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The Three-Boson System with Short-Range Interactions

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

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P. F. Bedaque, H. -W. Hammer, U. van Kolck. 1998-11-13. The Three-Boson System with Short-Range Interactions. https://doi.org/10.1016/s0375-9474(98)00650-2

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