Renormalization of singular potentials and power counting

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Abstract

We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1 / r2 potential perturbed by a 1 / r4 correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range counterterms that renormalize the scattering amplitude. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis.

Original languageEnglish (US)
Pages (from-to)1304-1323
Number of pages20
JournalAnnals of Physics
Volume323
Issue number6
DOIs
Publication statusPublished - Jun 2008

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Keywords

  • Effective field theory
  • Power counting rule
  • Renormalization
  • Singular potentials

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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