1. Rolf Ent, INT, September 18, 2009 GPD/TMD Studies with a Future Electron-Ion Collider Electron-Ion Collider: Status & Current Ideas Inclusive DIS Measurement Projections Semi-Inclusive DIS Measurement Projections Deep Exclusive Measurement Projections & Kinematics Summary Nuclear Science Goals: How do we understand the visible matter in our universe in terms of the fundamental quarks and gluons of QCD?  Explore the structure of the nucleon (it’s what we are made of)

2. EIC science has evolved from new insights and technical accomplishments over the last decade or so ~1996 development of Generalized Parton Distributions ~1999 high-power energy recovery linac technology ~2000 universal properties of strongly interacting glue ~2000 emergence of transverse-spin phenomenon ~2001 world’s first high energy polarized proton collider ~2003 tantalizing hints of saturation ~2006 electron cooling for high-energy beams Many recent and ongoing developments: constraints on gluon polarization, 1 st successful test of crab cavities, development of semi-inclusive DIS framework at NLO, 2 nd round of deep exclusive measurements, Lattice QCD progress, etc., etc.

3. “An Electron-Ion Collider (EIC) with polarized beams has been embraced by the U.S. nuclear science community as embodying the vision for reaching the next QCD frontier. EIC would provide unique capabilities for the study of QCD well beyond those available at existing facilities worldwide and complementary to those planned for the next generation of accelerators in Europe and Asia. In support of this new direction: We recommend the allocation of resources to develop accelerator and detector technology necessary to lay the foundation for a polarized Electron Ion Collider. The EIC would explore the new QCD frontier of strong color fields in nuclei and precisely image the gluons in the proton.” NSAC 2007 Long-Range Plan

4. Why an Electron-Ion Collider? Longitudinal and Transverse Spin Physics! - 70+% polarization of beam and target without dilution - transverse polarization also 70%! Detection of fragments far easier in collider environment! - fixed-target experiments boosted to forward hemisphere - no fixed-target material to stop target fragments - access to neutron structure w. deuteron beams (@ p m = 0!) Easier road to do physics at high CM energies! - E cm 2 = s = 4E 1 E 2 for colliders, vs. s = 2ME for fixed-target  4 GeV electrons on 60 GeV protons ~ 500 GeV fixed-target - Easier to produce many J/  ’s, high-p T pairs, jets, etc. - Easier to establish good beam quality in collider mode Targetf dilution, fixed_target P fixed_target f 2 P 2 fixed_target f 2 P 2 EIC p0.20.80.030.5 d0.40.50.040.5 Longitudinal polarization FOM

5. Current Ideas for a Collider Energiessluminosity ENC@GSIUp to 3 x 15180Few x 10 32 (M)EIC@JLabUp to 11 x 60150-2650Few x 10 34 Staged MeRHIC@BNL Up to 4 x 250(400-)4000Close to 10 33 Future ELIC@JLab Up to 11 x 25011000Close to 10 35 eRHIC@BNLUp to 20 x 32526000Few x 10 33 LHeC@CERNUp to 70 x 100028000010 33 Design Goals for Colliders Under Consideration World-wide Some of the slides are for a “generic” US version of an EIC: polarized beams (longitudinal and transverse, > 70%) luminosities of at least 10 33 energies up to 10 x 250, or s = 10000 Present focus of interest (in the US) are the (M)EIC and Staged MeRHIC versions, with s up to 2650 and 4000, resp.

6. 4 GeV e x 250 GeV p – 100 GeV/u Au MeRHIC 2 x 60 m SRF linac 3 passes, 1.3 GeV/pass STAR PHENIX V.N. Litvinenko, RHIC S&T Review, July 23, 2009 3 pass 4 GeV ERL Polarized e-gun Beam dump MeRHIC detector MeRHIC Medium Energy eRHIC @ IP2 of RHIC Up to 4 GeV e - x 250 GeV p L ~ 10 32 -10 33 cm -2 sec -1 90% of hardware can be reused s = (400-) 4000

7. (M)EIC Coverage A High-Luminosity (M)EIC at JLab Legend: MEIC =EIC@JLab 1 low-energy IR (s ~ 200) 3 medium-energy IRs (s < 2600) ELIC =high-energy EIC@JLab (s = 11000) (limited by JLab site) Use CEBAF “as-is” after 12-GeV Upgrade

