Xiangdong JiXiangdong Ji 季向东季向东University of MarylandUniversity of Maryland

& & 北京大学北京大学& & 中科院理论物理所中科院理论物理所

Outline Outline

1.1. Introduction to high-energy scatteringIntroduction to high-energy scattering

2.2. Quark-gluon plasmaQuark-gluon plasma

3.3. Small-x parton distributions?Small-x parton distributions?

4.4. High-energy elastic scatteringHigh-energy elastic scattering

5.5. pQCD at LHCpQCD at LHC

6.6. ConclusionConclusion

Introduction to high-energy Introduction to high-energy scatteringscattering

Frontiers in physics are mostly at the envelope Frontiers in physics are mostly at the envelope of physical parametersof physical parameters– Higher/lower densityHigher/lower density– Higher/lower pressureHigher/lower pressure– Higher/lower energyHigher/lower energy– Higher/lower temperature Higher/lower temperature – Higher/lower electromagnetic fields. Higher/lower electromagnetic fields. – ……

In this talk, we consider high-energy limit of In this talk, we consider high-energy limit of hadron/nuclei scattering hadron/nuclei scattering

Why high-energy?Why high-energy?

Asymptotic freedomAsymptotic freedom: strong coupling constant : strong coupling constant becomes weaker as momentum transfer becomes weaker as momentum transfer becomes large: becomes large:

Therefore, the high-energy scattering physics Therefore, the high-energy scattering physics might become simpler….might become simpler….

However, usually things are not so simple…However, usually things are not so simple…

Facilities for higher-energy Facilities for higher-energy scatteringscattering

RHICRHIC– High-energy nuclei-nuclei scattering (also High-energy nuclei-nuclei scattering (also

polarized proton scattering)polarized proton scattering)

Jlab at 12 GeVJlab at 12 GeV– High-energy (virtual)-photon-proton/nuclei High-energy (virtual)-photon-proton/nuclei

inclusive & exclusive processesinclusive & exclusive processes

LHCLHC– High-energy proton-proton scatteringHigh-energy proton-proton scattering

eRHIC (future)eRHIC (future)– High-energy electron-proton/nuclei High-energy electron-proton/nuclei

scatteringscattering

Quark-Gluon Plasma?Quark-Gluon Plasma?

Relativistic HeavyIon ColliderIn long IslandNew York

Theorists’ DreamTheorists’ Dream

1.1. Creating a thermally-equilibrated, weakly-Creating a thermally-equilibrated, weakly-coupled quark & gluon system with vacuum coupled quark & gluon system with vacuum quantum number: quantum number: A heated up vacuum?!A heated up vacuum?!

2.2. Studying the properties of this Studying the properties of this heated-up heated-up vacuum (vacuum engineering) vacuum (vacuum engineering) – quarks might be deconfined, and quarks might be deconfined, and – chiral symmetry might be restoredchiral symmetry might be restored

Creating the simple stateCreating the simple state

Thermalization?Thermalization?– It seems to occur very quickly at RHIC, but It seems to occur very quickly at RHIC, but

why?why?• Unruh-Hawking radiationUnruh-Hawking radiation: :

Radiation produced by strong external Radiation produced by strong external fields. Radiation spectrum is thermal. fields. Radiation spectrum is thermal.

[Similar electron-positron pairs production [Similar electron-positron pairs production

from strong external electric & magnetic fields.]from strong external electric & magnetic fields.]

• Strongly interacting partons…Strongly interacting partons…• ......

Phase Transition?Phase Transition?

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

Weak Interaction? Strong Weak Interaction? Strong Interaction!Interaction!

For a quark-gluon system near TFor a quark-gluon system near Tcc, there is no , there is no scale which is much large than Lambda QCD. scale which is much large than Lambda QCD. Therefore, it is natural that the interaction Therefore, it is natural that the interaction must be very strongmust be very strong 。。

Experimental evidences for strong interactionsExperimental evidences for strong interactions– Jet quenching Jet quenching – Small viscositySmall viscosity– Early equilibrationEarly equilibration– ……

Probing deconfinement and chiral Probing deconfinement and chiral symmtry breakingsymmtry breaking

Screening radius and disappearance of J/psiScreening radius and disappearance of J/psi

Rho meson peak

QuestionsQuestions

How to determine color de-confinement How to determine color de-confinement experimentally? experimentally?

Do we understand color confinement even if Do we understand color confinement even if we can create a color defined phase?we can create a color defined phase?

