Xiangdong Ji ???

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Open Questions in High-Energy Scattering
Open Questions in High-Energy Scattering

• Xiangdong Ji ???
• University of Maryland
• ????
• ????????

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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

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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

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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

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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

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

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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
• ...

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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.

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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

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Probing deconfinement and chiral symmtry breaking

• Screening radius and disappearance of J/psi

Rho meson peak
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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?

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Small-x parton distributionin nuclei
eRHIC A possible future
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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 (aslns)n
• Contain non-perturbative physics, need a new type
  of factorization theorem.
• Violate unitarity at very high-energy

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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?

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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.

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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?

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Large-angle hadron scattering
Jefferson Lab, Virginia
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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

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Examples
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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.

PRL90241601,2003
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Example for generalized counting rule
Pauli Form factor of the proton
N to Delta Transition
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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?

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

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Higgs boson production
Gluon-gluon fusion
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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 QTMH, with QT?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

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Resummation effects
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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)

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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)

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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 dont really understand the scaling rules.
• Is large double logarithms under control?
• There are unique opportunities for physicists
  from china to contribute!