Can a chaos solution in QCD evolution equation restrain high energy collider physics?

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Can a chaos solution in QCD evolution equation
restrain high energy collider physics?

• ??, ???, ???
• East China Normal University

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LHC - THE LARGE HADRON COLLIDER
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The kinematic domains probed by the various
experiments, shown together with the partons that
they constrain
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Gluon distribution and unintegrated gluon
distribution

• The gluon distributions of the nucleon cannot be
  extracted directly from the measured structure
  functions in deep inelastic scattering
  experiments.
• They mainly are predicted by using the QCD
  evolution equations.

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DGLAP or BFKL
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QCD????????
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QCD Evolution Equations
BFKL (by Balitsky, Fadin, Kuraev and Lipatov)
GLR-MQ (by Gribov, Levin and Ryskin , Mueller and
Qiu)
Small x
DGLAP (by Dokshitzer, Gribov, Lipatov, Altarelli
and Parisi )
Modified DGLAP (by Zhu, Ruan and Shen)
JIMWLK (by Jalilian-Marian, Iancu, McLerran,
Weigert, Leonidov and Kovner)
Balitsky-Kovchegov equation
Various versions of the evolution equations based
on the color dipole picture
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Fusion
Corrections of Gluon Fusion
DGLAP BFKL
DGLAP GLR-MQ-ZRS BFKL BK
to
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DGLAP Equation

• Dokshitzer-Gribov-Lipatov 1975
• Altarelli-Parisi 1977

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BFKL Equation

• Balitsky-Fadin-Kuraev-Lipatov 1975-1978

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GLR-MQ-ZRS Equation

• Gribov-Levin-Ryskin 1983

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Where is the GLR equations?
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Mueller-Qiu 1986
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Zhu-Ruan-Shen 1999-2005
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BK Equation

• Balitsky-Kovchegov 1996-2000

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JIMWLK Equation

• Jalilia-Marian, Iancu,McLerra,Weigert,Leonidov
  and Kovne 1997-2001

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Color Glass Condensation
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From saturation scale QS2, QCD evolution is
stopped
Saturation Scale
DGLAP
MD-DGLAP
JIMWLK
TRUE ?
Qs2 ?
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?????????????
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DGLAP amplitude (for gluon)
Impulse approximation

• At small x and fixed Q2, beyond impulse
  approximation

What will happen?
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BFKL
DGLAP
Modified BFKL
GLR-MQ-ZRS
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QCD, Parton Model, Tree Level


a
b
c


e
d
2


f
Beyond impulse approximation
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Some Results
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??

• ????
• ?????????,?????

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?????"??"

• ?????????????
• W. Zhu, Nucl. Phys. B551, 245 (1999).
• W. Zhu and J.H. Ruan, Nucl. Phys. B559,
  378(1999).
• W. Zhu, Z.Q. Shen and J.H. Ruan, Nucl. Phys.
  B692, 417 (2004)

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Time ordred perturbation theory

• The sum of cut graphs is necessary not only for
  infrared safety, but also for collecting the
  leading contributions and restoring unitarity.
• The TOPT-cutting rules are proposed to present
  the simple connections among the relating
  cut-diagrams including real- and virtual-diagrams.

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MD-BFKL Equation NEW
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Consistency of four evolution equations

• The DGLAP and BFKL equations have the same
  evolution dynamics, which evolve on the Q2-axis
  and the k_T-plane,respectively.
• The MD-DGLAP and MD-BFKL equations also have the
  same evolution dynamics , which evolve on the
  Q2-axis and the k_T-plane, respectively.

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Schematic kinematic regions of four evolution
equations
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Solutions of the MD-BFKL equation

• A stronger shadowing suppresses the gluon density
  and even leads to the gluon disappearance bellow
  the saturation region.
• This unexpected effect is caused by a chaotic
  solution of the new equation

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Input distribution
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Gluon disappearance bellower the saturation
region.
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Lyapunov exponents
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The rapid increase of the gluon density with
increasing energy will be stopped due to the
gluon disappearance when xltx_c
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Discussions

• Many higher order corrections areneglected, such
  as possible mixture of the operators with
  different twists, the NLL (next leading
  logarithmic) and NLO (next leading order)
  corrections, singularities from
  non-perturbativeparts in the factorization
  procedure.

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Will the chaos effect in the MD-BFKL equation
disappear after further corrections are
considered?

• We could expect that more interesting chaos
  phenomena will appear in new MD-BFKL
  equation.These phenomena will most be interested
  to high energy physics and nonlinear science.

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In summary

• ???????????????????????
• QCD???????????????????
• DGLAP, BFKL, GLR-MQ-ZRS, BK??
• ?????????
• . ?????????????????????QCD????MD-BFKL??.

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?MD-BFKL?????????????????Choas.

• ????????x???????,???????????????????????