On the limit cycle for the 1/r {sup 2} potential in momentum space
Journal Article
·
· Annals of Physics (New York)
- Institute for Nuclear Theory, University of Washington, Seattle, WA 98195 (United States)
The renormalization of the attractive 1/r {sup 2} potential has recently been studied using a variety of regulators. In particular, it was shown that renormalization with a square well in position space allows multiple solutions for the depth of the square well, including, but not requiring a renormalization group limit cycle. Here, we consider the renormalization of the 1/r {sup 2} potential in momentum space. We regulate the problem with a momentum cutoff and absorb the cutoff dependence using a momentum-independent counterterm potential. The strength of this counterterm is uniquely determined and runs on a limit cycle. We also calculate the bound state spectrum and scattering observables, emphasizing the manifestation of the limit cycle in these observables.
- OSTI ID:
- 20766983
- Journal Information:
- Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 321; ISSN 0003-4916; ISSN APNYA6
- Country of Publication:
- United States
- Language:
- English
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