Three Measurements at Electron Ion Collider

1. Three MeasurementsatElectron Ion Collider Jianwei Qiu Brookhaven National Laboratory Informal presentation to the EIC Task Force at BNL Brookhaven National Lab, February 24, 2010 Jianwei Qiu

2. QCD, quarks, and gluons • Questions about QCD? • EIC as the next QCD machine • Three (type) measurements at EIC Outline Jianwei Qiu

3. A non-abelian gauge field theory of quarks and gluons • Fields: Quark fields: spin-½ Dirac fermion (like electron) Color triplet: Flavor: Quantum Chromodynamics (QCD) Gluon fields: spin-1 vector field (like photon) Color octet: • QCD Lagrangian density: • Color matrices: Generators for the fundamental representation of SU3 color Jianwei Qiu

4. Quarks and gluons • No free quarks and gluons seen in the detector • Quarks and Gluons “live” in the world of strong interaction • Quarks “talk” to outside world via their fractional electric charge • Gluons do not directly interact with anyone else • (no gravity and beyond standard model here) • We “see” quarks directly via electromagnetic probes • “produce” them in pairs • We “feel” gluons’ existence via the scale dependence • of inclusive cross sections • “see” their trace from the jet events • “measure” them quantitatively from global QCD analysis • of cross sections and parton distribution functions Jianwei Qiu

5. Questions about QCD (biased list) • Confinement of color, or • why there is no free quarks and gluons at a long distance? Too hard a question for me to answer now • What is the quark-gluon structure inside a hadron? Probes to “see” and “locate” the quarks and gluons, without disturbing them or interfering with their dynamics? • How quarks and gluons form color neutral hadrons? Probes to “monitor” the hadronization process? • How to understand the spin of a hadron? A composite particle of quarks and gluons • What is the physics behind the QCD mass scale? • … Jianwei Qiu

6. The key to the solution The gluon! • It represents the difference between QED and QCD • Can’t “see” it directly, but, • it is behind the answers to all these questions Jianwei Qiu

7. Quark-gluon structure inside a hadron • Hadron is made of virtual loops of quarks and gluons Ideal solution: matrix elements of all possible parton fields • Colorless probes do not “see” gluons • No isolated/localized color probe • single parton “plus” a beam of color gluon with scalar polarization Jianwei Qiu

8. Quark-gluon structure inside a hadron? • send a probe to see what is inside the hadron • colorless probe - do not "see" gluon • no isolated/localized color probe • - long range color interaction before the hard collision • every parton could participate in the interaction with the probe • directly or indirectly • variation of the collision scale - EIC • power expansion - approximation • factorization - approximation Jianwei Qiu

9. Parton distribution functions • Only "one" active parton interacts with the probe • what really happens • a parton with a flux of longitudinally polarized gluons, • which do not change the quantum number of the active parton, • but, takes care of the color • a "probability" distribution • not necessarily positive definite - factorization scheme • no space-time information Jianwei Qiu

10. TMD parton distribution functions • parton'stransverse distribution • need a probe sensitive to the small transverse momentum scale • in a gauge theory, the transverse motion is always connected to the gauge field - covariant derivative • factorization and its process dependence • color flow along the parton momentum or hadron momentum? Jianwei Qiu

11. Multiparton correlation functions • Hard to complete with the leading power contribution! • Spin asymmetry to remove the leading power - SSA • A-dependence to measure multiparton correlation between • nucleons Jianwei Qiu

12. Multiparton correlation functions • Hard to complete with the leading power contribution! • Spin asymmetry to remove the leading power - SSA • A-dependence to measure multiparton correlation between • nucleons Jianwei Qiu

13. Physics behind QCD mass scale • QCD Lagrangian has no intrinsic mass scale other than the • current quark mass • quark condensate is believe to be responsible for the mass scale • of bound hadrons • In QCD, gluon self interaction could develop a natural scale to • form the glue ball, in principle, even in a pure gluon system • could such a scale or phenomenon exist inside a bound hadron • where there are also fermions? • If it exists, it must be in a region of phase space • where gluon-gluon interaction dominates – CGC? • could we probe this phenomenon without altering its properties • by the probe? • color of the probe! - EIC inclusive measurement with a wide • range of xand Q Jianwei Qiu

14. Inclusive measurements • EM probe does not interact with gluons directly • DIS Structure functions have contributions from all partons Probe quark loops with any number of gluons attached • Leading power – photon resolves one and only one active parton • Structure function PDFs – matrix elements of two fields: Valence “Gluon” “Sea” Approximation: • Low x: Valence suppressed Sea leading in power of Jianwei Qiu

15. Parton recombination • Saturation in structure function =\= saturation in gluon PDF • Gluon distribution is a concept at leading power approximation • Power corrections – parton recombination – saturation: valence “gluon” • Multiparton correlation: Jianwei Qiu

16. Nuclear structure functions • Saturation in gluon in nucleus: • Saturation in nuclear structure functions, or medium modification: • Characteristic parameter: Jianwei Qiu

17. Semi-inclusive measurement • Final-state event structure: Single jet: Sea quark Two jet: gluon Virtuality of the quark line: • Two particle correlation: Saturation of gluon – jet structure Saturation of SF – no jet structure Jianwei Qiu

18. Single transverse spin asymmetry • TMD factorization – collinear factorization • best probe of parton’s transverse motion • P and T remove the leading power contribution • EIC is ideal for TMD formalism • Separation of initial-state and final-state effect: Siversvs Collins • Drell-Yan is harder to measure • Transition between the TMD and Collinear formalism Jianwei Qiu

19. “Exclusive” process • Deep virtual, diffractive, … GPD But, all these contribute! Jianwei Qiu