POLARISATION IN QCD -  anomalous magn. moment, g-2 - Spin structure of the nucleon  q,  G, GPD,  t q

 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 BNL: - Pol.  from PV  decay - Precession  a  - PV in  decay - decay e in 24 Ecal µ t nene

E821 experiment (final) fit N(t) = N 0 e -t/   [1+Acos(  a t +  )] measure with NMR  a / → a  =(11,659,208±5±3) times better than earlier exp. hep-ex/ t (  s)

Theory vs experiment QED11,659, Had LO (*) Had LBL Had HO weak Total11,659, exp11,659,2086 Exp-the  2.7  → new physics ? SUSY, leptoquark,  substructure, anomalous W coupling  new proposal E969 - keep main ideas and ring - 5 times more  - reduced syst. →  a    improved theory → factor 2 in exp-the (*) Using e + e - data + KLOE (not  ) Contributions  10 10

The spin structure of the nucleon

 → f 1 (x)=½∑ e q 2 q(x)      → g 1 (x)=½∑ e q 2  q(x) with  q(x)=q + (x) -q - (x)  q=∫  q(x)dx inclusive Deep Inelastic Scatter. (DIS) quark contribution  q(x)

EMC (1988): ∫g 1 (x)dx =½∑e q 2  q where  q=∫  q(x)dx Hyperon  decay + SU f (3) :  = 12 ±9 ±14%  60% expected → “spin crisis” One of the 6 most cited exp. papers (SPIRES) Confirmed by SMC, SLAC and Hermes :  = % Uncertainty dominated by low x extrapolation The spin crisis  =  u+  d+  s

g 1 d (x) at low x COMPASS systematically > SMC at low x new data :  = → PLB 612 (2005) 154

final g 1 data Smearing (resolution and radiative corr.) → correlation between x bins

g 1 n (x) at high x pQCD + no L z →    u/u=  d/d=1 at high x Very accurate A 1 n at high x A 1 n > 0 at x > world A 1 p →  d/d < 0 so L z not negligible ?  u/u  d/d PRL 92, (2004)

Axial anomaly EMC : a 0 =  -(3  s /2  )  G if  G=0 →  =0.2 if  G  2.5 →  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 p t hadrons: more stat. but model dependent : Bkg: QCDC Resolved  (Q 2 <1)

Direct measure nt of  G(x) 2003 Open charm ( )  G/G=-1.08 ± 0.76 not enough stat yet High pt hadrons data Q 2 <1 GeV 2 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=LP 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  T q(x) = q - q  : transversity Transversity  T q(x)

Measure of  T q(x)  T q is chiral odd → not in inclusive DIS In Drell-Yan:  T q  T q SI DIS :  T q(x)   T D q h (z)

 T q(x) in SI DIS Collins Fragm. Funct. : hadron azimuthal asym Collins angle  col =  h +  s –  also Sivers angle  siv =  h –  s related to transverse k t interference FF (2 hadrons): azimuthal angle  RS =  R +  s – 

 T q(x) through Collins xzPtPt xz PtPt Clear evidence for both Collins and Sivers asymmetries Sivers → non zero L z

No sizeable effect: cancellation in isoscalar d target ? 3*statistic available on d, 2006 p target Collins Sivers  T q(x) through Collins

 T q(x) through interference P target Clearly A>0 No change of sign at  mass (≠ Jaffe)

 T q(x) through interference d target Asym. vs M inv, x, z consistent with 0 3*statistic expected, 2006 runs on p target (NH 3 )

       e + e - CMS frame: e-e- e+e+ Measurement of  T D q h (z) SI DIS :  T q(x)   T D q h (z)  =A +B cos(  1 +  2 )  T D q h (z 1 )  T D q h (z 2 )

Measurement of  T D q h (z) Non zero effect, increasing with z 10 times more stat available

Single spin asym. in pp Collins and Sivers not distinguishable A(  0 ) > 0 at x F >0 A(  0 ) = 0 at x F <0 STAR  0, h +, h - : A=0 for x F  0

Single spin asym. in pp x F <0 x F : p Measured asym: x F >0,  + >0 and  - <0 x F >0,  - =0 p=0

GPD Generalized Parton Distributions

Deep Virtual Compton Scattering (DVCS) H(x,0,t) → 3D view of nucleon (x,d  ) related to L z (Ji sum rule) GPD definition t

GPD measurement Interference BH with DVCS BH calculable → T DVCS Single Spin Asym. (beam) → Im H(x,  =x,t) sin  Beam Charge Asym. (e + versus e - ) → Re H(x, ,t) cos 

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: H q (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  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 b 1 d spin 1: 3 long. pdf: q 1 ↑ q 1 ↓ q 0 b 1  2q 0 -(q 1 ↑ +q 1 ↓ ) if p and n at rest b 1 =0 Exp: b 1 >0 at low x Hep-ex/

Intrinsic k T dependence of the quark distribution Sivers effects describes the spin-dependent part of the hadronisation of a transversely polarised quark q into a hadron h Collins effects

 G from QCD analysis of g 1 DGLAP equations: ∂  q/ ∂ lnQ 2 →  G not enough Q 2 range for g 1 AAC analysis Phys.Rev.D69:054021,2004

quark contributions Quark model:  = 1 Rel. corr. →   75% QCD:  =  u +  d +  s  s=0 →   60% EMC  = 12 ±9 ±14% → “spin crisis” One of the 6 most cited exp. papers (SPIRES)

 → f 1 (x)=½∑ e q 2 q(x)      → g 1 (x)=½∑ e q 2  q(x) with  q(x)=q + (x) -q - (x)  q=∫  q(x)dx Polarized Deep Inelastic Scatter. Q 2 =-q 2 µ probe resolution x=Q 2 /2M(e-e’) quark moment. fraction structure function (x,Q 2 ) scaling: no Q 2 dependence (first order)

EMC measures A 1 =g 1 (x)/F 1 (x) →  1 = ∫g 1 (x)dx =½∑e q 2  q Hyperon  decay + SU f (3) → a 3 =  u-  d a 8 =  u+  d-2  s 3 equations and 3 unknowns →  and  s Confirmed by SMC, SLAC and Hermes :  = % Uncertainty dominated by low x extrapolation The spin crisis