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 language | English (US) |
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Pages (from-to) | 1304-1323 |
Number of pages | 20 |
Journal | Annals of Physics |
Volume | 323 |
Issue number | 6 |
DOIs | |
State | Published - Jun 2008 |
Externally published | Yes |
Keywords
- Effective field theory
- Power counting rule
- Renormalization
- Singular potentials
ASJC Scopus subject areas
- General Physics and Astronomy