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Advances in QCD: DGLAP and BFKL Equations in Light Hadrons - Lecture 2 Summary

This lecture, presented by Wei Zhu from East China Normal University, explores key concepts in Quantum Chromodynamics (QCD) related to light hadrons, focusing on the DGLAP and BFKL equations. It includes derivations in the Bjorken frame, where the virtual probe has nearly zero energy and momentum, analyzing the implications for the amplitude, the structure of cold spots, and resolution of the probe. The discussion extends to the modified DGLAP and BFKL equations and their roles in understanding small-x physics and hadronic interactions.

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Advances in QCD: DGLAP and BFKL Equations in Light Hadrons - Lecture 2 Summary

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Presentation Transcript

  1. Topical Seminar on Frontier of Particle Physics 2004: QCD and Light Hadrons Lecture 2 Wei Zhu East China Normal University

  2. Outline of Lecture Two • DGLAP Equations • BFKL Equations

  3. 1. A simplest derivation of DGLAP equations Bjorken Frame, A+=0

  4. 2. A simplest derivation of BFKL equations Bjorken frame The virtual probe has almost zero-energy and zero-longitudinal momentum, so that the momentum of the probe is mainly transverse to the nucleon direction. Resolution of probe

  5. Cold spots Size of cold spot Resolution of probe Impulse approximation

  6. DGLAP amplitude (for gluon) Impulse approximation At small x and fixed Q2, beyond impulse approximation What will happen?

  7. QCD, Parton Model, Tree Level + + a b c + + e d 2 +…… + f Beyond impulse approximation

  8. BFKL DGLAP A New Equation? Modified DGLAP

  9. BFKL equation We separated out the probe vertex using the W -W approximation, where the transverse momenta of initial gluons are unvanished.

  10. Taking the leading logarithmic (1/x) approximation, one can get the total amplitude

  11. Impact Space (A. H. Mueller) Evolution Kernel

  12. Note that z1>>z2 at the LLA(1/x), we insert δ(z1-1) and obtain the evolution equation where y = ln(1/z) and

  13. Contributions from virtual diagrams Using the TOPT cutting rule

  14. Unintegrated distribution Integrated distribution

  15. Small x Physics

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