## Abstract

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 language | English (US) |
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Pages (from-to) | 444-466 |

Number of pages | 23 |

Journal | Nuclear Physics A |

Volume | 646 |

Issue number | 4 |

DOIs | |

State | Published - Feb 22 1999 |

## Keywords

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

## ASJC Scopus subject areas

- Nuclear and High Energy Physics