POLARISATION IN QCD

- anomalous magn. moment, g-2

- Spin structure of the nucleonq, G, GPD, tq

anomalous magn. moment, g-2

• Test of SM: if exp ≠ theory → new physics

• Calculation of a=(g-2)/2 : - QED (4 loops) - EW (2 loops) - hadronic (main error) • E821 experiment @ BNL: - Pol. from PV decay - Precession a

- PV in decay - decay e in 24 Ecal

µ

t

ne

E821 experiment (final)

• fit N(t) = N0 e-t/

[1+Acos(at + )] • measure <B> with NMR

• a/<B> →

a=(11,659,208±5±3) 10-10

• 15 times better than

earlier exp.hep-ex/0501053

t (s)

Theory vs experiment

QED 11,659,471.94

0.14

Had LO (*)

693.4

6.4

Had LBL 12.0 3.5

Had HO -10.0 0.6

weak 15.4

0.22

Total 11,659,182.7

7.3

exp 11,659,208 6

Exp-the 25.3

9.4

2.7 → new physics ? SUSY, leptoquark, substructure, anomalous W coupling

new proposal E969

- keep main ideas and ring

- 5 times more

- reduced syst.

→ a 2 10-10

improved theory

→ factor 2 in exp-the

(*) Using e+e- data + KLOE (not )

Contributions 1010

The spin structure of the nucleon

• → f1(x)=½∑ eq2q(x)

• → g1(x)=½∑ eq2q(x)

with q(x)=q+(x) -q-(x)

• q=∫q(x)dx

• inclusive Deep Inelastic Scatter. (DIS)

quark contribution q(x)

• EMC (1988): ∫g1(x)dx =½∑eq2q where q=∫q(x)dx

• Hyperon decay + SUf(3) : = 12 ±9 ±14%

60% expected → “spin crisis”

• One of the 6 most cited exp. papers (SPIRES)

• Confirmed by SMC, SLAC and Hermes : = 20 - 30%

• Uncertainty dominated by low x extrapolation

The spin crisis

zLG 2

1

2

1

=u+d+s

g1d(x) at low x

• COMPASS systematically > SMC at low x

• new data : =0.202 +0.042 -0.077 → 0.237 +0.024 -0.029

PLB 612 (2005) 154

final g1 data

Smearing (resolution and radiative corr.) →

correlation between x bins

g1n(x) at high

x• pQCD + no Lz →

u/u= d/d=1 at high x

• Very accurate A1n at high x

A1n > 0 at x > 0.5

• + world A1p → d/d < 0

so Lz not negligible ?

u/u

d/d

PRL 92, 012004 (2004)

Axial anomaly

• EMC : a0= -(3s/2)G

• if G=0 → =0.2• if G2.5 → 0.6

• We must measure G= ∫G(x)dx

gluon contribution G(x)

G(x) with a lepton beam

• Photon Gluon Fusion (PGF) to probe gluons

• Open charm = golden channel

• 2 high pt hadrons: more stat.

but model dependent : BkgGG

PGFPGF AaRA ||

Bkg: QCDC Resolved (Q2<1)

Direct measurent of G(x)

)(0 MeVMMDK

2003• Open charm (2002+2003)

G/G=-1.08 ± 0.76 not enough stat yet

• High pt hadrons

2002+2003 data Q2<1 GeV2

Bkg estimated using Pythia correction for Bkg asym.

G/G=0.024 ±0.089 ±0.057

Curves G=∫G(x)dx = 0.2, 0.6, 2.5

→ either G small or G(x) crosses 0

G(x) with pp collider

• Prompt (golden channel)

• 0 prod : much more stat

G(x) at RHIC

• 0 prod. from run 3 and 4 favors GRSV standard

• Run 5 just finished : FoM=LP4 100 times larger

• Spin program at STAR also

At leading twist 3 pdf for the nucleon

•q(x) : unpolarized

q(x) = q- q = q+- q- : helicity

Tq(x) = q- q: transversity

Transversity Tq(x)

Measure of Tq(x)

• Tq is chiral odd →

not in inclusive DIS

• In Drell-Yan: Tq Tq

• SI DIS : Tq(x) TDqh(z)

Tq(x) in SI DIS

• Collins Fragm. Funct. : hadron azimuthal asym

Collins angle col=h +s –

also Sivers angle siv=h –s

related to transverse kt

• interference FF (2 hadrons): azimuthal angle RS=R +s –

Collins Sivers

Tq(x) through Collins

x z Pt x z Pt

Clear evidence for both Collins and Sivers asymmetries Sivers → non zero Lz

No sizeable effect: cancellation in isoscalar d target ?