8. Approximate staged EIC coverage s ~ 2500 sufficient to transcend into region of large rise of gluon density

9. Electron-Ion Collider – further info EIC (eRHIC/ELIC) webpage: http://web.mit.edu/eicc/http://web.mit.edu/eicc/ Upcoming meeting: January 10-12, 2010 @ Stony Brook 2 nd joint BNL/JLab EIC Advisory Committee meeting: November 2 + 3, 2009 (@JLab) Week-long meeting at the INT, intermixed with the ongoing JLab 12-GeV program: Oct. 19-23 (dedicated to physics of staging options) 2010: long INT program dedicated to science @ EIC Weekly meetings at both BNL and JLab Series of topical workshops planned in 2010

10. Where does the spin of the proton originate? Input from DIS, SIDIS, pp (RHIC) and Global Fits… De Florian, Sassot, Stratmann and Vogelsang, Phys. Rev. Lett. 101, 072001 (2008)  G < 0.1? (constrained in narrow region of x only)

11. Where does the spin of the proton originate? Generalized Parton Distributions provide access to total quark contribution to proton angular momentum in (deep) exclusive processes: e + N  e’ + N + X ½ = J q + J g = ½  + L q + J g H(x, ,t), E(x, ,t),.. “Generalized Parton Distributions” Accessible through deep exclusive reactions (and Lattice QCD) Quark angular momentum (Ji’s sum rule) X. Ji, Phy.Rev.Lett.78,610(1997) k k'k' ** q q'q'  pp'p' e

12. Where does the spin of the proton originate? … and input from Lattice QCD on GPD moments (also from deep exclusive scattering) LHPC Collaboration, Phys. Rev. D77, 094502 (2008) L u and L d separately quite substantial (~0.15), but cancel (disconnected diagrams not yet included)

13. (polarized) e-p at medium energies Exclusive processes and GPDs – Deeply-Virtual Meson Production: spin/flavor/spatial quark structure (Q 2 ~ 10 GeV 2 ) – DVCS: helicity GPDs, spatial quark and gluon imaging Charm as direct probe of gluons – J/ ψ, exclusive : spatial distribution of gluons – D Λ c, open charm (including quasi-real D 0 photoproduction for Δ G) Semi-inclusive DIS – Flavor decomposition: q ↔ q, u ↔ d, strangeness s, s – TMDs: spin-orbit interactions from azimuthal asymmetries, p T dependence – Target fragmentation and fracture functions Inclusive DIS – Δ G and Δ q+ Δ q from global fits (+ RHIC-spin, COMPASS, JLab 12 GeV) – Neutron structure from spectator tagging in D(e,e’p)X -- -

14. Luminosity of 1x10 33 cm -2 sec -1 One day  50 events/pb Supports Precision Experiments Lower value of x scales as s -1 DIS Limit for Q 2 > 1 GeV 2 implies x down to 1.0 times 10 -4 Significant results for 200 events/pb for inclusive scattering If Q 2 > 10 GeV 2 required for Deep Exclusive Processes can reach x down to 1.0 times 10 -3 Typical cross sections factor 100- 1,000 smaller than inclusive scattering Significant results for 20,000- 200,000 events/pb  high luminosity essential Luminosity Considerations for EIC eRHIC (20 GeV e - ) eRHIC, ELIC (W 2 > 4) x Q 2 (GeV 2 ) W 2 <4 eRHIC: x = 10 -4 @ Q 2 = 1 ELIC : x = 10 -4 @ Q 2 = 1 12 GeV: x = 4.5x10 -2 @ Q 2 = 1 Include low-Q 2 region Staging example: s ~ 1000  x = 1.0x10 -3 @Q 2 =1

15. The Gluon Contribution to the Proton Spin at small x Superb sensitivity to  g at small x! (Antje Bruell, Abhay Deshpande, RE) Example for s = 4200

16. Projected data on  g/g with an EIC, via  + p  D 0 + X K - +  + assuming vertex separation of 100  m. Access to  g/g is also possible from the g 1 p measurements through the QCD evolution, and from di-jet measurements. RHIC-Spin The Gluon Contribution to the Proton Spin Advantage: measurements directly at fixed Q 2 ~ 10 GeV 2 scale! Uncertainties in x  g smaller than 0.01 Measure 90% of  G (@ Q 2 = 10 GeV 2 )  g/g (Antje Bruell, RE)

