1. 1 DIS - Madrid, April 2009 E.C. Aschenauer The Quest for the spin of the proton ! or “You think you understand something? Now add spin…” - R. Jaffe

2. Nobel Prize, 1943: "for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton"  p = 2.5 nuclear magnetons, ± 10% (1933) Otto Stern Proton spins are used to image the structure and function of the human body using the technique of magnetic resonance imaging. Paul C. Lauterbur Sir Peter Mansfield Nobel Prize, 2003: "for their discoveries concerning magnetic resonance imaging" The Spin of the Proton E.C. Aschenauer 2 DIS - Madrid, April 2009

3. How do the partons contribute 3 DIS - Madrid, April 2009 E.C. Aschenauer qqqqqqqq GGGG LgLgLgLg qLqqLqqLqqLq qqqq qqqqqqqq GGGG LgLgLgLg qLqqLqqLqqLq qqqq Is the proton looking like this? “Helicity sum rule” total u+d+s quark spin angular momentum gluon spin Where do we stand solving the “spin puzzle” ?

4.  q &  G contributions to the proton spin E.C. Aschenauer 4 DIS - Madrid, April 2009 γ*γ*γ*γ* u,d, s,g polarized DIS  q  q,  G γ*γ*γ*γ* u,d,s ,K polarized SIDIS  q f polarized pp scattering  q f,  G u,d,s, g ,K jet Existing data from: to extract polarized  PDFs ! a “global QCD analysis” is required !  all processes tied together: universality of pdfs & Q 2 – evolution  each reaction provides insights into different aspects and kinematics  in NLO DSSV PRL101:072001,2008

5. Inclusive World data 5 DIS - Madrid, April 2009 E.C. Aschenauer new : input to the old GRSV-analysis : input to the DIS & SIDIS – analysis by DNS Inclusive DIS-Data:

6. Semi-Inclusive World Data 6 DIS - Madrid, April 2009 E.C. Aschenauer not in DNS Semi-inclusive DIS-Data:

7. 7 DIS - Madrid, April 2009 E.C. Aschenauer includes all world data from DIS, SIDIS and pp includes all world data from DIS, SIDIS and pp Kretzer FF favor SU(3) symmetric sea, not so for KKP, DSS  ~25-30% in all cases D. De Florian et al. arXiv:0804.0422 NLO @ Q 2 =10 GeV 2 NLO FIT to World Data Kretzer KKP   DIS   SIDIS uvuv uu dvdv dd ss gg                DSSV 

8. Polarized Strangeness 8 DIS - Madrid, April 2009 E.C. Aschenauer Driven by SIDIS K-Asymmetries K-FF dominated by Driven by SU(3); (3F-D) New Results from isoscaler method A K++K- & A incl “Purity” Method using FF Results are completely consistent with Hermes sea quark polarizations ~ 0

9. 9 DIS - Madrid, April 2009 E.C. Aschenauer More on Strangeness PDF Kaon multiplicities from Deuterium target Kaon multiplicities from Deuterium target strange quark sea in proton and neutron identical strange quark sea in proton and neutron identical fragmentation simplifies fragmentation simplifies Only assumptions used: Only assumptions used: isospin symmetry between proton and neutron isospin symmetry between proton and neutron charge-conjugation invariance in fragmentation charge-conjugation invariance in fragmentation Fit x-dependence of multiplicities using PDFs from CTEQ-6 dotted: CTEQ-6L & fit dotted: dashed:dashed: solid:S(x)= Q(x): CTEQ-6L & DSS solid:S(x)= s(x) + sbar(x) dashed-dotted:dashed-dotted:

10. The Gluon Polarization 10 DIS - Madrid, April 2009 E.C. Aschenauer unpolarised cross sections nicely reproduced in NLO pQCD in NLO RHIC: many sub-processes with a dominant gluon contribution high-p T jet, pion, heavy quark, …

11. RHIC Data 11 DIS - Madrid, April 2009 E.C. Aschenauer STAR GRSV curves with cone radius 0.7 and - 0.7 <  < 0.9 2005 jet data: PRL 100, 232003 (2008) 2005: PRD 76, 051106 2006: arXiv:0810.0694  0 @ 200 GeV

12. The Gluon Polarization 12 DIS - Madrid, April 2009 E.C. Aschenauer x RHIC range 0.05 · x · 0.2 small-x 0.001 · x · 0.05 large-x x ¸ 0.2  g(x) very small at medium x best fit has a node at x ~ 0.1 huge uncertainties at small x small-x behavior completely unconstrained  g(x) small !?

