1. Explore the new QCD frontier: strong color fields in nuclei
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

2. ERL-based eRHIC Design
2 different eRHIC Design options
ERL-based eRHIC Design
PHENIX
STAR
e-cooling (RHIC II)
Four e-beam passes
e+ storage ring
5 GeV - 1/4 RHIC circumference
Main ERL (3.9 GeV per pass)
RHIC
5 – 10 GeV e-ring
e-cooling
(RHIC II)
5 -10GeV full energy injector
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

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

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

6. World Data on F2p World Data on g1p 4 orders of magnitude in x and Q2
< 2 orders of magnitude, precision much worse !

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

8. G from scaling violations of g1

9. G from scaling violations of g1
EIC will allow precision determination of g1(x,Q2) over very large kinematic range
and thus will:
precisely determine the integral of G
allow to distinguish between different functional forms of g(x)
Measurement of G is likely to be limited by systematic uncertainty in polarization measurement
---- needs careful investigation (similar for existing global fits)

10. Polarized gluon distribution via charm production
very clean process ! c
D mesons
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
starting assumptions for EIC:
vertex separation of better than 100m
full angular coverage (3<<177 degrees)
perfect particle identification for pions and kaons
(over full momentum range)
detection of low momenta particles (p>0.5 GeV)
measurement of scattered electron
(even at very small scattering angles)
100% efficiency
very demanding detector requirements !

13. Polarized gluon distribution via charm production
invariant mass of K  system
incl PID
Background suppression:
Separation of primary and
secondary vertex absolutely
essential !
Pion/kaon separation very
helpful !

14. Polarized gluon distribution via charm production
Momenta of decay
kaon and pion:
1.5 < p < 10 (15) GeV
Angles of decay kaon
and pion:
1600 <  < 1770 

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

16. Polarized gluon distribution via charm production
Precise determination
of  G/G for
0.003 < xg < 0.4
at common Q2 of 10 GeV2
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 to better than 100 m ()
We understand the fragmentation of charm quarks ()
We can control the contributions of resolved photons
We can calculate higher order QCD corrections ()

17. charm production: influence of fragmentation
xgrec = x(shat/Q2+1)
shat = 4 Minv2
correction presently by
simple parametrisation
of xg-xrec vs xg

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

19. Polarized gluon distribution vs Q2

20. Other processes G from dijet production
promising channel for determination of G
needs more detailed study !

21. Next Steps
determine sensitivity of g1 to different “realistic” models for G (including different functional forms !)
generate pseudo EIC data and include in full QCD fit procedure (including estimates of systematic uncertainties !)
study fragmentation in charm production
include other charm decay channels (including D* tagging)
understand the possibility to determine the charm mass from charm cross section measurements

22. Summary
EIC is the ideal machine to finally determine the contribution of the gluons to the nucleon spin!
measurements of g1 will allow
a precise determination of G from its scaling violation
systematics due to uncertainty in proton beam polarization ?
measurements of charm cross section asymmetries will provide a precise determination of G/G for 0.003<x<0.5 at a fixed value of Q2 of ~10 GeV2
……. provided we can
measure the scattered electron at extremely small angles
separate the primary and secondary vertex with sufficient precision
control the contribution of resolved photons
understand NLO corrections and the mass of the charm quark

24. g1 and the Bjorken Sum Rule

25. determination of as(Q2)
Bjorken Sum Rule: Γ1p - Γ1n = 1/6 gA [1 + Ο(αs)]
Needs:
O(1%) Ion Polarimetry!!!
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