How do we determine chiral symmetry How do we determine chiral symmetry restoration at high T?restoration at high T?

Can we understand the mechanism for chiral Can we understand the mechanism for chiral symmetry restorationsymmetry restoration

Do we understand the origin of mass for Do we understand the origin of mass for hadrons?hadrons?

Small-x parton distributionSmall-x parton distributionin nucleiin nuclei

eRHIC:A possiblefuture

Small-xSmall-x

Consider scattering inConsider scattering in

the high energy limit. The well-know results the high energy limit. The well-know results include constant scattering cross section include constant scattering cross section (unitarity limit) and Pomeron exchanges.(unitarity limit) and Pomeron exchanges.

Can pQCD say anything about it? Can pQCD say anything about it?

BFKL pomeronBFKL pomeron, resumming large , resumming large logarithms of type logarithms of type ((ααsslns)lns)nn

– Contain non-perturbative physics, need a Contain non-perturbative physics, need a new type of factorization theorem. new type of factorization theorem.

– Violate unitarity at very high-energyViolate unitarity at very high-energy

High-energy factorizationHigh-energy factorization

High-energy factorization must involve High-energy factorization must involve transverse-momentum dependent parton transverse-momentum dependent parton distributions (TMD) which has been discussed distributions (TMD) which has been discussed also in other context (single spin asymmetry)also in other context (single spin asymmetry)

As xAs x0, there is a diffusion of transverse 0, there is a diffusion of transverse momentum down to non-perturbative region.momentum down to non-perturbative region.

The usual concept of twist expansion breaks The usual concept of twist expansion breaks down, all twist must be considereddown, all twist must be considered Feynman Feynman parton concept disappears.parton concept disappears.

Gauge invariance?Gauge invariance?

Unitarity and parton saturationUnitarity and parton saturation

At very small-x, BFKL must be corrected with At very small-x, BFKL must be corrected with higher-order contribution to obtain a unitarized higher-order contribution to obtain a unitarized cross section cross section – There has been a large literature on this in There has been a large literature on this in

recent yearsrecent years

Because of the unitarity constraint, parton Because of the unitarity constraint, parton diffusion in kdiffusion in kTT stops eventually to yield a stops eventually to yield a saturated distribution in the phase space.saturated distribution in the phase space.

2 2 4

( , , )

2cNdxg x r k

d r d k

Probing parton saturationProbing parton saturation

Parton saturation happens in the phase space. Parton saturation happens in the phase space. How to probe this?How to probe this?

a large nucleus helps! (Mclerran et al.)a large nucleus helps! (Mclerran et al.)

difficulty:difficulty:– factorization theoremsfactorization theorems– Twist-2 level shadowing (strikman et al)Twist-2 level shadowing (strikman et al)– Coherent final state rescattering (qiu et al)Coherent final state rescattering (qiu et al)

More general questionsMore general questions– Can one prove this model indepednentlyCan one prove this model indepednently– Relation with QGP physics?Relation with QGP physics?

Large-angle hadron scatteringLarge-angle hadron scattering

JeffersonLab, Virginia

Scaling ruleScaling rule

String theory was originated from hadron-String theory was originated from hadron-hadron scattering at high-energy at which the hadron scattering at high-energy at which the cross sections approach to a constant.cross sections approach to a constant.

However, string theory was ruled out as a However, string theory was ruled out as a fundamental theory of strong interaction fundamental theory of strong interaction because of the large angle hadron-hadron because of the large angle hadron-hadron scatteringscattering

ExamplesExamples

Generalized power countingGeneralized power counting

Helicity counting rule is established without the Helicity counting rule is established without the consideration of the orbital motion of parton.consideration of the orbital motion of parton.

Ji, Ma, & Yuan have considered the orbital Ji, Ma, & Yuan have considered the orbital motion of partons and derived a generalized motion of partons and derived a generalized counting.counting.

The counting has been verified by Brodsky and The counting has been verified by Brodsky and de Teramond through ADS/CFT correspondence. de Teramond through ADS/CFT correspondence.

H

zHH ln

sdt

d )1||(2

~ PRL90:241601,2003

Example for generalized counting Example for generalized counting rulerule

PauliForm factorof the proton

N to DeltaTransition:

Why does scaling rule work so well?Why does scaling rule work so well?

There is no reason to work at such low energyThere is no reason to work at such low energy– Leading-order contribution typically gives Leading-order contribution typically gives

very small part of the total.very small part of the total.– High-twist contribution is expected to be High-twist contribution is expected to be

largelarge

Yet, scaling works so beautifully.Yet, scaling works so beautifully.