17. 5 on 50 EIC projected data 10 -3 10 -2 10 -1 x Bj Flavor Decomposition @ EIC Lower x ~ 1/s 5 on 50  s = 1000 10 -3 10 -2 10 -1 x Bj 100 days at 10 33 (Ed Kinney, Joe Seele)  quark polarization  q(x)  first 5-flavor separation  u > 0  d < 0 10 on 250  s = 10000 10 on 250 EIC projected data 10 -3 10 -2 10 -1 x Bj

18. RHIC-Spin region Precisely image the sea quarks Spin-Flavor Decomposition of the Light Quark Sea | p = + + + … > u u d u u u u d u u d d d Many models predict  u > 0,  d < 0 No competition foreseen! 100 days at 10 33

19. New Spin Structure Function: Transversity Nucleon’s transverse spin content  “tensor charge” No transversity of Gluons in Nucleon  “all-valence object” Chiral Odd  only measurable in semi-inclusive DIS  first glimpses from HERMES  COMPASS 1 st results: ~0 @ low x  valence region only?  Future: Flavor decomposition (started by Anselmino et al.) - (in transverse basis)  q(x) ~ Need (high) transverse ion polarization (Naomi Makins, Ralf Seidl)

20. ELIC Vanish like 1/p T (Yuan) Correlation between Transverse Spin and Momentum of Quarks in Unpolarized Target All Projected Data Perturbatively Calculable at Large p T - (Harut Avakian, Antje Bruell) Assumed 100 days of 10 35 luminosity

21. Sivers effect: Pion electroproduction EIC measurements at small x will pin down sea contributions to Sivers function S. ArnoldS. Arnold et al arXiv:0805.2137 M. AnselminoM. Anselmino et al arXiv:0805.2677 GRV98, Kretzer FF (4par) GRV98, DSS FF (8par) (Harut Avakian)

22. Sivers effect: Kaon electroproduction At small x of EIC Kaon relative rates higher, making it ideal place to study the Sivers asymmetry in Kaon production (in particular K - ). Combination with CLAS12 data will provide almost complete x-range. EIC CLAS12 (Harut Avakian)

23. Sivers effect: sea contributions Negative Kaons most sensitive to sea contributions. Biggest uncertainty in experimental measurements (K - suppressed at large x). GRV98, DSS FF S. ArnoldS. Arnold et al arXiv:0805.2137 M. AnselminoM. Anselmino et al arXiv:0805.2677 GRV98, Kretzer FF (Harut Avakian)

24. P t = p t + z k t + O(k t 2 /Q 2 ) Final transverse momentum of the detected pion P t arises from convolution of the struck quark transverse momentum k t with the transverse momentum generated during the fragmentation p t. Linked to framework of Transverse Momentum Dependent Parton Distributions SIDIS – k T Dependence This workshop (Anselmino): Get rid of convolution by measuring jets  Map k t dependence directly Sets a lower threshold in s: Assume jet requires 50 GeV energy and 2 GeV transverse energy  E cm ~ 30-50?

25. What E cm and Luminosity are needed for Semi-Inclusive DIS Processes? Find that 100 days of measurements with a luminosity of 10 33 is in general sufficient (for p T < 1 GeV) Useful to include lower-energies to improved data quality at larger x values (~ 0.1) Include higher energies (E cm = 30-50) to access jets (and diffraction) but, for SIDIS need multiple conditions: Longitudinal, Transverse, 1 H, 2 H, 3 He, heavy A, low, high E cm  10 33 really seems minimum  full program requires (n times 100 days) simulations at large p T were done assuming 10 35 luminosity  Likely needs more than 10 33 luminosity

26. What E cm and Luminosity are needed for Deep Exclusive Processes? New Roads:   and  Production give access to gluon GPD’s at small x (<0.2)  Deeply Virtual Meson Production @ Q 2 > 10 GeV 2 Well suited processes for the EIC  transverse spatial distribution of gluons in the nucleon Can we do such measurements at fixed x in the valence quark region? Important to disentangle flavor and spin… fixed x:  ~ s/Q 2 (Mott) x 1/Q 4 (hard gluon exchange) 2 sLQ 2 reach DVCS Q 2 reach (e,e’  ) 12-GeV2110 35 = 7 EIC example10003 x 10 34 ~100~17

