function
Collins FF H1(z,kT
2) correlates transverse spin of fragmenting quark and transverse momentum Ph of produced hadron h
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Non-zero Sivers DF requires non-vanishing orbital angular momentum in the nucleon wave function
Chiral – even & naïve T – odd
requires a quark rescattering via soft gluon exchange (gauge link) (Brodsky, Hwang, Schmidt)
The Sivers distribution function f1T
Describes correlation between intrinsic quark pT and transverse nucleon spin f1T
q(pT2) describes probability to find an unpolarised
quark with transverse momentum in a transversely polarised nucleon
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The Sivers effect
Attractive FSI deflects quark inwards
Impact parameter formalism (M. Burkardt hep-ph/030926) Orbital angular momentum of quarks Virtual photon sees different x for different b
Left-right distribution asymmetry is converted into right-left momentum asymmetry
Quark distributions depend on b
anti-green remnant
green quark
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: angle between lepton scattering plane and hadron production planeS: angle between lepton scattering plane and transverse spin component S of target nucleon
Angular distributions in SIDIS
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Azimuthal angular asymmetries in SIDIS
U: unpol. e-beamT: transv. pol. Target
Collins
Sivers
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Extraction of SSA amplitudes
Maximum likelihood fits of SSA amplitudes for pions and charged kaons:
F( 2sin( + S)hUT, 2sin( - S)hUT, 2sin(2 - S)hUT,
2sin(3 - S)hUT, 2sin(S)hUT)
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Collins amplitudes for +/- (2002-05)
Surprisingly large - asymmetry
Non-zero Collins effect
Possible source: large contribution (with opposite sign) from unfavored fragmentation, i.e. u -
H1,disf - H1,fav
Both Collins FF and transversity DF sizeable
also: A. Airapetian et al, P. R. L. 94 (2005) 0120022sin( + S)h
UT ~q(x)H1
q(z)
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also: A. Airapetian et al, P. R. L. 94 (2005) 0120022sin( + S)h
UT ~q(x)H1
q(z)
Collins amplitudes for +/- und K+/-
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Collins amplitudes for +/- und K+/-
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orbital angular momentum Lz
q
But: Contribution of Lzq to
nucleon spin unclear- asymmetry consistent with zero
Sivers amplitudes for +/- (2002-05)
also: A. Airapetian et al, P. R. L. 94 (2005) 012002+ asymmetry significantly different from zero and positiveFirst hint of naive T-odd DF from DIS
FF D1 known Sivers DF can be extracted from HERMES data
2sin(-S)h
UT~f1Tq(x)D1
q(z)
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Sivers amplitudes for +/- and K+/-
also: A. Airapetian et al, P. R. L. 94 (2005) 012002
2sin(-S)h
UT~f1Tq(x)D1
q(z)large!
K+ amplitudes larger than + amplitudes Possibly substantial contribution of sea quarks to Sivers DF
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SSA amplitudes for neutral pions
Isospin symmetry of -mesons is fullfilled within the statistical uncertainties
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Quark orbital angular momentum
Lq
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Q2
t
Final state sensitive to different GPDsVector mesons (, , ) H, EPseudoscalar mesons(,) H, EDVCS () H, E, H, E
Determination of Lq
Jq =1/2 + Lq = lim dx x [H(x,,t) + E(x,,t)] H(x,,t), E(x,,t): Generalised Parton Distributions (GPDs)
Ji sum rule:
Access: exclusive processes
1
1t 0
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e+/- p → e+/- p X<1.7 GeVin HERMES acceptance
Regge, D-term
Regge, no D-term
fac., D-termfac., no D-term
DVCS: Beam charge asymmetry
Determination of Lq
DVCS: Transv. target spin asymmetry (SA)
DVCS: Long. target SA
0: Transv. target SA
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Determination of LqProgram until July 3rd 2007:
Detailed study of exclusive processes with Recoil-Detector:
Q2
t
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Nucleon Spin Structure & HERMES
Unpolarised DISSLAC, BCDMS, NMC,
HERA…g/g = 0.071
±0.035(exp)
Signals for GPDs Ju+Jd
a0=0.330±0.025(exp)
q(x) 0
individualquark helicitydistributions
Lq 0
After Delia Hasch, Spin06, Kyoto
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Further results - Outlook Many more results on various subjects: at present 40 publications with in average 62 citations each hadronisation in nuclei quark hadron duality in A1
p Q2 dependence of GDH-integral SSA for inclusive and exclusive production
DIS on nuclear targets DSA for exclusive VM production Nuclear attenuation of coherent and incoherent ‘s (coherence length, colour transparency) pion multiplicities and fragmentation functions longitudinal and transverse polarisation vector meson production
LNF
HERMES is a big success !!
