1 can a chaos solution in qcd evolution equation restrain high energy collider physics? 朱伟,...
TRANSCRIPT
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Can a chaos solution in QCD evolution equation restrain high
energy collider physics?
朱伟 , 沈祯祺 , 阮建红East China Normal University
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LHC - THE LARGE HADRON COLLIDER
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),( 21 QxG
),( 22 QxG
New
Physics
YT es
kx 2,1
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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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0
2,QxG
x
? DGLAP or BFKL
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QCD 演化方程研究现状
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QCD Evolution Equations
DGLAP(by Dokshitzer, Gribov, Lipatov, Altarelli and Parisi )
Small x
BFKL (by Balitsky, Fadin, Kuraev and Lipatov)GLR-MQ (by Gribov, Levin and Ryskin , Mueller and Qiu)
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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0x
DGLAP
BFKL
Corrections of Gluon Fusion
toDGLAP GLR-MQ-ZRS
BFKL BK
Fusion
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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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Multi pole Wilson lineBare gluon
Nuclear classical QCD field
(W-W field)
x
y
z
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Impulse app. Beyond Impulse app.
Saturation
GLR-MQ-ZRS equationDGLAP equations JIMWLK equations
Color Glass Condensation
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From saturation scale QS2, QCD evolution is
stoppedSaturation Scale
Qs2 ?
TRUE ?
MD-DGLAP
JIMWLK
DGLAP
2ln k
kd
kxdxg2
2 ),(
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一个人人可以想到的理论框架
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At small x and fixed Q2, beyond impulse approximation
DGLAP amplitude (for gluon)
Impulse approximation
NQ xx
What will happen?
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DGLAP
BFKL
GLR-MQ-ZRS
Modified BFKL
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QCD, Parton Model, Tree Level
+ +
++
+ +……2
a b c
d e
fBeyond impulse approximation
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αs, twist-2, a2 + virtual diagrams
BFKLαs, twist-2, b2 + virtual diagrams
DGLAP
αs2, twist-4, c2 +2ae + virtual
diagrams
GLR-MQ-ZRS
αs2, twist-4, d2 +2bf + virtual
diagrams MD-BFKL
Some Results
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难点
红外安全
如何计祘所有切割图,包括虚图?
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我们掌握的 " 绝技 "
• 基於时序微扰理论的切割法则
• 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 Q^2-axis and the k_T-plane,respectively.
• The MD-DGLAP and MD-BFKL equations also have the same evolution dynamics , which evolve on the Q^2-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 x<x_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
• 胶子分布函数是研究高能强子碰撞物理的必需知识。
• QCD 演化方程是预言胶子分布函数的可靠工具。
• DGLAP, BFKL, GLR-MQ-ZRS, BK 方程 是常用的四个方程。. 我们在一个更普遍的部分子图像中导出了
第五个 QCD 演化方程 MD-BFKL 方程 .
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在 MD-BFKL 方程中首次出现了非线性方程中常见的 Choas.
• 它预言在某一临界 x 值胶子突然消失 , 从而中断高能强子碰撞中新粒子事例随能量的增加。