3*statistic available on d, 2006 p target

Collins

Sivers

Tq(x) through Collins

Tq(x) through interference

• P target

• Clearly A>0

• No change of sign at mass (≠ Jaffe)

Tq(x) through interference

d target

Asym. vs Minv, x, z consistent with 0

3*statistic expected, 2006 runs on p target (NH3)

1hP

2hP

e+e- CMS frame:

e-

e+

Measurement of TDqh(z)

SI DIS : Tq(x) TDqh(z)

=A +B cos(1+2) TDqh(z1) TDq

h(z2)

Measurement of TDqh(z)

Non zero effect, increasing with z10 times more stat available

Single spin asym. in pp

• Collins and Sivers not distinguishable

A(0) > 0 at xF>0A(0) = 0 at xF<0

STAR

0, h+, h-: A=0 for xF 0

Single spin asym. in pp

xF <0

xF : 0.17 - 0.32

p

Measured asym:

• xF>0, +>0 and -<0

• xF>0, -=0

• p=0

GPD

GeneralizedParton

Distributions

• Deep Virtual Compton Scattering (DVCS)

• H(x,0,t) → 3D view of nucleon (x,d)

related to Lz (Ji sum rule)

GPD definition

)(),,(

)()0,0,(~

)()0,0,(

~,,

~),,,(

tFdxtxH

xqxH

xqxH

EEHtxH

t

GPD measurement

• Interference BH with DVCS

• BH calculable → TDVCS

• Single Spin Asym. (beam)

→ Im H(x,=x,t) sin

• Beam Charge Asym. (e+ versus e-)

→ Re H(x,,t) cos

),,( txHT ixdx

DVCS

DVCS at HERMES

Beam charge asym.

more stat → constrain GPD models

Also single spin asym.

DVCS at Hera

e-bt with b=6 GeV-2

Also gluons GPD :

model: Hq(x,,t)=q(x)e-

bt

t-dependence of measured

Conclusions

• g-2: 2.7 effect = new physics ? new exp and progress in theory → reduce error by

2

• Spin structure of the nucleon is a very active field- more topics, e.g. tensor SF of d- G might be small ? a surprise → indeed 0.2-0.3- transversity : clear signal seen by Hermes Collins fragmentation function nonzero (Belle) - GPD : opening field

• New projets- PAX at GSI pp collider: ideal for transversity in DY- ERHIC ep collider : low x, NLO analysis, G(x), DVCS

Spare slides

Tensor structure fct b1

d

• spin 1: 3 long. pdf: q1↑

q1↓ q0

• b1 2q0 -(q1↑ +q1

↓)

• if p and n at rest b1=0

Exp: b1>0 at low x

Hep-ex/0506018

Intrinsic kT dependence of the quark distribution

Coll10hh sinΦA1NN

CollT1 ADPfA SivT1 ADPfA

Siv10hh sinΦA1NN

qh

qDq

2

qe

qh

qD

0

TΔq

TΔ

2

qe

CollA

qhqDq

2qe

qhqDq

T

0

2qe

SivA

Sivers effects

h

qD

0

TΔ

describes the spin-dependent part of the hadronisation of a transversely polarised quark q into a hadron h

Ssin).

2T

k(x, qT0

)2

Tkq(x,)k(x,

Tq T

Collins effects

G from QCD analysis of g1

• DGLAP equations: ∂q/ ∂ lnQ2 → G

• not enough Q2 range for g1

• AAC analysis Phys.Rev.D69:054021,2004

quark contributions

• Quark model: = 1• Rel. corr. → 75%

• QCD: = u +d +s

• s=0 → 60%

zLG 2

1

2

1

• EMC = 12 ±9 ±14% → “spin crisis”

One of the 6 most cited exp. papers (SPIRES)

• → f1(x)=½∑ eq2q(x)

• → g1(x)=½∑ eq2q(x)

with q(x)=q+(x) -q-(x)

• q=∫q(x)dx

Polarized Deep Inelastic Scatter.

• Q2 =-q2µ probe resolution

• x=Q2/2M(e-e’) quark moment. fraction

• structure function (x,Q2)• scaling: no Q2 dependence (first order)

• EMC measures A1=g1(x)/F1(x)

→ 1 = ∫g1(x)dx =½∑eq2 q

• Hyperon decay + SUf(3) → a3=u-d a8=u+d-2s

• 3 equations and 3 unknowns → and s

• Confirmed by SMC, SLAC and Hermes : = 20 - 30%

• Uncertainty dominated by low x extrapolation

The spin crisis