13. 13 DIS - Madrid, April 2009 E.C. Aschenauer Compass & Hermes: The golden channels for  g Idea: Direct measurement of  G Isolate the photon gluon fusion process detection of hadronic final states detection of hadronic final states charmed mesons charmed mesons high p T pairs of hadrons high p T pairs of hadrons single high p T hadrons single high p T hadrons h±h±h±h±h±h±h±h± h±h±h±h± less sub-processes contributing less sub-processes contributing more sub-processes contributing  higher statistics higher statistics less sub-processes contributing less sub-processes contributing more sub-processes contributing  higher statistics higher statistics + + +.. Several possible contributions to the measured asymmetry MC needed to determine R and a LL q g q g qg Important at Q2<0.1 h ± h ± vs. h ± : h ± more inclusive → pQCD NLO calculations (easier) possible

14.  g from electro production 14 DIS - Madrid, April 2009 E.C. Aschenauer DSSV gluon agrees well with model-dependent “LO” extractions of  g/g not in global fit [NLO not available] a future global NLO fit will use measured A LL not derived  g/g need first to check unpolarized cross section

15. Beyond form factors and quark distributions 15 DIS - Madrid, April 2009 E.C. Aschenauer Generalized Parton Distributions Proton form factors, transverse charge & current densities Structure functions, quark longitudinal momentum & helicity distributions X. Ji, D. Mueller, A. Radyushkin (1994-1997) Correlated quark momentum and helicity distributions in transverse space - GPDs

16. How to access GPDs? quantum number of final state selects different GPDs:  theoretically very clean H, E, H, E DVCS (  ): H, E, H, E H E  VM (   H E  info on quark flavors H E PS mesons (  : H E~ ~~ ~ ρ0ρ0 2u  d, 9g/4 ω 2u  d, 3g/4  s, g ρ+ρ+ udud J/ψg 00 2  u  d  2  u  d E.C. Aschenauer 16 DIS - Madrid, April 2009

17. W & t dependences: probe transition from soft  hard regime VM production @ small x   J/    ~ W  steep energy dependence of  in presence of the hard scale  ~ e  b|t| universality of b-slope parameter: point-like configurations dominate E.C. Aschenauer 17 DIS - Madrid, April 2009

18. 18 DIS - Madrid, April 2009 E.C. Aschenauer HERMES / JLAB kinematics: BH >> DVCS Deeply Virtual Compton Scattering DVCS two experimentally undistinguishable processes: DVCS Bethe-Heitler (BH) p +  isolate BH-DVCS interference term non-zero azimuthal asymmetries most clean channel for interpretation in terms of GPDs I can measure DVCS – cross section and I

19. 19 DIS - Madrid, April 2009 E.C. Aschenauer HERMES: combined analysis of charge & polarization dependent data  separation of interference term + DVCS 2 DVCS Beam Charge Asymmetry higher twist Beam Spin Asymmetry DVCS

20. DVCS from & 20 DIS - Madrid, April 2009 E.C. Aschenauer Archiv: 0812.2517 only some appetizers on existing data lets see what theory says

21. Hermes BCA CLAS BSA Hall A different GPD parametrisations Results from Theory 21 DIS - Madrid, April 2009 E.C. Aschenauer contribution to nucleon spin m  2 GeV 2 LHPC Collab. hep-lat/0705.4295 Lattice: K. Kumericki & D. Mueller arXiv: 0904.0458 t=0 t=-0.3 First hints for a small J q  L q

22. More insights to the proton - TMDs 22 DIS - Madrid, April 2009 E.C. Aschenauer Unpolarized distribution function q(x), G(x) Helicity distribution function  q(x),  G(x) Transversity distribution function  q(x) Correlation between and Sivers distribution function Boer-Mulders distribution function Explore spin orbit correlations peculiarities of f  1T chiral even naïve T-odd DF related to parton orbital angular momentum violates naïve universality of PDFs QCD-prediction: f  1T,DY = -f  1T,DIS

23. Transverse Polarization Effects @ RHIC 23 DIS - Madrid, April 2009 E.C. Aschenauer Left -Right Naive pQCD (in a collinear picture) predicts A N ~ m q /sqrt(s) ~ 0 However, large A N observed in forward pions / Kaons. Proposed mechanisms - Sivers - Collins - twist-3 process -... need correlations between particles (  jet) to disentangle underlying process

24. Boer-Mulders 24 DIS - Madrid, April 2009 E.C. Aschenauer Unpol. SIDIS cross section: Boer-Mulders x Collins FF  remember Collins FF: Boer-Mulders fct. for u and d quark seem to have same sign consistent with Fermi-lab DY-experiments E605++

25. K + > 0 K - ~ 0 K + > 0 K - ~ 0 K + >  + K + >  + importance of sea quarks? importance of sea quarks? Deuterium ~ 0 Deuterium ~ 0 u and d quark cancel u and d quark cancel 25 DIS - Madrid, April 2009 E.C. Aschenauer HERMES & COMPASS Measurements Proton Proton: Proton: Sivers moment: Sivers moment:  + > 0  - ~ 0 hep-ex/0802.2160 Deuterium Fit M. Anselmino et al. arXiv:0805.2677

26. Sivers function and OAM 26 DIS - Madrid, April 2009 E.C. Aschenauer Anselmino et al. arXiv:0809.2677 Model dependent statement: anomalous magnetic moment:  u = 1.67  d = -2.03 x M. Burkardt et al. Lattice: P. Haegler et al. lowest moment of distribution of unpol. q in transverse pol. proton and of transverse pol. quarks in unpol. proton

27. Conclusions 27 DIS - Madrid, April 2009 E.C. Aschenauer many avenues for further important measurements and theoretical developments we have just explored the tip of the iceberg you are here L q,g ss gg  u tot,  d tot  u,  d spin sum rule Thank you for your attention & to everybody, who helped preparing the talk, especially Werner and Marco

28. 28 DIS - Madrid, April 2009 E.C. Aschenauer BACKUP SLIDES

29. 29 DIS - Madrid, April 2009 E.C. Aschenauer good agreement with NLO-QCD Polarised opposite to proton spin Polarized Quark Densities  u(x) > 0 First complete separation of First complete separation of pol. PDFs without assumption on pol. PDFs without assumption on sea polarization sea polarization Polarised parallel to proton spin  d(x) < 0 ~ 0   u(x),  d(x) ~ 0 No indication for< 0 No indication for  s(x) < 0 In measured range (0.023 – 0.6) In measured range (0.023 – 0.6)

30. DSS: good global fit of all e + e -, ep, and pp hadron data 30 DIS - Madrid, April 2009 E.C. Aschenauer de Florian, Sassot, MS main results: results for  , K ±, chg. hadrons full flavor separation for D i H (z) and D g H uncertainties (L.M.) well under control fits all LEP, HERMES, SMC, RHIC, … data supersede old fits based only on e + e - data

31.  apart from cross-over trajectory (  x ) GPDs not directly accessible: deconvolution needed ! (model dependent) but only  and t accessible experimentally x is mute variable (integrated over): GPD moments cannot be directly revealed, extrapolations t  0 are model dependent e.g. cross sections & beam-charge asymmetry ~ Re(T DVCS ) beam or target-spin asymmetries ~ Im(T DVCS ) accessing GPDs: some caveats t=0 q(x)  =0  q(x) E.C. Aschenauer 31 DIS - Madrid, April 2009

32. detour: DSS kaon FF’s D i K (z) 32 DIS - Madrid, April 2009 E.C. Aschenauer RHIC pp data (BRAHMS, STAR) explain different D g smaller u & larger s-frag. required by SIDIS note: some issues with K - data (slope! ) await eagerly final HERMES data

33. 33 DIS - Madrid, April 2009 E.C. Aschenauer  UT ~ sin  ∙Im{k(H - E) + … }  C ~ cos  ∙Re{ H +  H +… } ~  LU ~ sin  ∙Im{H +  H + kE} ~  UL ~ sin  ∙Im{H +  H + …} ~ polarization observables:  polarization observables:  UT beam target kinematically suppressed H H H, E ~ different charges: e + e - (only @HERA!):  different charges: e + e - (only @HERA!): H DVCS ASYMMETRIES  = x B /(2-x B ),k = t/4M 2

34. 34 DIS - Madrid, April 2009 E.C. Aschenauer [M. Burkardt, M. Diehl 2002] FT (GPD) : momentum space  impact parameter space: probing partons with specified long. momentum @transverse position b T polarized nucleon: [  =0] from lattice What does theory tell d-quark u-quark

35. 35 DIS - Madrid, April 2009 E.C. Aschenauer Hermes: Charge and Beam Spin Asymmetry Heavy Targets Beam Charge Asymmetry Beam Spin Asymmetry Why nuclear DVCS: constrain nuclear GPDs constrain nuclear GPDs constrain models attempting constrain models attempting to describe nuclear matter to describe nuclear matter neutron and proton matter neutron and proton matter distribution in nuclei distribution in nuclei

36. Beam: 27.5 GeV e ± ; % polarization Target: (un)-polarized gas targets; polarization Lumi: pol: 5x10 31 cm -2 /s -1 ; unpol: 3x10 32-33 cm -2 /s -1 Data taking finished June 2007 36 The contemporary experiments E.C. Aschenauer DIS - Madrid, April 2009 SM1 SM2 6 LiD Target 160 GeV μ RICH ECal & HCal μ Filter Trigger-hodoscopes Silicon Micromegas SciFi Gems Drift chambers Straws MWPC 50 m Beam: 160 GeV  : 80% polarization Target: 6 LiD: 50% polarization (2002-2006) NH 3 : 80% polarisation (2007) NH 3 : 80% polarisation (2007) Lumi: 5x10 32 cm -2 s -1 STAR Detector Beams: √s=200 GeV pp; 50% polarization Lumi: 50 pb -1