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On the limit cycle for the 1/r^2 potential in momentum space

H. -W. Hammer·Brian G. Swingle
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Abstract

The renormalization of the attractive 1/r^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^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.

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H. -W. Hammer, Brian G. Swingle. 2005-03-08. On the limit cycle for the 1/r^2 potential in momentum space. https://doi.org/10.1016/j.aop.2005.04.017

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