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M. Anselmino et al., hep-ph/0701006
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M. Anselmino et al., hep-ph/0701006
Transversity DFs Collins FFs
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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
Verschiedene Targets und Hadronen
h: Löse lineares Gl.-System für Q mitA = (A1,p, A1,d, A1,p , A1,d , A1,p K )
A = P Q
P.L. B 464 (1999) 123
In führender Ordnung:
Semi-inklusive Asymmetrien – Proton,3He
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s(x) from Kaon asymmetries
Inputs:Multiplicities for K+ and K- with deuteron targetInclusive deuteron symmetry A1
d
Asymmetries for K+ and K- from deuteron: A1K+ ,
A1K-
0.1 0.5x
xs(
x)/2
0.1
-0.1
-0.05
0
0.05s(x)dx = 0.0060.0290.0070.02
1
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,K, p identifiziert mit RICH Pionen Kaonen
Statistik ausreichend für Fit mit 5-Parametern Q(x) = , , , , , = 0
P.R.L.92 (2004) 012005
u(x) d(x) u(x) d(x) s(x) s(x) u(x) d(x) u(x) d(x) s(x) s(x)
Semi-inklusive Asymmetrien – Deuteron
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0
0.1
0.2
0.3
0.4
0.5
0.001 0.01 0.1 1
-0.2
-0.1
0
0.001 0.01 0.1 1
x
xuv(x)
xdv(x)
Q2 = 1 GeV2
DIS (AAC03)DIS (AAC06)
-0.04
-0.03
-0.02
-0.01
0
0.01
0.001 0.01 0.1 1
x
-1
0
1
2
0.001 0.01 0.1 1
xg(x)
xq(x)
DIS (AAC03)DIS (AAC06)
Typical example: AAC06, hep-ph/0603213
NLO QCD (MS) fitsAssumptions:Helicity distribution of sea quarks flavour symmetricuv and dv constraint by F and D (SU(3) symmetry) Results for Q0
2 = 1 GeV2:
= 0.25 0.10 G = 0.47 1.08
G undetermined by only DISNote: From g1
d (0.01<x<1)exp 0.33 0.03 From NLO fits (0<x<0.01)fit -0.13 0.11
Low-x data urgently needed e-RHIC
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sub-process contributions R
• VMD decreases with pT • DIS increases with pT
• DIS increases with pT (x) - positiv
sub-process asymmetries(with GRSV std.)
Sub-processes
•Signal processes PGF&QCD2->2(g) are about the same size
• |PGF| increases with pT - negativ
• Alle others flat and small, but:• important for background-asymmetry!
• Hard QCD2->2(q) small contrib.
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Collins Asymmetries – D target
auch: V. Yu. Alexakhin et al, PRL 94 (2005) 202002
Hinweis: andere Konvention : Coll = + S -
Collins und Sivers Amplituden verträglich mit Null. Grund: Verteilungen kompensieren sich beim Deuteron ?
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[Efremov et al. hep-ph/0603054]
x-Abhängigkeit: Parameter für Ansatz für Collins FF aus Fit an Hermes Daten
z-Abhängigkeit: Fit an BELLE Daten
Interpretation der Collins Amplituden
q von QSMCollins FF: