2. E.C. Aschenauer RHIC-AGS Users Metting, June 2010 1

3. How do the partons form the spin of protons E.C. Aschenauer RHIC-AGS Users Metting, June 2010 2 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” in IMF total u+d+s quark spin angular momentum gluon spin Where do we stand solving the “spin puzzle” ?

4. Kretzer KKP   DIS   SIDIS uvuv uu dvdv dd ss gg                DSSV     What do we know: NLO Fit to World Data E.C. Aschenauer RHIC-AGS Users Metting, June 2010 3  includes all world data from DIS, SIDIS and pp Kretzer FF favor SU(3) symmetric sea, not so for KKP, DSS  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 But how do we access L q and L g in the IMF ???

5. Beyond form factors and quark distributions 4 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 E.C. Aschenauer RHIC-AGS Users Metting, June 2010

6. The Hunt for Lq 5E.C. Aschenauer RHIC-AGS Users Metting, June 2010 Study of hard exclusive processes allows to access a new class of PDFs Generalized Parton Distributions possible way to access orbital angular momentum exclusive: all reaction products are detected missing energy (  E) and missing energy (  E) and missing Mass (M x ) = 0 missing Mass (M x ) = 0 DIS: ~0.3 Spin Sum Rule in PRF:

7. GPDs Introduction E.C. Aschenauer RHIC-AGS Users Metting, June 2010 6 How are GPDs characterized? unpolarized polarized conserve nucleon helicity flip nucleon helicity not accessible in DIS DVCSDVCSDVCSDVCS quantum numbers of final state select different GPD pseudo-scaler mesons vector mesons 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  Q 2 = 2E e E e ’(1-cos  e’ )  x B = Q 2 /2M  =E e -E e’  x+ξ, x-ξ long. mom. fract.  t = (p-p’) 2   x B /(2-x B )

8. accessing GPDs: some caveats E.C. Aschenauer RHIC-AGS Users Metting, June 2010 7  apart from cross-over trajectory (x=  ) GPDs not directly accessible: deconvolution needed ! (model dependent)  but only  and t accessible experimentally  x is not acessible (integrated over):  GPD moments cannot be directly revealed, extrapolations t  0 are model dependent cross sections & beam-charge asymmetry ~ Re(T DVCS ) beam or target-spin asymmetries ~ Im(T DVCS ) t=0 q(x) =0  q(x)

9. factorization of forward Compton scattering  related to total cross section via optical theorem  final-state obtained by cutting the diagram  lower blob represents standard universal PDF  upper blob denotes hard interaction factorization of DVCS  exclusive cross section is square of amplitude  final-state proton has different momentum  difference of long. momentum is called “skewness”  lower blob represents generalized PDFs  upper blob denotes hard interaction inclusive vs exclusive processes 8 E.C. Aschenauer RHIC-AGS Users Metting, June 2010

10.  distinguish two kinematical regimes: partons emitted and reabsorbed reduce to PDFs in forward limit probes emission of mesonic d.o.f. no PDF counterpart physics of generalized parton densities  Q 2 evolution depends on x region (technically rather involved) generalization of DGLAP to evolution as for meson distribution ampl. (“ERBL regime”)  GPDs in impact parameter space = localization of partons e.g.where gives distribution of quarks with  longitudinal momentum fraction x  transverse distance b from proton center Burkardt find, e.g.: dyn. relation of GPD E with Sivers effect & link to spin-orbit correlations 9 E.C. Aschenauer RHIC-AGS Users Metting, June 2010

11. 10E.C. Aschenauer RHIC-AGS Users Metting, June 2010 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 GPDs in impact parameter space d-quark u-quark

12. Sivers function and OAM 11E.C. Aschenauer RHIC-AGS Users Metting, June 2010 Anselmino et al. arXiv:0809.2677 Extremely Model dependent statement: anomalous magnetic moment:  u = +1.67  d = -2.03 x M. Burkardt et al. Lattice: QCDSF collaboration lowest moment of distribution of unpol. q in transverse pol. proton and transverse pol. quarks in unpol. proton

13. E.C. Aschenauer RHIC-AGS Users Metting, June 2010 m  2 [GeV 2 ] HERMES value LHPC hep-lat/0705.4295 disconnected diagrams not yet included OAM can be accessed as well find:  u > 0 and L u 0 but in any quark model L u > 0, L d < 0 sign due to strong scale evolution of L q ? Myhrer, Thomas L u + L d ~ 0contribution from disconnected diagrams? if  g ~ 0, does this leave us with gluon OAM as culprit in spin audit? note: using AdS/CFT nucleon spin comes entirely from OAM Hatta, Ueda, Xiao arXiv:0905.2493 1st moments can be computed on the lattice … 12

14. manifest gauge invariant local operators contain interactions  interpretation ? L q +  q/2, J g  GPDs (DVCS) intuitive; partonic interpretation  g, L 0 q,g local only in A + = 0 gauge how to determine L 0 q,g experimentally ? Ji Jaffe, Manohar; Bashinsky, Jaffe ambiguities arise when decomposing proton spin in gauge theories reshuffling of ang. momentum between matter and gauge degrees only  unchanged  lattice results for L q are for Ji’s sum rule and cannot be mixed with  g  num. difference between L q and L q can be sizable Burkardt, BC arXiv:0812.1605 latest twist: 3 rd decomposition: like Jaffe, Manohar but w/ manifest gauge inv. operators physical interpretation? requires new def. of PDFs – relation to experiment? Chen, Lu, Sun, Wang, Goldman arXiv:0806.3166; 0904.0321 complication: “different” spin sum rules E.C. Aschenauer RHIC-AGS Users Metting, June 2010 13 LqLq LgLg  GG LqLq JgJg

15. photoproduction of VM at HERA soft interaction W δ described by Regge “theory” hard interaction W δ governed by small x evolution of gluon distribution exclusive processes: from soft to hard 14 E.C. Aschenauer RHIC-AGS Users Metting, June 2010

16. 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 15E.C. Aschenauer RHIC-AGS Users Metting, June 2010

17. 16E.C. Aschenauer RHIC-AGS Users Metting, June 2010 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

18. 17E.C. Aschenauer RHIC-AGS Users Metting, June 2010  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

19. Exclusivity: How is it constrained E.C. Aschenauer RHIC-AGS Users Metting, June 2010 18  missing mass (energy) technique  background estimated by MC MC associated BH Bethe-Heitler + data Hermes & H1 and Zeus for most of the data no recoil detection e’ t (Q 2 ) e L*L* x+ξ x-ξ H, H, E, E (x,ξ,t) ~ ~  p p’ e + /e - 27.5 GeV P b =55%

20. 19E.C. Aschenauer RHIC-AGS Users Metting, June 2010 HERMES: combined analysis of charge & polarization dependent data  separation of interference term + DVCS 2 DVCS: Hydrogen Target Beam Charge Asymmetry higher twist Beam Spin Asymmetry DVCS

21. 20E.C. Aschenauer RHIC-AGS Users Metting, June 2010 observables sensitive to E: (J q input parameter in ansatz for E)  DVCS A UT : HERMES  nDVCS A LU : Hall A First model dependent attempt to constrain J q Hermes DVCS-TTSA [arXiv: 0802.2499]: VGG Hall A nDVCS-BSA (PRL99 (2007)): x=0.36 and Q 2 =1.9GeV 2  Neutron obtained combining deuterium and proton deuterium and proton  F 1 small u & d cancel in Model dependent

22. DVCS: Deuterium Target E.C. Aschenauer RHIC-AGS Users Metting, June 2010 21

23. Latest Measurements from JLab E.C. Aschenauer RHIC-AGS Users Metting, June 2010 22 DVCS-BSA: arXiv: 0711.4805 x=0.249 Q 2 =1.95 x=0.249 Q 2 =1.95 VGG VGG+twist3 Laget more data on: A LU, A LL, cross section @ 6GeV 12 GeV: a lot to come with Q 2 max ~ 13 GeV, t>0.1 GeV x>0.2

24. DVCS from & E.C. Aschenauer RHIC-AGS Users Metting, June 2010 23 Zeus: ArXiv: 0812.2517 H1: PLB 681 (2009) 391

25. time for crude models is over – use data to determine GPDs from global QCD fits first attempt to extract H(x,x) from DVCS data: Mueller, Kumericki, Passek-Kumericki  so far, very good fits but only the beginning; will be an ongoing effort for years  need to incorporate useful information from meson production (gluon GPD!) but theory considerably more difficult and less mature towards a global analysis of GPDs E.C. Aschenauer RHIC-AGS Users Metting, June 2010 24

26. Hermes BCA CLAS BSA Hall A different GPD parametrisations More Results from MKK E.C. Aschenauer RHIC-AGS Users Metting, June 2010 25 arXiv: 0904.0458 t=0 t=-0.3 Other Fits: M. Guidal PLB 689 (2010) 156 M. Guidal & H. Moutarde EPJ A42 (2009) 71 H. Moutarde PRD 79 (2009) 094021 but all to limited data sets

27. Charge and Beam Spin Asymmetry Heavy Targets E.C. Aschenauer RHIC-AGS Users Metting, June 2010 26 Beam Charge Asymmetry Beam Spin Asymmetry Why nuclear DVCS:  How does the nuclear medium modify parton-parton correlations? parton-parton correlations?  How do nucleon properties change in the nuclear medium? in the nuclear medium?  Enhanced ‘generalized EMC effect’, rise of  DVCS with A? rise of  DVCS with A?  arXiv: 0911.0091

28. eRHIC Scope E.C. Aschenauer RHIC-AGS Users Metting, June 2010 e-e- e+e+ p Unpolarized and polarized leptons 4-20 (30) GeV Polarized light ions (He 3 ) 215 GeV/u Light ions (d,Si,Cu) Heavy ions (Au,U) 50-100 (130) GeV/u Polarized protons 50-250 (325) GeV Electron accelerator RHIC 70% e - beam polarization goal polarized positrons? Center mass energy range: √s=28-200 GeV; L~100-1000xHera longitudinal and transverse polarisation for p/He-3 possible e-e- Mission: Studying the Physics of Strong Color Fields 27

29. eSTAR ePHENIX The latest design of eRHIC E.C. Aschenauer RHIC-AGS Users Metting, June 2010 100m |----- ---| 6 pass 2.5 GeV ERL Coherent e-cooler 22.5 GeV 17.5GeV 12.5 GeV 7.5 GeV Common vacuum chamber 27.5 GeV 2.5 GeV Beam-dump Polarized e-gun eRHIC detector 25 GeV 20 GeV 15 GeV 10 GeV Common vacuum chamber 30 GeV 5 GeV 0.1 GeV The most cost effective design RHIC: 325 GeV p or 130 GeV/u Au eRHIC staging all-in tunnel 28

30. A detector integrated into IR E.C. Aschenauer RHIC-AGS Users Metting, June 2010 ZDC FPD  Dipoles needed to have good forward momentum resolution  Solenoid no magnetic field @ r ~ 0  DIRC, RICH hadron identification  , K, p  high-threshold Cerenkov  fast trigger for scattered lepton  radiation length very critical  low lepton energies FED a lot of space for polarimetry and luminosity measurements 29

31. eRHIC Detector in Geant-3 E.C. Aschenauer RHIC-AGS Users Metting, June 2010  DIRC: not shown because of cut; modeled following Babar  no hadronic calorimeter in barrel yet  investigate ILC technology to combine  ID with HCAL central tracking ala BaBar Silicon Strip detector ala Zeus EM-Calorimeter LeadGlas High Threshold Cerenkov fast trigger on e’ e/h separation Dual-Radiator RICH ala HERMES Drift Chambers ala HERMES FDC Hadronic Calorimeter 30

32. Can we detect DVCS-protons and Au break up p E.C. Aschenauer RHIC-AGS Users Metting, June 2010  track the protons through solenoid, quads and dipole with hector proton track  p=10% proton track  p=20% proton track  p=40% Equivalent to fragmenting protons from Au in Au optics (197/79:1 ~2.5:1)  will need roman pots as used in pp2pp DVCS protons are fine, need more optimization for break-up protons 31

33. DVCS @ eRHIC 32  at low x dominated by gluon contributions  Need wide x and Q 2 range to extract GPDs  Need sufficient luminosity to bin in multi-dimensions E.C. Aschenauer RHIC-AGS Users Metting, June 2010

34. Summary E.C. Aschenauer RHIC-AGS Users Metting, June 2010 33 EIC many avenues for further important measurements and theoretical developments we have just explored the tip of the iceberg you are here  u tot,  d tot L q,g ss gg spin sum rule Knowledge about Gluons in p /A Come and join us The BNL EIC Taskforce

35. E.C. Aschenauer RHIC-AGS Users Metting, June 2010 34

36. Summary E.C. Aschenauer RHIC-AGS Users Metting, June 2010 35 qqqq GGGG LgLgLgLg LqLqLqLq qqqq qqqq GGGG LgLgLgLg LqLqLqLq qqqq 300 pb -1 DIS&pp x

37. More insights to the proton - TMDs E.C. Aschenauer RHIC-AGS Users Metting, June 2010 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 beyond collinear picture 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 36

38. : What can we learn about the nucleon spin E.C. Aschenauer RHIC-AGS Users Metting, June 2010 37 x interesting questions at small x charm contribution to g 1 any deviations from DGLAP behavior? precision study of Bjorken sum rule (rare example of a well understood fundamental quantity in QCD) positive  g translates into Anticipated precision for one beam energy combination Integrated Lumi: 5fb -1 ~ 1 week data taking

39.   g(x) very small at medium x  best fit has a node at x ~ 0.1  huge uncertainties at small x small-x behavior still completey unconstrained The Gluon Polarization (HP12) E.C. Aschenauer RHIC-AGS Users Metting, June 2010 x RHIC range 0.05< x < 0.2 small-x 0.001 < x < 0.05 large-x x > 0.2  g(x) small !? 38 de Florian, Sassot, Stratmann, and Vogelsang PRL101 072001

40. Deeply Virtual Compton Scattering and GPDs e’ t (Q 2 ) e L*L* x+ξ x-ξ H, H, E, E (x,ξ,t) ~ ~  p p’ « Handbag » factorization valid in the Bjorken regime: high Q 2,  (fixed x B ) Q 2 = - (e-e’) 2 x B = Q 2 /2M  =E e -E e’ x+ξ, x-ξ longitudinal momentum fractions t = (p-p’) 2  x B /(2-x B )   0,x  ),(Ex q  2 1 Hxdx q  J G =  2 1 J q  1 1  )0,,( Quark angular momentum (Ji’s sum rule) X. Ji, Phy.Rev.Lett.78,610(1997) GPDs: Correlation between quark distributions both in momentum and coordinate space 39 E.C. Aschenauer RHIC-AGS Users Metting, June 2010

41. Hard exclusive meson production and GPDs 4 Generalized Parton Distributions (GPDs) H H conserve nucleon helicity E E flip nucleon helicity Vector mesons (  Pseudoscalar mesons (  ~ ~ ρ0ρ0 2u+d ω 2u-d ρ+ρ+ u-d quark flavor decomposition accessible via meson production x+ξ x-ξ t π, ρ, ω… (Q 2 ) e e’ L*L* Factorization proven only for longitudinally polarized virtual photons and valid at high Q 2 and small t 00 2  u+  d  2  u-  d H, H, E, E (x,ξ,t) ~ ~  0 )~ | ∫ dx H(x, ,t) | 2 ~ 40 E.C. Aschenauer RHIC-AGS Users Metting, June 2010

42. t-slopes b decreasing as a function of x b Valence (high x) quarks at the center (small b) Sea (small x) quarks at the perifery (high b) IF GPD formalism applies!! y x z Guidal, Polyakov, Radyushkin, Vanderhaeghen (2005) b (fm) x 41 E.C. Aschenauer RHIC-AGS Users Metting, June 2010

43. Questions about QCD  Confinement of color, or why are there no free quarks and gluons at a long distance?  A very hard question to answer  What is the internal landscape of the nucleons?  What is the nature of the spin of the nucleon?  What is the three-dimensional spatial landscape of nucleons?  Need probes to “see” and “locate” the quarks and gluons, without disturbing them or interfering with their dynamics?  What governs the transition of quarks and gluons into pions and nucleons  What is the role of gluons and gluon self-interactions in nucleons and nuclei?  What is the physics behind the QCD mass scale? E.C. Aschenauer RHIC-AGS Users Metting, June 2010  It represents the difference between QED and QCD  Can’t “see” it directly, but, it is behind the answers to all these questions these questions The key to the solution The Gluon 42

44. Transversity and Sivers, what do we know E.C. Aschenauer RHIC-AGS Users Metting, June 2010 Anselmino et al. arXiv:0809.2677 x 43 Q 2 =2.4 GeV 2 Fit to SIDIS and e+e- Lattice: P. Haegler et al. lowest moment of distribution of unpol. q in transverse pol. proton ANL ZGS  s=4.9 GeV BNL AGS  s=6.6 GeV FNAL  s=19.4 GeV Big single spin asymmetries in p  p !! Naive pQCD (in a collinear picture) predicts A N ~  s m q /sqrt(s) ~ 0 What is the underlying process? Do they survive at high √s? Relation to SIDIS?  HP13

45. Exclusive  + production 44E.C. Aschenauer RHIC-AGS Users Metting, June 2010 [PLB659(2008)] GPD model for  L : VGG LO LO+power corrections  NLO corrections moderate << size of power corrections [Diehl,Kugler] Regge model: JML d  /dt d  L /dt  data support order of power corrections

46. 45E.C. Aschenauer RHIC-AGS Users Metting, June 2010 VGG: [Vanderhaegen, Guichon, Guidal 1999] double distributions ; factorized or regge-inspired t-dependence D-term to restore full polynomiality skweness depending on free parameters b val & b sea includes tw-3 (WW approx) dual: [Guzey, Teckentrup 2006] GPDs based on infinite sum of t channel resonances factorized or regge-inspired t-dependence tw-2 only  describes well A C and A UT data  fails for A LU  A c favor ‘no D-term’  contradicts  QSM & lattice results contradicts  QSM & lattice results  describes well spin-asymmetries  fails for unpol. cross sections (HallA)  call for new, more sophisticated parameterizations of GPDs … more models on the way: e.g. generalization of Mellin transform technique transform technique The GPD Models

47. GPDs depend on x, ξ, t, Q 2 convenient: symmetric choice of mom. fractions  x, ξ: mom. fractions w.r.t. where in DVCS: x integrated and  t: trade for trans. momentum transfer  pioneering work by Leipzig group (‘85-’94) : Muller, Robaschik, Geyer, … hep-ph/9812448 (rediscovered in ‘96 by Ji and Radyushkin – connection to proton spin sum rule)  represent interference between amplitudes for different nucleon states (in general not a probability)  transverse structure of proton accessible through t dependence (proton “tomography”: how are partons distributed in the transverse plane)  rich spin structure allows access to, e.g., OAM physics of generalized parton densities 46 E.C. Aschenauer RHIC-AGS Users Metting, June 2010