Solvability, Consistency and the Renormalization Group in Large-$N_c$ Models of Hadrons

Abstract

We establish the following fundamentals about Lagrangian models of meson-baryon interactions in the large-$N_c$ limit: 1. Calculating the leading-order contribution to $1$-meson/$2$-baryon Green's functions in the $1/N_c$ expansion involves summing an infinite class of divergent Feynman diagrams. So long as the bare Lagrangian properly obeys all large-$N_c$ selection rules, this all-loops resummation is accomplished exactly by solving coupled classical field equations with a short-distance cutoff. 2. The only effect of the resummation is to renormalize the bare Yukawa couplings, baryon masses and hyperfine baryon mass splittings of the model. 3. In the process, the large-$N_c$ renormalization group flow of these bare parameters is completely determined. We conjecture that variants of the Skyrme model emerge as UV fixed points of such flows.

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References in corpus (4)

• Baryon-Pion Couplings from Large-N QCD
• 1/N Corrections to the Baryon Axial Currents in QCD
• On Spin Independence in Large $N_c$ Baryons
• Baryon Hyperfine Mass Splittings in Large N QCD

Cited by in corpus (11)

• On the Manifestation of Chiral Symmetry in Nuclei and Dense Nuclear Matter
• The Spin-Flavor Dependence of Nuclear Forces from Large-N QCD
• Baryon Mass Splittings in the 1/N_c Expansion
• From Chiral Mean Field to Walecka Mean Field and Kaon Condensation
• Large-N_c Baryons
• Chiral Lagrangian for Baryons in the $1/N_c$ Expansion
• Skyrmion Quantization and the Decay of the Delta
• Semiclassical Meson-Baryon Dynamics from Large-Nc QCD
• Heavy Meson Electromagnetic Mass Differences from QCD
• From Effective Lagrangians, to Chiral Bags, to Skyrmions with the Large-N_c Renormalization Group
• Chiral Divergent Properties of Hadrons in the Large-N_c Limit