27. GPDs and Transverse Imaging Deep exclusive measurements in ep/eA with an EIC: diffractive:transverse gluon imagingJ/ ,  o,  (DVCS) non-diffractive:quark spin/flavor structure , K,  +, … [ or J/ , ,  0 , K,  +, … ] Describe correlation of longitudinal momentum and transverse position of quarks/gluons  Transverse quark/gluon imaging of nucleon (“tomography”)

28. GPDs and Transverse Gluon Imaging Goal: Transverse gluon imaging of nucleon over wide range of x: 0.001 < x < 0.1 Requires: - Q 2 ~ 10-20 GeV 2 to facilitate interpretation - Wide Q 2, W 2 (x) range - luminosity of 10 33 (or more) to do differential measurements in Q 2, W 2, t Q 2 = 10 GeV 2 projected data Simultaneous data at other Q 2 -values EIC enables gluon imaging! (Andrzej Sandacz)

29. GPDs and Transverse Gluon Imaging Simultaneous measurements over large range in x, Q 2, t at EIC! At small x (large W):  ~ G(x,Q 2 ) 2 Or more… Differential DVCS measurements at moderate-large Q 2 (> 10 GeV 2 ), moderate x (~0.05) and t ~ 1 GeV 2 would benefit from luminosities larger than 10 33

30.  Diffractive Channels: Transverse Gluon Imaging Two-gluon exchange dominant for J/ , ,  production at large energies  sensitive to gluon distribution squared! LO factorization ~ color dipole picture  access to gluon spatial distribution in nuclei Measurements at DESY of diffractive channels ( J/ , , ,  ) confirmed the applicability of QCD factorization: t-slopes universal at high Q 2 flavor relations  :  Unique access to transverse gluon imaging at EIC! Fit with d  /dt = e -Bt

31. Exclusive Processes: EIC Potential and Simulations Diffractive channels - data/experience from HERA:  p (DVCS),  0 p,  p, J/  p - DVCS simulations by A. Sandacz et al., see e.g. http://web.mit.edu/eicc/SBU07/index.html - Found to be feasible with luminosity of 10 33 Non-diffractive channels - New territory for collider! - Much more demanding in luminosity: 10 34 minimum? - Physics closely related to JLab 6/12 GeV - quark spin/flavor separations, nucleon/meson structure - Feasibility study of  + n,  0 p, K +  - T. Horn, A. Bruell, V. Guzey, and C. Weiss

32. - New territory for collider! - Much more demanding in luminosity (see example) - Physics closely related to JLab 6/12 GeV - quark spin/flavor separations - nucleon/meson structure Γ dσ/dt (  b/GeV 2 ) Extend to Quark Imaging: Non-Diffractive Channels Pushes for lower and more symmetric energies (to obtain sufficient  M x ) Simulation for charged  + production, assuming 100 days at a luminosity of 10 34, with 5 on 50 GeV (s = 1000) V. Guzey, Ch. Weiss: Regge model T. Horn: π + empirical parameterization 10<Q 2 <15 15<Q 2 <20 35<Q 2 <40 (Tanja Horn, Antje Bruell, Christian Weiss)

33. Extend to Quark Imaging: Non-Diffractive Channels Pushes for lower and more symmetric energies (to obtain sufficient  M x ) and luminosity > 10 34 Rate estimate for KΛ Using an empirical fit to kaon electroproduction data from DESY and JLab assuming 100 days at a luminosity of 10 34, with 5 on 50 GeV (s = 1000) (Tanja Horn, David Cooper) 10<Q 2 <15 15<Q 2 <20 35<Q 2 <40 0.01<x<0.02 0.02<x<0.050.05<x<0.1 Consistent with earlier back-of- the-envelope scaling arguments

34. 1 H(e,e’ π + )n – Kinematics MEIC@JLab 4 on 12 GeV 2 MEIC@JLab 4 on 60 GeV 2 MEIC@JLab 11 on 60 GeV 2 Staged eRHIC 4 on 250 GeV 2 Staged eRHIC 2 on 250 GeV 2 ~ ENC@GSI