Frozen effective coupling?Frozen effective coupling? A bit similar to constituent quark model, A bit similar to constituent quark model,

– The three-quark configuration contributes a The three-quark configuration contributes a small amount to any physical observablesmall amount to any physical observable

– Higher-Fock states must be important.Higher-Fock states must be important. Constituent quark mass?Constituent quark mass?

Re-summation of large double Re-summation of large double logarithmslogarithms

Large-hadronCollider, CERN

LHC MissionLHC Mission

Search for mechanisms responsible for Search for mechanisms responsible for electroweak symmetry breakingelectroweak symmetry breaking– Higgs boson productionHiggs boson production– How is the electroweak scale generated?How is the electroweak scale generated?

Search for physics beyond standard modelSearch for physics beyond standard model– SupersymmetrySupersymmetry– Large extra dimensionLarge extra dimension– Low-scale string compatificationLow-scale string compatification

Heavy-ion collisionHeavy-ion collision

Higgs boson productionHiggs boson production

Gluon-gluonfusion

Transverse-momentum DistributionsTransverse-momentum Distributions

Inclusive Higgs production is usually swamped by QCD Inclusive Higgs production is usually swamped by QCD background. However, signal identification and signal background. However, signal identification and signal to background ratio can be improved by looking at to background ratio can be improved by looking at production at finite Qproduction at finite QTT..

The most important cross section is dominated by low The most important cross section is dominated by low QQTT«M«MHH, with Q, with QTT»»ΛΛQCDQCD

In perturbative expansions, there are large double In perturbative expansions, there are large double logarithms associate with each coupling constant.logarithms associate with each coupling constant.

To have accurate prediction, one must some over To have accurate prediction, one must some over these large logarithms.these large logarithms.– Higgs production, jet production at LHCHiggs production, jet production at LHC

2

2ln ( 2 )n m T

sH

Qm n

M

Resummation effectsResummation effects

Methods of resummationMethods of resummation

Physical approachPhysical approach: all of these logarithms arise : all of these logarithms arise from the soft-gluon radiations. Study these soft from the soft-gluon radiations. Study these soft radiations systematically radiations systematically (Dokshitzer et al)(Dokshitzer et al)

Factorization:Factorization: Develop factorization theorems for Develop factorization theorems for processes involving multiple perturbative scales processes involving multiple perturbative scales and derive rapidity evolution equation (Collins-and derive rapidity evolution equation (Collins-Soper equation) Soper equation) (collins, soper & sterman…)(collins, soper & sterman…)

Soft-collinear effective field theorySoft-collinear effective field theory: Integrate out : Integrate out hard modes, collinear modes systematically.hard modes, collinear modes systematically.

(Bauer, fleming, et al) (Bauer, fleming, et al)

Soft-Collinear Theory & ChallengeSoft-Collinear Theory & Challenge

Methodology:Methodology: – Step-I: Integrate out the hard mode at scale Q.Step-I: Integrate out the hard mode at scale Q.– Step-II: integrate out the collinear mode at Step-II: integrate out the collinear mode at

scale Qscale QTT. .

Progress: Progress: – Confirmed the existing results in DIS, Drell-Confirmed the existing results in DIS, Drell-

Yan, & Higgs production up to next-to-leading Yan, & Higgs production up to next-to-leading logarithms. (Manohar, Idilbi & Ji, C. S. Li et al)logarithms. (Manohar, Idilbi & Ji, C. S. Li et al)

Challenge:Challenge:– Extending the method to next-to-next-to Extending the method to next-to-next-to

leading logarithms (NNLO). (Idilbi, Ji & Yuan)leading logarithms (NNLO). (Idilbi, Ji & Yuan)

ConclusionConclusion

Asymptotic freedom discovered more than 30 Asymptotic freedom discovered more than 30 years ago still chart directions in high-energy years ago still chart directions in high-energy nuclear research.nuclear research.

There are many outstanding questions which There are many outstanding questions which can only be answered by going beyond simple can only be answered by going beyond simple perturbative analysis…perturbative analysis…– We cannot really creating weakly interacting plasmaWe cannot really creating weakly interacting plasma– Very small-x region has a small coupling, but not Very small-x region has a small coupling, but not

perturbative.perturbative.– We don’t really understand the scaling rules.We don’t really understand the scaling rules.– Is large double logarithms under control?Is large double logarithms under control?

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