A Multiple Commutator Formula for the Sum of Feynman Diagrams

Abstract

In the presence of a large parameter, such as mass or energy, leading behavior of individual Feynman diagrams often get cancelled in the sum. This is known to happen in large-$N_c$ QCD in the presence of a baryon, and also in the case of high-energy electron-electron as well as quark-quark scatterings. We present an exact combinatorial formula, involving multiple commutators of the vertices, which can be used to compute such cancellations. It is a non-abelian generalization of the eikonal formula, and will be applied in subsequent publications to study the consistency of large-$N_c$ QCD involving baryons, as well as high-energy quark-quark scattering in ordinary QCD.

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References in corpus (12)

• The 1/N Expansion for Baryons
• Baryon-Pion Couplings from Large-N QCD
• Spin-Flavor Structure of Large N Baryons
• 1/N Corrections to the Baryon Axial Currents in QCD
• Baryons from Quarks in the $1/N$ Expansion
• On Spin Independence in Large $N_c$ Baryons
• Baryon Hyperfine Mass Splittings in Large N QCD
• Baryon Magnetic Moments in a Simultaneous Expansion in $1/N$ and $m_s$
• Light Quark Spin-Flavor Symmetry for Baryons Containing a Heavy Quark in Large N QCD
• Hyperfine Mass Splittings of Baryons Containing a Heavy Quark in Large N QCD
• Baryons with Many Colors and Flavors
• Pion-Nucleon Scattering in a Large-N Sigma Model

Cited by in corpus (12)

• Decomposition of Time-Ordered Products and Path-Ordered Exponentials
• The large-N(c) nuclear potential puzzle
• Resolving the Large-N Nuclear Potential Puzzle
• Consistency of the Baryon-Multimeson Amplitudes for Large-N_c QCD
• Bose-Einstein Interference in the Passage of a Jet in a Dense Medium
• Time Ordering, Energy Ordering, and Factorization
• Feynman Amplitude Approach to study the Passage of a Jet in a Medium
• Unitarized Diffractive Scattering in QCD and Application to Virtual Photon Total Cross Sections
• Small-Recoil Approximation
• Novel Bose-Einstein Interference in the Passage of a Fast Particle in a Dense Medium
• Unitarization of Total Cross Section and Coherent Effect in pQCD
• Evaluation of Multiloop Diagrams via Lightcone Integration