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

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

Introduction and Motivation

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

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

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.)

HERMES

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

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

Electron beam:E = 27,5 GeV, Ie < 50 mA

HERMES @ HERA

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

The polarised atomic gas target

Longitudinal target polarisation (1995-2000)

Transverse target polarisation (2002-2005)

Num

ber o

f DIS

eve

nts

x106

Data taking with polarised targets

Determination of

The Asymmetry A1 g1/F1P. R. D 75 (2007)

012007

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

g1

P. R. D 75 (2007) 012007

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

Quark helicity distributions q(x)

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

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

Gluon helicity distribution g(x)

])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

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

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

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

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

Transverse spin physics

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

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

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

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

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

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

: 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

Azimuthal angular asymmetries in SIDIS

U: unpol. e-beamT: transv. pol. Target

Collins

Sivers

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)

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)

also: A. Airapetian et al, P. R. L. 94 (2005) 0120022sin( + S)h

UT ~q(x)H1

q(z)

Collins amplitudes for +/- und K+/-

Collins amplitudes for +/- und K+/-

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)

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

SSA amplitudes for neutral pions

Isospin symmetry of -mesons is fullfilled within the statistical uncertainties

Quark orbital angular momentum

Lq

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

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

Determination of LqProgram until July 3rd 2007:

Detailed study of exclusive processes with Recoil-Detector:

Q2

t

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

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 !!

M. Anselmino et al., hep-ph/0701006

M. Anselmino et al., hep-ph/0701006

Transversity DFs Collins FFs

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

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

,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

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

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.

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 ?

[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: