Renormalization of Singular Potentials and Power Counting

Details Renormalization of Singular Potentials and Power Counting Renormalization of Singular Potentials and Power Counting

2007-07-30

arxiv.org/abs/0707.4325v2

AnnalsPhys.323:1304-1323,2008

Physics

Quantum Physics

23 pages, 6 figures

Scientific paper

10.1016/j.aop.2008.01.003

We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r^2 potential perturbed by a 1/r^4 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.

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