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

Outline 1.Introduction to high-energy scattering 2.Quark-gluon plasma 3.Small-x parton distributions? 4.High-energy elastic scattering 5.pQCD at LHC 6.Conclusion

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

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

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

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

Theorists’ Dream 1.Creating a thermally-equilibrated, weakly-coupled quark & gluon system with vacuum quantum number: A heated up vacuum?! 2.Studying the properties of this heated-up vacuum (vacuum engineering) –quarks might be deconfined, and –chiral symmetry might be restored

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

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.

Weak Interaction? Strong Interaction!  For a quark-gluon system near T c, 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 –…

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

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?

Small-x parton distribution in nuclei eRHIC: A possible future

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 (α s lns) n BFKL pomeron, resumming large logarithms of type (α s lns) n –Contain non-perturbative physics, need a new type of factorization theorem. –Violate unitarity at very high-energy

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?

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 k T stops eventually to yield a saturated distribution in the phase space.

Probing parton saturation  Parton saturation happens in the phase space. How to probe this? a large nucleus helps! (Mclerran et al.) 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?

Large-angle hadron scattering Jefferson Lab, Virginia

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

Examples

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

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

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. Yet, scaling works so beautifully. Frozen effective coupling? 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? Constituent quark mass?

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

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

Higgs boson production Gluon-gluon fusion

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 Q T.  The most important cross section is dominated by low Q T «M H, with Q T »Λ QCD  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

Resummation effects

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)

Soft-Collinear Theory & Challenge  Methodology: –Step-I: Integrate out the hard mode at scale Q. –Step-II: integrate out the collinear mode at scale Q T.  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)

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! There are unique opportunities for physicists from china to contribute!