What is the Leading Color Approximation in QCD?

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SUMMARY

The leading color approximation in Quantum Chromodynamics (QCD) is defined under the condition Nc ∼ Nf ≫ 1, often referred to as the large-Nc limit. This approximation allows for the simplification of algebraic relations in SU(N) by neglecting terms that scale with 1/N. The seminal paper by 't Hooft, titled "A planar diagram theory for strong interactions" (Nucl. Phys. B72, 1974), establishes that only planar diagrams contribute in this limit, which are characterized by the absence of crossing quark lines.

PREREQUISITES
  • Understanding of Quantum Chromodynamics (QCD)
  • Familiarity with SU(N) group theory
  • Knowledge of large-Nc approximations
  • Basic grasp of Feynman diagrams and their representations
NEXT STEPS
  • Read 't Hooft's paper on large-Nc approximations in QCD
  • Explore the implications of planar diagrams in QCD calculations
  • Investigate the role of color structures in particle interactions
  • Study advanced topics in QCD, such as non-perturbative effects
USEFUL FOR

Researchers and students in theoretical physics, particularly those focusing on Quantum Chromodynamics and particle physics, will benefit from this discussion.

earth2
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Hey folks,

i recently stumbled across the notion "leading color" in some qcd paper. What puzzles me is, how can the color structure in qcd give rise to leading terms? Does any of you have an example for this? Or an explanation?

Thanks!
earth2
 
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Leading color approximation is defined as Nc ∼ Nf ≫ 1; sometimes you will find leading color = large-Nc. This may be slightly different.

In the large-Nc approximation you make use of the fact that in certain algebraic relations in SU(N), e.g. in contractions of SU(N) matrices, you get terms with 1/N which you neglect in this limit. The first paper on large-Nc from 't Hooft (A planar diagram theory for strong interactions. Nucl. Phys. B72 (1974) 461 - 473.) shows that for large-Nc only planar diagrams contribute; planar means that there are no diagrams where two quark lines cross.
 

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