Renormalization of the Three-Body System with Short-Range Interactions

P. F. Bedaque; H.-W. Hammer; U. van Kolck

doi:10.1103/PhysRevLett.82.463

Renormalization of the Three-Body System with Short-Range Interactions

P. F. Bedaque, H.-W. Hammer, and U. van Kolck

Phys. Rev. Lett. 82, 463 – Published 18 January 1999

Abstract

We discuss renormalization of the nonrelativistic three-body problem with short-range forces. The problem becomes nonperturbative at momenta of the order of the inverse of the two-body scattering length, and an infinite number of graphs must be summed. This summation leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in a single three-body counterterm and compute the running of the three-body force with the cutoff. We comment on the relevance of this result for the effective field theory program in nuclear and molecular physics.

Received 9 September 1998

DOI:https://doi.org/10.1103/PhysRevLett.82.463

Authors & Affiliations

P. F. Bedaque^1,*, H.-W. Hammer^2,†, and U. van Kolck^3,4,‡

¹Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195
²TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, Canada V6T 2A3
³Kellogg Radiation Laboratory, 106-38, California Institute of Technology, Pasadena, California 91125
⁴Department of Physics, University of Washington, Seattle, Washington 98195

^*Email address: bedaque@mocha.phys.washington.edu
^†Email address: hammer@triumf.ca
^‡Email address: vankolck@krl.caltech.edu