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Wei Zhu East China Normal University KITPC 20 12 . 07. QCD evolution equations at s mall x (A simple physical picture). A simple physical picture. Two strange things that you have never heard. I. Strange behavior of QGP II. A lost equation.

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## QCD evolution equations at s mall x (A simple physical picture)

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**Wei Zhu**East China Normal University KITPC 2012.07. QCD evolution equations at small x (A simple physical picture) A simple physical picture**Two strange things that you have never heard**• I. Strange behavior of QGP • II. A lost equation**Review of QCD evolution equations at small x**in a unified partonic framework • At small x, beyond impulse approximation DGLAP amplitude (for gluon) Impulse approximation**Small x**Beyond Impulse app. Impulse app. What will be happen?**The correlations among the initial partons are neglected in**the derivation of the DGLAP equation. This assumption is invalid in the higher density region of partons, where the parton wave functions begin tospatially overlap. The corrections of the correlations among initial gluons to the elementary amplitude at small x should be considered. We add a possible initial gluon to Fig.1a step by step.**Dokshitzer, Gribov, Lipatov,**Altarelli and Parisi Balitsky, Fadin, Kuraev and Lipatov BFKL Nonperturbative correlation DGLAP Perturbative correlation GLR-MQ-ZRS GLR-MQ-ZRS Gribov, Levin and Ryskin Mueller and Qiu Zhu, Ruan Shen**DGLAP**DGLAP**Infrared divergences**• The evolution kernel has singularities ,which relate to the emission or absorption of quantawith zero momentum. • Since a correct theory is IR safe, the IR divergences are cancelled by combining real-and virtual-soft gluon emissions.**TOPT Cutting Rules**• F.E. Close, J. Qiu and R.G. Roberts, Phys. Rev. D 40 (1989) 2820. • 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);**TOPT-Cutting rule**• List all possible TOPT diagrams with different cuts. • The contributions of the cut diagrams • have the identical integral kernel with only the following different factors R:**(a)The sign in the first factor is determined by the energy**deficits; • (b)The second factor takes a value of 1/2 if the probe-vertex inserts in the initial line; • (c) function relates to the probe vertex.**BFKL**2**Comparing with the dipole picture**A strong assumption in the dipole approach is that the transverse size of the dipole is "frozen" during the interacting time.**BFKL**DGLAP**BFKL**DGLAP GLR-MQ-ZRS GLR-MQ-ZRS**GLR-MQ vs ZRS**• AGK cutting rule vs TOPT cutting rule**Different predictions**• Only shadowing effect Shadosing • and • Antishadowing effects • Looking for the antishadowing effect

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