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QCD and the Spin Structure of the Nucleons

QCD and the Spin Structure of the Nucleons

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QCD and the Spin Structure of the Nucleons

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  1. QCD and the Spin Structure of the Nucleons Experimental Overview of Nucleon Spin Structure I Gerhard Mallot CERN/PH

  2. Plan • Introduction • DIS and structure functions • Why is ΔΣ so small • Experiments • Inclusive results • Semi-inclusive results • ΔG from photon-gluon fusion • RHIC pp collisions Tübingen, 26 November 2009

  3. Spin Experiments are Puzzling Wolfgang Pauli and Niels Bohr, 1954 wondering about a tippe top toy A theory of the nucleon needs to describe the dynamics of quarks and gluons including spin. Tübingen, 26 November 2009

  4. 1. Introduction Friedman, Kendall, Taylor 1990 Electron scattering at SLAC in the late 1960ies revealed point-like partons in the nucleon → quarks Structure function is Q2 independent (scaling) Tübingen, 26 November 2009

  5. Static Quark model → up and down quarks carry the nucleon spin! Tübingen, 26 November 2009

  6. Baryon weak decays The weak decay constants are linked to quark polarisationsvia the axial vector currents matrix elements, e.g. assuming → up and down quarks carry 58% of the nucleon spin! (deviation from 100% due to relativistic motion) Tübingen, 26 November 2009

  7. Spin puzzle: EMC 1987 20thanniversary (2007) → quark spin contribution to nucleon spin is consistent with zero! Strange quark polarisation negative. Tübingen, 26 November 2009

  8. 2. DIS and structure functions • What did the EMC actually measure? • How severe is the spin puzzle? • Can the Quark Model expectation ΔΣ = 0.6 be restored? Tübingen, 26 November 2009

  9. Deep inelastic scattering • probing partons • inclusive lepton − nucleon scattering • large momentum and energy transfer Q 2 and ν • finite ratio Q 2 / ν • large c.m. energy of the hadronic final state W > 2 GeV Tübingen, 26 November 2009

  10. Deep Inelastic Scattering Bjorken-x: fraction of longitudinal momentum carried by the struck quark in infinite- momentum frame (Breit) Tübingen, 26 November 2009

  11. Kinematics 160 GeV μ beam energy c.m. energy of hadronic final state, W: DIS: Q 2, W2 large, x fix Tübingen, 26 November 2009

  12. Distance scales • longitudial • transverse • for the longitudinal scale is 1 fm • for the transverse scale is 0.2 fm Tübingen, 26 November 2009

  13. DIS cross section spin lepton nucleon cross section: leptonic tensor : kinematics (QED) hadronic tensor : nucleon structure factorise Tübingen, 26 November 2009

  14. Quark−Parton Model unpolarised SF, momentum distributions polarised SF, spin distributions • no Q2 dependence (scaling) • Calan−Gross relation • g2 twist-3 quark−gluon correlations in the QPM: for massless spin-½ partons Tübingen, 26 November 2009

  15. Sum rules for g1 • first moment 1of g1 with Neutron decay a3 = ga Hyperon decay (3F-D)/3 ∆Σ From 1, a3 and a8we obtain∆Σwithout assuming ∆s = 0 Tübingen, 26 November 2009

  16. Sum Rules if wrong  QCD wrong, “worthless equation”, needs neutron measurement Bjorken sum rule PR 148 (1966) 1467 Ellis-Jaffe sum rule PR D9 (1974) 1444 formulated for ∆s=0, unpolarised strange quarks Consequences of violation: EMC 1987 Tübingen, 26 November 2009

  17. 3. Why is ΔΣ so small (1988) PLB 206 (1988) 309 ZPC 41 (1988) 239 PLB 212 (1988) 391 Tübingen, 26 November 2009

  18. Considered Options • Skyrmions: model, all orbital angl. mom. ( BEK) maybe • Bjorken sum rule broken?Measurement wrong? (LA) no! • Large ΔG ~ 2-3-6 at EMC Q2 could mask measurequark spin via axial anomaly (ET, AR) gluon!requires fine tuning of cancelation of ΔG and orbital angular momentum (orb. ang. mom. is generated at gluon emision) Tübingen, 26 November 2009

  19. Lepton-Photon 1989 Need ∆G ≈ 6 at Q2 = 10 GeV2 for ∆Σ = 0.7, to be compared to ½ => measure ∆G G.G. Ross 1989 Tübingen, 26 November 2009

  20. ∆G and ∆Σ in AB/jet scheme αs strong coupling constant Now: Need: Tübingen, 26 November 2009

  21. Where is the proton spin? small unknown Still poorly knowncertainly not 6 Tübingen, 26 November 2009

  22. 4. Experiments (flavours ignored) • Photoabsorption: • only quarks with opposite helicity can absorb the polarised photon via spin-flip • Measure asymmetry need polarised photons & nucleons 1/2 Jz: 3/2 Tübingen, 26 November 2009

  23. unpolarised: longitudinally polarised nucleon: β=0,π transversely polarised nucleon: β=±π/2 Cross Section Asymmetries Measure asymmetries: Tübingen, 26 November 2009

