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POLARISATION IN QCD

POLARISATION IN QCD. - m anomalous magn. moment, g-2 - Spin structure of the nucleon D q, D G, GPD, D t q. µ. n e. t. m anomalous magn. moment, g-2. Test of SM : if exp ≠ theory → new physics Calculation of a m =(g m -2)/2 : - QED (4 loops) - EW (2 loops)

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POLARISATION IN QCD

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  1. POLARISATION IN QCD - manomalous magn. moment, g-2 - Spin structure of the nucleon Dq, DG, GPD, Dtq

  2. µ ne t m anomalous magn. moment, g-2 • Test of SM: if exp ≠ theory → new physics • Calculation of am=(gm-2)/2 : - QED (4 loops) - EW (2 loops) - hadronic (main error) • E821 experiment @ BNL: - Pol. m from PV p decay - Precession  am - PV in m decay - decay e in 24 Ecal

  3. E821 experiment (final) • fit N(t) = N0e-t/t  [1+Acos(wat + f)] • measure <B> with NMR • wa/<B> → am=(11,659,208±5±3) 10-10 • 15 times better than earlier exp. hep-ex/0501053 t (ms)

  4. Theory vs experiment Contributions 1010 • 2.7 s→new physics ? SUSY, leptoquark, m substructure, anomalous W coupling • new proposal E969 - keep main ideas and ring - 5 times more m - reduced syst. → dam 2 10-10 • improved theory → factor 2 in exp-the (*) Using e+e- data + KLOE (not t)

  5. The spin structure of the nucleon

  6. quark contribution Dq(x) • inclusive Deep Inelastic Scatter. (DIS) • s → f1(x)=½∑ eq2q(x) • Ds = s -s→g1(x)=½∑ eq2Dq(x) with Dq(x)=q+(x) -q-(x) • Dq=∫Dq(x)dx

  7. The spin crisis • EMC (1988): ∫g1(x)dx =½∑eq2Dq where Dq=∫Dq(x)dx • Hyperon b decay + SUf(3) : DS = 12 ±9 ±14%  60% expected → “spin crisis” • One of the 6 most cited exp. papers (SPIRES) • Confirmed by SMC, SLAC and Hermes : DS= 20 - 30% • Uncertainty dominated by low x extrapolation DS=Du+Dd+Ds

  8. g1d(x) at low x PLB 612 (2005) 154 • COMPASS systematically > SMC at low x • new data : DS =0.202 +0.042 -0.077→ 0.237 +0.024 -0.029

  9. final g1 data Smearing (resolution and radiative corr.) → correlation between x bins

  10. g1n(x) at high x • pQCD + no Lz→ A1=Du/u= Dd/d=1 at high x • Very accurate A1n at high x A1n > 0 at x > 0.5 • + world A1p →Dd/d < 0 so Lz not negligible ? Du/u Dd/d PRL 92, 012004 (2004)

  11. Axial anomaly • EMC : a0=DS -(3as/2p)DG • if DG=0 →DS=0.2 • if DG2.5 →DS0.6 • We must measure DG= ∫DG(x)dx

  12. gluon contribution DG(x)

  13. DG(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 : Bkg: QCDC Resolved g (Q2<1)

  14. Direct measurent of DG(x) 2003 • Open charm (2002+2003) DG/G=-1.08 ± 0.76 not enough stat yet • High pt hadrons 2002+2003 data Q2<1 GeV2 Bkg estimated using Pythia correction forBkg asym. DG/G=0.024 ±0.089 ±0.057 Curves DG=∫DG(x)dx = 0.2, 0.6, 2.5 → either DG small or DG(x) crosses 0

  15. DG(x) with pp collider • Prompt g (golden channel) • p0 prod : much more stat

  16. p0 prod. from run 3 and 4 favors GRSV standard Run 5 just finished : FoM=LP4 100 times larger Spin program at STAR also DG(x) at RHIC

  17. Transversity DTq(x) At leading twist 3 pdf for the nucleon • q(x):unpolarized • q(x)= q- q = q+- q- :helicity • Tq(x)= q- q:transversity

  18. DTq is chiral odd → not in inclusive DIS In Drell-Yan: DTq DTq SI DIS : DTq(x) DTDqh(z) Measure of DTq(x)

  19. DTq(x) in SI DIS • Collins Fragm. Funct. : hadronazimuthal asym Collins angle fcol=fh +fs –p also Sivers angle fsiv=fh –fs related to transverse kt • interference FF(2 hadrons): azimuthal angle fRS=fR +fs –p

  20. DTq(x) through Collins x z Pt Pt x z Clear evidence for both Collins and Sivers asymmetries Sivers → non zero Lz

  21. Collins Sivers DTq(x) through Collins • No sizeable effect: cancellation in isoscalar d target ? • 3*statistic available on d, 2006 p target

  22. DTq(x) through interference • P target • Clearly A>0 • No change of sign • at r mass (≠ Jaffe)

  23. DTq(x) through interference d target Asym. vs Minv, x, z consistent with 0 • 3*statistic expected, 2006 runs on p target (NH3)

  24. e+e- CMS frame: j2-p e- Q j1 e+ Measurement of DTDqh(z) SI DIS : DTq(x) DTDqh(z) j1 j2 s =A +B cos(f1+f2) DTDqh(z1) DTDqh(z2)

  25. Measurement of DTDqh(z) Non zero effect, increasing with z 10 times more stat available

  26. Single spin asym. in pp • Collins and Sivers not distinguishable STAR A(p0) > 0 at xF>0 A(p0) = 0 at xF<0 p0, h+, h-: A=0 for xF 0

  27. p Single spin asym. in pp • Measured asym: • xF>0, p+>0 and p-<0 • xF>0, p-=0 • p=0 xF : 0.17 - 0.32 xF <0

  28. GPD Generalized Parton Distributions

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

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

  31. DVCS at HERMES Beam charge asym. Also single spin asym. more stat → constrain GPD models

  32. DVCS at Hera Also gluons GPD : t-dependence of s measured e-bt with b=6 GeV-2 model: Hq(x,x,t)=q(x)e-bt

  33. Conclusions • g-2: 2.7 s 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 - DG might be small ? a surprise → indeedDS =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, DG(x), DVCS

  34. Spare slides

  35. Tensor structure fct b1d • 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

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

  37. DG from QCD analysis of g1 • DGLAP equations: ∂Dq/ ∂ lnQ2 → DG • not enough Q2 range for g1 • AAC analysis Phys.Rev.D69:054021,2004

  38. Quark model: DS = 1 Rel. corr. → DS 75% QCD: DS = Du +Dd +Ds Ds=0 → DS 60% quark contributions • EMC DS = 12 ±9 ±14%→ “spin crisis” One of the 6 most cited exp. papers (SPIRES)

  39. 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) • s → f1(x)=½∑ eq2q(x) • Ds = s -s→g1(x)=½∑ eq2Dq(x) with Dq(x)=q+(x) -q-(x) • Dq=∫Dq(x)dx

  40. The spin crisis • EMC measures A1=g1(x)/F1(x) →G1 = ∫g1(x)dx =½∑eq2Dq • Hyperon b decay + SUf(3) → a3=Du-Dd a8=Du+Dd-2Ds • 3 equations and 3 unknowns → DS and Ds • Confirmed by SMC, SLAC and Hermes : DS= 20 - 30% • Uncertainty dominated by low x extrapolation

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