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Nucleon Polarized Parton Distribution Functions

This paper presents an in-depth analysis of polarized parton distribution functions (PDFs) within nucleons, highlighting their significance in understanding the structure of baryons composed of quarks and gluons. The findings reveal that quarks and gluons equally share longitudinal momentum and that quark spins contribute approximately 30% to the overall nucleon spin. The analysis utilizes experimental data from various sources, including polarized deep inelastic scattering (DIS) and semi-inclusive DIS, to address uncertainties in distributions and develop global analysis frameworks.

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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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