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Nucleon Polarized Parton Distribution Functions

Nucleon Polarized Parton Distribution Functions. G. K. Mallot CERN/PH. PANIC 08, 9-14 November 2008, Eilat, Israel. Quarks, Gluons & the Nucleon. Baryons make up all of the visible matter. How are they made up from quarks and gluons ? In QCD many cross-sections factorize in

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Nucleon Polarized Parton Distribution Functions

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  1. Nucleon Polarized Parton Distribution Functions G. K. Mallot CERN/PH PANIC 08, 9-14 November 2008, Eilat, Israel

  2. Quarks, Gluons & theNucleon • Baryons make up all of the visible matter. • How are they made up from quarks and gluons? • In QCD many cross-sectionsfactorize in • calculable hard part and • universal soft part (PDFs) • Experimental findings: • Quarks & gluons share longitudinal momentum 50/50 • Quark spins carry only about 30% of the nucleon spin G.K. Mallot

  3. Spin Structure: a Global Endeavour • polarized DIS (long. double spin asymmetries): • fixed-target (FT) lepton–nucleon scattering • lepton-nucleon collider (HERA unpol., future EIC) • polarized semi-inclusive DIS • polarized pp collisions (RHIC) EMC EMC G.K. Mallot

  4. DIS G.K. Mallot

  5. World Data on xg1 (x,Q2) p d G.K. Mallot

  6. CLAS Proton data • very precise CLAS data (EG1) • mostly resonance region • low Q2, W • used to determine higher twist terms (Leader et al., PRD75, 074027, 2007) from V. Burkhard, arXiv:0711.1703v2 G.K. Mallot

  7. QCD Analysis of data NLO DGLAP: • choose renormalization scheme (MS, AB, jet, …) and Q02 • optionally fix non-singlet moments from hyperon decays • choose PDF parametrizations for non-singlet and singlet quark and for gluon • fit to g1 or A1 data • functional form of PDFs may bias error bands (and more) • NNLO, higher twist, … G.K. Mallot

  8. QCD analysis of pol. DIS data • extra problems in polarized case: • no positivity constraint for PDFs • no momentum sum rule • non-singlet distributions well determined • singlet quark distribution rather well determined • however, anti-quark and strange distributions still have large uncertainties • gluon distribution has stilllarge uncertainties, information only from scaling violations G.K. Mallot

  9. DIS: Unpolarizedvs Polarized F2 (x,Q2) proton g1(x,Q2) Q 2 Q 2 (GeV2) Q 2 (GeV2) G.K. Mallot

  10. QCD analyses • many groups performing World Data fits • AAC06, LSS06,BB02, GRSV01, …; exp: COMPASS06, … • most recent DSSV08, AAC08 • most complete DSSV08 → later AAC06 Singlet gluon note: errors of AAC account for simultaneous deviation of all parameters G.K. Mallot

  11. COMPASS deuteron g1 • about 6 times more precise at low x than SMC • find +ve and –ve ΔG solutions Q2 = 3 GeV2 G.K. Mallot

  12. LSS06 / COMPASS06 ∆G > 0 • Compass and LSS06 find two solutions with small ∆G > 0 and∆G < 0 • LSS06 includes HT and CLAS data • How to tell sign of ∆G? ∆G < 0 G.K. Mallot

  13. Polarized e + N at EIC Range of a Future EIC at BNL G.K. Mallot

  14. (SI)DIS G.K. Mallot

  15. Flavour-tag: Semi-inclusive DIS dh 1 = 0 d z Factorization! G.K. Mallot

  16. Semi-inclusive asymmetries • E.g.: Asymmetries with an additional positive hadron Ah+ (deuteron) G.K. Mallot

  17. Flavour separated PDF xΔu Asymmetries can in LO be related to q by where xΔd xΔu xΔd xΔs G.K. Mallot

  18. Strange quark sea • semi-inclusive data incl. kaon • ΔQ = Δq+Δq • ΔS = 0.037± 0.019 ± 0.027 • range 0.02 < x < 0.6Q2 = 2.5 GeV2 • ΔS < 0 expectedfrom incl. data Q2= 2.5 GeV2 G.K. Mallot

