Spin Physics with an Electron-Ion-Collider

1. Spin Physics with an Electron-Ion-Collider Antje Bruell, Jlab RHIC&AGS Users Meeting, May 27, 2008 • What is the EIC ? • Central Questions in Nucleon Structure • The Gluon Contribution to the Nucleon Spin • TMDs and GPDs at EIC • Sumary

2. What is the EIC ? • Electron Ion Collider as the ultimate QCD machine • Variable center of mass energy between 20 and 100 GeV • High luminosity • Polarized electron and proton (deuteron, 3He) beams • Ion beams up to A=208 Explore the new QCD frontier: strong color fields in nuclei Precisely image the sea-quarks and gluons in the nucleon

3. e-cooling (RHIC II) 5 – 10 GeV e-ring 5 -10GeV full energy injector RHIC PHENIX Main ERL (3.9 GeV per pass) STAR e+ storage ring 5 GeV - 1/4 RHIC circumference e-cooling (RHIC II) Four e-beam passes ERL-based eRHIC Design 2 different eRHIC Design options • Electron energy range from 3 to 20 GeV • Peak luminosity of 2.6  1033 cm-2s- • high electron beam polarization (~80%) • full polarization transparency at all energies • multiple electron-hadron interaction points •  5 meter “element-free” straight section(s) • ability to take full advantage of electron cooling of the hadron beams; • easy variation of the electron bunch frequency to match the ion bunch frequency at different ion energies. • Based on existing technology • Collisions at 12 o’clock interaction region • 10 GeV, 0.5 A e-ring with 1/3 of RHIC circumference (similar to PEP II HER) • Inject at full energy 5 – 10 GeV • Polarized electrons and positrons

4. ELIC design at Jefferson Lab 30-225 GeV protons 30-100 GeV/n ions 3-9 GeV electrons 3-9 GeV positrons • Polarized H, D, 3He, • Ions up to A = 208 • Average Luminosity from 1033to 1035 cm-2 sec-1 per Interaction Point Green-field design of ion complex directly aimed at full exploitation of science program.

5. The Gluon Contribution to the Nucleon Spin Antje Bruell, Jlab EIC meeting, MIT, April 7 2007 • Introduction • G from scaling violations of g1(x,Q2) • The Bjorken Sum Rule • G from charm production

6. Precisely image the sea quarks Spin-Flavor Decomposition of the Light Quark Sea u u u > u d Many models predict Du > 0, Dd < 0 | p = + + + … u u u u d d d d RHIC-Spin region

8. Region of existing g1p data World Data on F2p EIC Data on g1p An EIC makes it possible!

9. G from scaling violations of g1

10. c D mesons c D mesons Polarized gluon distribution via charm production very clean process ! LO QCD: asymmetry in D production directly proportional to G/G

11. Polarized gluon distribution via charm production problems:luminosity, charm cross section, background !

12. Polarized gluon distribution via charm production Precise determination of  G/G for 0.003 < xg < 0.4 at common Q2 of 10 GeV2 however RHIC SPIN

13. Precise determination of  G/G for 0.003 < xg < 0.4 at common Q2 of 10 GeV2 Polarized gluon distribution via charm production • If: • We can measure the scattered electron even at angles close to 00 (determination of photon kinematics) • We can separate the primary and secondary vertex down to about 100 m • We understand the fragmentation of charm quarks () • We can control the contributions of resolved photons • We can calculate higher order QCD corrections ()

14. Polarized gluon distribution vs Q2

15. g1 and the Bjorken Sum Rule

16. Bjorken Sum Rule:Γ1p - Γ1n = 1/6 gA [1+Ο(αs)] Needs: O(1%) Ion Polarimetry!!! Holy Grail: excellent determination of as(Q2) • Sub-1% statistical precision at ELIC • (averaged over all Q2) • 7% (?) in unmeasured region, in future • constrained by data and lattice QCD • 3-4% precision at various values of Q2

17. The Gluon Contribution to the Nucleon Spin Antje Bruell, Jlab EIC meeting, MIT, April 7 2007 • Introduction • G from scaling violations of g1(x,Q2) • The Bjorken Sum Rule • G from charm production

