Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances

Resonances are of particular importance in the scattering of composite particles in quantum mechanics. We build an effective field theory for two-body scattering which includes a low-energy S -wave resonance. Our starting point is the most general Lagrangian with short-range interactions. We demonstrate that these interactions can be organized into various orders so as to generate a systematic expansion for an S matrix with two low-energy poles. The pole positions are restricted by renormalization at leading order, where the common feature is a non-positive effective range. We carry out the expansion explicitly to next-to-leading order and illustrate how it systematically accounts for the results of a toy model — a spherical well with a delta shell at its border.

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23 pages, 12 figures

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Figures(12)

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