1. 1 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

2. 2 LHC - THE LARGE HADRON COLLIDER

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4. 4 New Physics 1

5. 5 The kinematic domains probed by the various experiments, shown together with the partons that they constrain

6. 6 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.

7. 7 ? DGLAP or BFKL 2

8. 8 QCD 演化方程研究现状

9. 9 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

10. 10 DGLAP BFKL Corrections of Gluon Fusion to DGLAP GLR-MQ-ZRS BFKL BK Fusion 3

11. 11 DGLAP Equation Dokshitzer-Gribov-Lipatov 1975 Altarelli-Parisi 1977

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13. 13 BFKL Equation Balitsky-Fadin-Kuraev-Lipatov 1975-1978

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15. 15 GLR-MQ-ZRS Equation Gribov-Levin-Ryskin 1983

16. 16 Where is the GLR equations?

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18. 18 Mueller-Qiu 1986

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20. 20 Zhu-Ruan-Shen 1999-2005

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22. 22 BK Equation Balitsky-Kovchegov 1996-2000

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25. 25 JIMWLK Equation Jalilia-Marian, Iancu,McLerra,Weigert,Leonidov and Kovne 1997-2001

26. 26 Multi pole Wilson line Bare gluon Nuclear classical QCD field (W-W field) x y z

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28. 28 Impulse app. Beyond Impulse app. Saturation GLR-MQ-ZRS equationDGLAP equationsJIMWLK equations Color Glass Condensation 28

29. 29 From saturation scale Q S 2, QCD evolution is stopped Saturation Scale Q s 2 ? TRUE ? MD-DGLAP JIMWLK DGLAP

30. 30 一个人人可以想到的理论框架

31. 31 At small x and fixed Q 2, beyond impulse approximation DGLAP amplitude (for gluon) Impulse approximation What will happen?

32. 32 DGLAP BFKL GLR-MQ-ZRS Modified BFKL

33. 33 QCD, Parton Model, Tree Level ++ ++ + +…… 2 ab c d e f Beyond impulse approximation

34. 34 α s, twist-2, a 2 + virtual diagrams BFKLα s, twist-2, b 2 + virtual diagrams DGLAP α s 2, twist-4, c 2 +2ae + virtual diagrams GLR-MQ-ZRS α s 2, twist-4, d 2 +2bf + virtual diagramsMD-BFKL Some Results

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36. 36 难点 红外安全 如何计祘所有切割图，包括虚图？

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41. 41 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);

42. 42 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.

43. 43 MD-BFKL Equation NEW

44. 44 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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48. 48 Schematic kinematic regions of four evolution equations

49. 49 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

50. 50 Input distribution

51. 51 Gluon disappearance bellower the saturation region.

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57. 57 Lyapunov exponents

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60. 60 The rapid increase of the gluon density with increasing energy will be stopped due to the gluon disappearance when x<x_c

61. 61 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.

62. 62 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.

63. 63 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.

64. 64 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。