Xiangdong Ji 季向东 University of Maryland & 北京大学 & 中科院理论物理所

1. Open Questions in High-Energy Scattering Open Questions in High-Energy Scattering Xiangdong Ji季向东 University of Maryland & 北京大学 & 中科院理论物理所

2. Outline • Introduction to high-energy scattering • Quark-gluon plasma • Small-x parton distributions? • High-energy elastic scattering • pQCD at LHC • Conclusion

3. Introduction to high-energy scattering • Frontiers in physics are mostly at the envelope of physical parameters • Higher/lower density • Higher/lower pressure • Higher/lower energy • Higher/lower temperature • Higher/lower electromagnetic fields. • … • In this talk, we consider high-energy limit of hadron/nuclei scattering

4. Why high-energy? • Asymptotic freedom: strong coupling constant becomes weaker as momentum transfer becomes large: Therefore, the high-energy scattering physics might become simpler…. • However, usually things are not so simple…

5. Facilities for higher-energy scattering • RHIC • High-energy nuclei-nuclei scattering (also polarized proton scattering) • Jlab at 12 GeV • High-energy (virtual)-photon-proton/nuclei inclusive & exclusive processes • LHC • High-energy proton-proton scattering • eRHIC (future) • High-energy electron-proton/nuclei scattering

6. Quark-Gluon Plasma? Relativistic Heavy Ion Collider In long Island New York

7. Theorists’ Dream • Creating a thermally-equilibrated, weakly-coupled quark & gluon system with vacuum quantum number: A heated up vacuum?! • Studying the properties of this heated-up vacuum (vacuum engineering) • quarks might be deconfined, and • chiral symmetry might be restored

8. Creating the simple state • Thermalization? • It seems to occur very quickly at RHIC, but why? • Unruh-Hawking radiation: Radiation produced by strong external fields. Radiation spectrum is thermal. [Similar electron-positron pairs production from strong external electric & magnetic fields.] • Strongly interacting partons… • ...

9. Phase Transition? • It seems that high-T phase of the vacuum is achieved not by a phase transition (no thermal singularity), but by a crossover.

10. Weak Interaction? Strong Interaction! • For a quark-gluon system near Tc, there is no scale which is much large than Lambda QCD. Therefore, it is natural that the interaction must be very strong。 • Experimental evidences for strong interactions • Jet quenching • Small viscosity • Early equilibration • …

11. Probing deconfinement and chiral symmtry breaking • Screening radius and disappearance of J/psi Rho meson peak

12. Questions • How to determine color de-confinement experimentally? • Do we understand color confinement even if we can create a color defined phase? • How do we determine chiral symmetry restoration at high T? • Can we understand the mechanism for chiral symmetry restoration • Do we understand the origin of mass for hadrons?

13. Small-x parton distributionin nuclei eRHIC: A possible future

14. Small-x • Consider scattering in • the high energy limit. The well-know results include constant scattering cross section (unitarity limit) and Pomeron exchanges. • Can pQCD say anything about it? BFKL pomeron, resumming large logarithms of type (αslns)n • Contain non-perturbative physics, need a new type of factorization theorem. • Violate unitarity at very high-energy

15. High-energy factorization • High-energy factorization must involve transverse-momentum dependent parton distributions (TMD) which has been discussed also in other context (single spin asymmetry) • As x0, there is a diffusion of transverse momentum down to non-perturbative region. • The usual concept of twist expansion breaks down, all twist must be considered Feynman parton concept disappears. • Gauge invariance?

16. Unitarity and parton saturation • At very small-x, BFKL must be corrected with higher-order contribution to obtain a unitarized cross section • There has been a large literature on this in recent years • Because of the unitarity constraint, parton diffusion in kT stops eventually to yield a saturated distribution in the phase space.

17. Probing parton saturation • Parton saturation happens in the phase space. How to probe this? a large nucleus helps! (Mclerran et al.) difficulty: • factorization theorems • Twist-2 level shadowing (strikman et al) • Coherent final state rescattering (qiu et al) • More general questions • Can one prove this model indepednently • Relation with QGP physics?

18. Large-angle hadron scattering Jefferson Lab, Virginia

19. Scaling rule • String theory was originated from hadron-hadron scattering at high-energy at which the cross sections approach to a constant. • However, string theory was ruled out as a fundamental theory of strong interaction because of the large angle hadron-hadron scattering

20. Examples

21. Generalized power counting • Helicity counting rule is established without the consideration of the orbital motion of parton. • Ji, Ma, & Yuan have considered the orbital motion of partons and derived a generalized counting. • The counting has been verified by Brodsky and de Teramond through ADS/CFT correspondence. PRL90:241601,2003

22. Example for generalized counting rule Pauli Form factor of the proton N to Delta Transition:

23. Why does scaling rule work so well? • There is no reason to work at such low energy • Leading-order contribution typically gives very small part of the total. • High-twist contribution is expected to be large Yet, scaling works so beautifully. Frozen effective coupling? • A bit similar to constituent quark model, • The three-quark configuration contributes a small amount to any physical observable • Higher-Fock states must be important. Constituent quark mass?

24. Re-summation of large double logarithms Large-hadron Collider, CERN

25. LHC Mission • Search for mechanisms responsible for electroweak symmetry breaking • Higgs boson production • How is the electroweak scale generated? • Search for physics beyond standard model • Supersymmetry • Large extra dimension • Low-scale string compatification • Heavy-ion collision

26. Higgs boson production Gluon-gluon fusion

27. Transverse-momentum Distributions • Inclusive Higgs production is usually swamped by QCD background. However, signal identification and signal to background ratio can be improved by looking at production at finite QT. • The most important cross section is dominated by low QT«MH, with QT»ΛQCD • In perturbative expansions, there are large double logarithms associate with each coupling constant. • To have accurate prediction, one must some over these large logarithms. • Higgs production, jet production at LHC

28. Resummation effects

29. Methods of resummation • Physical approach: all of these logarithms arise from the soft-gluon radiations. Study these soft radiations systematically (Dokshitzer et al) • Factorization: Develop factorization theorems for processes involving multiple perturbative scales and derive rapidity evolution equation (Collins-Soper equation) (collins, soper & sterman…) • Soft-collinear effective field theory: Integrate out hard modes, collinear modes systematically. (Bauer, fleming, et al)

30. Soft-Collinear Theory & Challenge • Methodology: • Step-I: Integrate out the hard mode at scale Q. • Step-II: integrate out the collinear mode at scale QT. • Progress: • Confirmed the existing results in DIS, Drell-Yan, & Higgs production up to next-to-leading logarithms. (Manohar, Idilbi & Ji, C. S. Li et al) • Challenge: • Extending the method to next-to-next-to leading logarithms (NNLO). (Idilbi, Ji & Yuan)

31. Conclusion • Asymptotic freedom discovered more than 30 years ago still chart directions in high-energy nuclear research. • There are many outstanding questions which can only be answered by going beyond simple perturbative analysis… • We cannot really creating weakly interacting plasma • Very small-x region has a small coupling, but not perturbative. • We don’t really understand the scaling rules. • Is large double logarithms under control? There are unique opportunities for physicists from china to contribute!