35. 1 H(e,e’ π + )n – Pion Kinematics – P Lower proton energies better to map cones around hadrons for deep exclusive and SIDIS. Also better for  M resolution and particle Id. (Tanja Horn) 4 on 124 on 6011 on 60 4 on 2502 on 250

36. 1 H(e,e’ π + )n – Electron Kinematics – P More symmetric and lower energies are better for energy resolution (Tanja Horn) 4 on 124 on 6011 on 60 4 on 2502 on 250

37. 1 H(e,e’ π + )n – Neutron Kinematics – t  = 5  = 1.3  = 0.3  t/t ~ t/E p  lower E p better (Tanja Horn) Want 0 < t < 1 GeV! 4 on 12 4 on 60 4 on 250 Conclusion: deep exclusive charged meson production will likely require proton energies up to 60 GeV or so.  s ~ 1000  @Q 2 = 10 GeV 2 access down to x = 0.01  Drives large detector space (MeRHIC: 20 m ~ (M)EIC: 18m)

38. Summary - I Fundamental requirements of EIC: Range of energies, 10 < E cm < 50? And variable! Need to also be able to run at more symmetric energies High polarization, both longitudinal and transverse Optimize luminosity and detection fraction together Exact luminosity required for many processes complicated - Depends on x, Q 2 and p T phase space to cover - Depends on multi-dimensional binning & statistics - Depends on which physics processes will be of highest scientific value – opinions differ Next slide: an attempt at a science/luminosity matrix for the FULL (?) EIC science potential (note that this requires an iteration process, for now several versions are worked upon)

39. Luminosity [cm -2 s -1 ] s [GeV 2 ] 10 35 10 34 10 33 10 32 10 100 1000 10000100000 COMPASS JLAB6&12 HERMES ENC@GSI (M)EIC MeRHIC DIFFSaturation DIS SIDIS EW DES JETS

40. Summary - II Both BNL and JLab have emphasized staging ideas for an EIC as their immediate priority: MeRHIC: 400 < s < 4000, L close to 10 33 (M)EIC : 100 < s < 2600, L few times 10 34 Processes requiring most luminosity are: deep exclusive pion and kaon (!) electroproduction large p T semi-inclusive DIS electroweak studies Processes driving to a center-of-mass energy of 30-50 are: jet production (to map quark transverse momentum?) factorization? diffraction (E cm > 40?) But, deep exclusive charged meson production drives more symmetric energies and E cm of 10-30 The EIC will indeed allow a unique GPD & TMD program Optimization of such EIC remains, with your input, ongoing!

42. Four Electron-Ion Collider Facilities Considered LHeC: L = 1.1x10 33 cm -2 s -1 E cm = 1.4 TeV EICx2: L > 1x10 33 cm -2 s -1 E cm = 20-100+ GeV Add 70-100 GeV electron ring to interact with LHC ion beam Use LHC-B interaction region High luminosity mainly due to large  ’s (= E/m) of beams Variable energy range Polarized and heavy ion beams High luminosity in energy region of interest for nuclear science Nuclear science goals: Explore the new QCD frontier: strong color fields in nuclei Precisely image the sea-quarks and gluons to determine the spin, flavor and spatial structure of the nucleon. High-Energy physics goals: Parton dynamics at the TeV scale - physics beyond the Standard Model - physics of high parton densities (low x) ENC@GSI: L ~ few x 10 32 cm -2 s -1 E cm = 13 GeV Add 3 GeV electron accelerator to interact with FAIR ion beam Nuclear science goal: Precisely image the sea-quark and gluon structure of the nucleon.

43. 60° Medium Energy IP Low Energy IP Snake Insertion Medium Energy: 30-60 on 3-5 (11) (M)EIC@JLab Interaction Region Concept IR4: Low Energy detector IR3: Diffractive/Low-Q 2 detector IR1: General Purpose detector (but not diffractive/low-Q 2 ?) p e Low Energy: 12 on 3-5 [sqrt(s) only factor of three higher than 12-GeV program] IR2: Polarimetry etc. IR Regions: +/- 9 meter

44. Reaching Saturation: EIC Options Energiesss EIC /s HERA boost in gluon density over HERA “virtual” x reach boost over HERA at Q 2 = const 11 x 2410501/961.514 4 x 10016001/631.716 10 x 10040001/252.2515 G ~ A 1/3 x s 0.3 (A = 208) Energies for heavy-ion beams