18. Exclusive Processes: Collider Energies

19. Exclusive Processes: EIC Potential and Simulations

20. The Gluon Contribution to the Nucleon Spin Antje Bruell, Jlab EIC meeting, MIT, April 7 2007 • Introduction • G from scaling violations of g1(x,Q2) • The Bjorken Sum Rule • G from charm production

21. The Gluon Contribution to the Nucleon Spin Antje Bruell, Jlab EIC meeting, MIT, April 7 2007 • Introduction • G from scaling violations of g1(x,Q2) • The Bjorken Sum Rule • G from charm production

22. 5 GeV  50 GeV/c (e P) • Q2=4 GeV2 • 2= 0.2 • P’ tagging required • Exclusivity •  Resolution • () ≈ 0.3GeV2 without tagging • Transverse Imaging

23. Rates and coverage in different Event Topologies Assume: 100 days, Luminosity=10E34 Detect the neutron Ep=50 GeV Ee=5 GeV Missing mass reconstruction 10<Q2<15 10<Q2<15 15<Q2<20 15<Q2<20 35<Q2<40 35<Q2<40 Γ dσ/dt (ub/GeV2) Γ dσ/dt (ub/GeV2) 0.02<x<0.05 0.05<x<0.1 0.01<x<0.02 0.05<x<0.1 -t (GeV2) -t (GeV2) • Neutron acceptance limits the t-coverage • The missing mass method gives full t-coverage for x<0.2 Assume dp/p=1% (pπ<5 GeV)

25. Transversity and friends Unpol. DF Helicity Transversity q(x) Dq(x) dq(x) Sivers function Boer-Mulders function EIC workshop, May 21th R.Seidl: Transversity measurements at EIC 25

26. First successful attempt at a global analysis for the transverse SIDIS and the BELLE Collins data HERMES AUTp data COMPASS AUT d data Belle e+ e- Collins data Kretzer FF  First extraction of transversity (up to a sign) Anselmino et al: hep-ex 0701006 R.Seidl: Transversity measurements at EIC 26 EIC workshop, May 21th

27. What can ne expected at EIC? • Larger x range measured b y existing experiments COMPASS ends at ~ 0.01, go lower by almost one order of magnitude, but asymmetries become small • Have some overlap at intermediate x to test evolution of Collins function and higher twist but at higher Q2 EIC workshop, May 21th R.Seidl: Transversity measurements at EIC 27

28. The Gluon Contribution to the Nucleon Spin Antje Bruell, Jlab EIC meeting, MIT, April 7 2007 • Introduction • G from scaling violations of g1(x,Q2) • The Bjorken Sum Rule • G from charm production

29. The Gluon Contribution to the Nucleon Spin Antje Bruell, Jlab EIC meeting, MIT, April 7 2007 • Introduction • G from scaling violations of g1(x,Q2) • The Bjorken Sum Rule • G from charm production

30. Sivers effect: Kaon electroproduction EIC CLAS12 • 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.

31. Correlation between Transverse Spin and Momentum of Quarks in Unpolarized Target All Projected Data Perturbatively Calculable at Large pT Vanish like 1/pT (Yuan) ELIC

32. Summary • EIC is the ideal machine to provide the final answers on the structure of the proton, especially in the region where ea quarks and gluons dominate • It will allow to : • measure precisely the gluon distribution at low x and moderate Q2 • determine the polarized sea quark distributions in the nucleon • map out the polarized gluon distribution in the nucleon • perform a precision test of the Bjorken Sum Rule ---> s • do gluon “tomography” via exclusive processes • determine transverse spin effects and orbital momenta • provide a understanding of the fragmentation process • + investigate the low x phyiscs of saturation in the nucleus

34. World Data on F2p Structure Function Next-to-Leading-Order (NLO) perturbative QCD (DGLAP) fits

35. The Gluon Contribution to the Nucleon Spin Antje Bruell, Jlab EIC meeting, MIT, April 7 2007 • Introduction • G from scaling violations of g1(x,Q2) • The Bjorken Sum Rule • G from charm production

36. The Gluon Contribution to the Nucleon Spin Antje Bruell, Jlab EIC meeting, MIT, April 7 2007 • Introduction • G from scaling violations of g1(x,Q2) • The Bjorken Sum Rule • G from charm production

37. Future: x g(x,Q2) from RHIC and EIC EIC 0.003 < x < 0.5 uncertainty in xg typically < 0.01 !!! EIC