  24. Experimental essentials I • up to now only pol. DIS experiments with fixed-target geometry • need polarised targets and beams • need detection of scattered lepton (or all hadrons), energy, direction, identification • need to know energy and direction of incoming lepton • detection or given by accelerator • measurable asymmetries very small • need excellent control of fake asymmetries, e.g. time variations of detector efficiencies Tübingen, 26 November 2009

  25. Experimental essentials II • Beams & targets: target beam pol • SLAC 48 GeV, solid/gas e, pol. source 0.01 • DESY 28 GeV, gas internal e, Sokolov-Ternov0.02 • CERN 200 GeV, solid μ, pion decay 0.0025 ( RHIC 100/250 GeV pp collider pol. Source - ) • fake asymmetries: • rapid variation of beam polarisation (SLAC) • rapid variation of target polarisation (HERMES) • simultaneous measurement of two oppositely polarised targets (CERN) • bunch trains of different polarisation (RHIC) Tübingen, 26 November 2009

  26. Measurable asymmetries Pb, Ptbeam and target polarisations, ftarget dilution factor = polarisable N/total N note: linear in error: f=1/2 => requires 4 times statistics huge rise of F2 / 2xat small x D depolarisation factor, kinematics, polarisation transfer from polarised lepton to photon, D ≈ y Even bigg1 at small x causes very small asymmetries Tübingen, 26 November 2009

  27. Pol. DIS experiments Spin Crisis /D running Tübingen, 26 November 2009

  28. SLAC E155 Spectrometer beam Tübingen, 26 November 2009

  29. Gas to polarisation measurement Gas inlet 100 mm beam HERMES Target cell beam polarisation built-up by Sokolov-Ternov effect Tübingen, 26 November 2009

  30. HERMES Tübingen, 26 November 2009

  31. and proton (NH3) Tübingen, 26 November 2009

  32. COMPASS Hodoscopes E/HCAL2 E/HCAL1 SM2 RICH1 Muon Wall 2, MWPC SM1 Polarised Target MWPC, Gems, Scifi, W45 (not shown) SPS 160 GeV m beam Muon Wall 1 Straws, Gems Micromegas, SDC, Scifi Scifi, Silicon Tübingen, 26 November 2009

  33. COMPASS Spectrometer Tübingen, 26 November 2009

  34. Polarised target • 6LiD/NH3 • 50/90% polarisation • 50/16% dilution fact. • 2.5 T • 50 mK μ Tübingen, 26 November 2009

  35. Tübingen, 26 November 2009

  36. Target system solenoid 2.5T dipole magnet 0.5T 3He – 4He dilution refrigerator (T~50mK) new magnet acceptance± 180 mrad μ Reconstructed interaction vertices Tübingen, 26 November 2009

  37. RHIC pp Tübingen, 26 November 2009

  38. absolute polarimeter (H jet) pC polarimeters BRAHMS & PP2PP PHOBOS snakes snakes PHENIX STAR spin rotators spin rotators pol. H− source LINAC BOOSTER 5% snake AGS 200 MeV polarimeter pC polarimeter 20 % snake RHIC polarised pp Collider Siberian Snake Tübingen, 26 November 2009

  39. 2.6 m 2.6 m Siberian Snakes (helical dipoles) from Th. Roser AGS partial snakes, 1.5T (RT) & 3T(SC) RHIC full Siberian Snakes: 4 x 4 T (SC), each 2.4 9.6 m w/o: 1000 depolarising resonances Tübingen, 26 November 2009

  40. Phenix Tübingen, 26 November 2009

  41. Tübingen, 26 November 2009

  42. 5. Inclusive Results Unpolarised structure function: Polarised structure function : Experiments often present data as A1: Tübingen, 26 November 2009

  43. Structure function xg1(x,Q2) p d COMPASS deuteron data:a0 = 0.33±0.03±0.05Δs+Δs = −0.08±0.01±0.02 Hermes similar (evol. to Q2=∞) Tübingen, 26 November 2009

  44. F2(x,Q2) g1(x,Q2) p Tübingen, 26 November 2009

  45. Scaling violations • with increasing Q2 more details are resolved • quarks/gluons split and produce more partons • the ‘new’ partons have smaller x-Bjorken • PDFs and SFs became functions of Q2: P(x) → P(x,Q2) • the Q 2 evolution is calculable in perturbativeQCD, if the PDFs P(x,Q20) are known at some Q20 (DGLAP equations) • x dependence is non-perturbative and not described in pQCD • The gluon distribution can be deterimined from these “scaling violations” Tübingen, 26 November 2009

  46. Proton & deuteron g1(x,Q2) d p CLAS HERMES Tübingen, 26 November 2009

  47. QCD Fits Marco Stratmann (tomorrow) Tübingen, 26 November 2009

  48. 6. Semi-inclusive results Factorisation! Tübingen, 26 November 2009

  49. Fragmentation functions final hadron remembers flavour of initially struck quark Integrate over used z region Tübingen, 26 November 2009

  50. Incl. & semi-incl. A1 incl. π+ K+ π– K− proton Tübingen, 26 November 2009