The large-N{sub c} renormalization group

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In this talk, we review how effective theories of mesons and baryons become exactly soluble in the large-N{sub c}, limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N{sub c}, selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N{sub c}. We show how all these leading-order dia, grams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius {Lambda}{sup {minus}1} ({Lambda} being the UV cutoff of the ... continued below

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18 p.

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Dorey, N. & Mattis, M.P. May 1, 1995.

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  • Dorey, N. University Coll. of Swansea (United Kingdom). Dept. of Physics
  • Mattis, M.P. Los Alamos National Lab., NM (United States)

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Description

In this talk, we review how effective theories of mesons and baryons become exactly soluble in the large-N{sub c}, limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N{sub c}, selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N{sub c}. We show how all these leading-order dia, grams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius {Lambda}{sup {minus}1} ({Lambda} being the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r {le} {Lambda}{sup {minus}1}. The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-{Delta} hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N{sub c}, renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as {Lambda} {yields} {infinity}.

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18 p.

Notes

INIS; OSTI as DE95011992

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  • Nuclear and particle physics conference, Seoul (Korea, Republic of), 6-10 Feb 1995

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  • Other: DE95011992
  • Report No.: LA-UR--95-1490
  • Report No.: CONF-950293--2
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 100310
  • Archival Resource Key: ark:/67531/metadc618617

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • May 1, 1995

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

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  • July 28, 2016, 7:36 p.m.

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Dorey, N. & Mattis, M.P. The large-N{sub c} renormalization group, article, May 1, 1995; New Mexico. (digital.library.unt.edu/ark:/67531/metadc618617/: accessed August 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.