  19. PDF from SIDIS (LO) EMC and DSS FF • Δuv + Δdv,Δu -bar+Δd-bar insensitive to FF • Δu+Δd-bar consistent with 0 • Δs and errors 2-3 times larger with EMC with DSS FF G.K. Mallot

  20. Dependence of Δs on FF • Compass data 0.004 < x < 0.3 from kaon A1 a • first momentΔs =-0.01±0.01±0.01(= Δs ) • 0.004 < x < 0.3,Q2 = 3 GeV2 and DSS 2007 FF G.K. Mallot

  21. pp at RHIC G.K. Mallot

  22. Inclusive π0 Cross-section • Excellent agreement of NLL with data G.K. Mallot

  23. √s=200 and 64.2 GeV 64.3 GeV from: K. Nakano, Spin 2008 200 GeV • big improvement with Run6 • π0 data incompatible with large ΔG • rather strong NLL effect in 64.2 GeV G.K. Mallot

  24. Sensitivity to xg • no xg info on event-by-event basis • √s = 200GeV: 0.02 < xg < 0.3 • √s = 62.4GeV: 0.06 < xg < 0.4 • slightly higher xg, better statistics √s = 200GeV from: K. Nakano, Spin 2008 G.K. Mallot

  25. pp → jet + X • 2005 inclusive data: 2 pb−1, ~50% pol. PRL 100, 232003 (2008) • 2006 di-jet data in progress: G.K. Mallot

  26. Global Analysis DSSV08: De Florian, Sassot, Stratmann, Vogelsang; PRL101 (2008) 072001 DIS SIDIS pp G.K. Mallot

  27. Global Analysis of (SI)DIS and pp • Data: EMC, SLAC-Exxx, SMC, HERMES, COMPASS, Hall-A, CLAS, PHENIX, STAR • NLO/NLL, MS, Q20=1 GeV2, εSU(2,3) fitted • Fragmentation functions from new DSS fit (PRD75 (2007) 114010 ; D76 074033) G.K. Mallot

  28. DSSV08 PDFs G.K. Mallot

  29. DSSV08 & AAC08 gluon PDFs x • DSSV08 AAC08 RHIC M. Hirai, S. Kumano arXiv:0808.0413v1 G.K. Mallot

  30. Comparisonofgluon PDFs G.K. Mallot

  31. Δs x • Δs positive at large x (Hermes SIDIS) • Compass kaon asymm. not yet included • first moment < 0 from DIS • node in strangenessdistribution G.K. Mallot

  32. PDF first moments (DSSV08) EMC (1988): G.K. Mallot

  33. Δg/g from FT hadrons G.K. Mallot

  34. Hadron production in DIS via PGF Principle: Gluon polarization enters via photon-gluon fusion (PGF) q • measure • calculate , and • background by Monte Carlo q G.K. Mallot

  35. Analysed channels analysed data sets: • high-pThadron pairs (no ID, pions/kaons) • Q2 > 1 GeV2 Lepto • Q2 < 1 GeV2 or unmeasured Pythia • high-pTsingle hadron • small Q2 or unmeasured Pythia • single charmed meson • quasi-real photons Aroma, Rapgap All analyses in LO till now (plus parton showers) G.K. Mallot

  36. Δg/g from FT hadrons all Q2 Q2 < 1 GeV2 qg,gg + g q q q,g Photon Gluon Fusion ~ 30% Resolved g ~50% Leading Order QCD Compton use also inclusive ALL G.K. Mallot

  37. Δg/g from open charm • cleanest process • no or little physics background (LO, QCDC) • observe asymmetry in D meson production • statistics limited • only one D meson via D→πK (BR ~ 4%) • combinatorial background large • drastically reduced when looking to D* decay in coincidencewith slow pion G.K. Mallot

  38. Δg/g from FT hadrons (LO) (2000) high-pT data points at different scales ~ 1 – 10 GeV2 single low-pT (2004) charm G.K. Mallot

  39. Summary • All results point to small Δg/g • The strange sea is strange • First global analysis of DIS, SIDIS and pp • Very precise data for hadron production in FT • These data must be included in the gobal analyses • However, the full NLO description needs to be worked out first (in progress) Details during this session and in the plenary talks by D. Haschand W. Vogelsangon Wednesday morning G.K. Mallot

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