The three-boson system with short-range interactions

P. F. Bedaque, H. W. Hammer, U. Van Kolck

Research output: Contribution to journalArticlepeer-review

323 Scopus citations


We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be summed, which 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 one local three-body force counterterm and compute the running of the three-body force with the cutoff. This allows a calculation of the scattering of a particle and the two-particle bound state if the corresponding scattering length is used as input. We also obtain a model-independent relation between binding energy of a shallow three-body bound state and this scattering length. We comment on the power counting that organizes higher-order corrections and on relevance of this result for the effective field theory program in nuclear and molecular physics.

Original languageEnglish (US)
Pages (from-to)444-466
Number of pages23
JournalNuclear Physics A
Issue number4
StatePublished - Feb 22 1999


  • Effective field theory
  • He molecular systems
  • Three-body force
  • Three-body system

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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