Renormalization of singular potentials and power counting

B. Long; U. van Kolck

doi:10.1016/j.aop.2008.01.003

Renormalization of singular potentials and power counting

B. Long
, U. van Kolck

Research output: Contribution to journal › Article › peer-review

95 Scopus citations

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)
Pages (from-to)	1304-1323
Number of pages	20
Journal	Annals of Physics
Volume	323
Issue number	6
DOIs	https://doi.org/10.1016/j.aop.2008.01.003
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

Access to Document

10.1016/j.aop.2008.01.003

Cite this

@article{8cb0bf7af85a406c90afe04ea2c5c085,

title = "Renormalization of singular potentials and power counting",

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.",

keywords = "Effective field theory, Power counting rule, Renormalization, Singular potentials",

author = "B. Long and \{van Kolck\}, U.",

note = "Funding Information: This work was supported in part by the US Department of Energy (BL, UvK), by a Galileo Circle Scholarship from the College of Science of the University of Arizona (BL), by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (UvK), and by Brazil{\textquoteright}s FAPESP under a Visiting Professor grant (UvK). UvK would like to thank the hospitality of the Kernfysisch Versneller Instituut at Rijksuniversiteit Groningen, the Instituto de F{\'i}sica Te{\'o}rica of the Universidade Estadual Paulista, and the Instituto de F{\'i}sica of the Universidade de S{\~a}o Paulo where part of this work was completed.",

year = "2008",

month = jun,

doi = "10.1016/j.aop.2008.01.003",

language = "English (US)",

volume = "323",

pages = "1304--1323",

journal = "Annals of Physics",

issn = "0003-4916",

publisher = "Academic Press Inc.",

number = "6",

}

TY - JOUR

T1 - Renormalization of singular potentials and power counting

AU - Long, B.

AU - van Kolck, U.

N1 - Funding Information: This work was supported in part by the US Department of Energy (BL, UvK), by a Galileo Circle Scholarship from the College of Science of the University of Arizona (BL), by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (UvK), and by Brazil’s FAPESP under a Visiting Professor grant (UvK). UvK would like to thank the hospitality of the Kernfysisch Versneller Instituut at Rijksuniversiteit Groningen, the Instituto de Física Teórica of the Universidade Estadual Paulista, and the Instituto de Física of the Universidade de São Paulo where part of this work was completed.

PY - 2008/6

Y1 - 2008/6

N2 - 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.

AB - 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.

KW - Effective field theory

KW - Power counting rule

KW - Renormalization

KW - Singular potentials

UR - https://www.scopus.com/pages/publications/42649112039

UR - https://www.scopus.com/pages/publications/42649112039#tab=citedBy

U2 - 10.1016/j.aop.2008.01.003

DO - 10.1016/j.aop.2008.01.003

M3 - Article

AN - SCOPUS:42649112039

SN - 0003-4916

VL - 323

SP - 1304

EP - 1323

JO - Annals of Physics

JF - Annals of Physics

IS - 6

ER -

Renormalization of singular potentials and power counting

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this