Diagrammatic Approach to Four-Boson Systems in Effective Field Theory*

We use a diagrammatic approach to study four-boson systems using effective field theory with both two- and three-body contact interactions. Four-boson calculations (see, e.g., Ref.[1]) have been hindered by deeply bound trimers (i.e., Efimov states) which appear at relatively high cutoffs. We present a method to systematically include the deeply bound trimers in four-boson calculations, which allows us to compute tetramer binding energies at high cutoffs where deeply bound trimers exist. By using high cutoffs and including the deeply bound trimers in our calculations, we demonstrate numerically that high cutoffs are in fact needed to obtain converging and accurate tetramer binding energies. We also study the correlation between the trimer and tetramer binding energies by approaching the unitary limit. Our results agree with Ref.[2] and may be used as a benchmark for similar calculations. This method could also be used to study four-nucleon systems by including spin and isospin.

[1]Platter, H. W. Hammer, and U.-G. Meissner, The Four boson system with short range interactions, Phys. Rev. A 70, 052101 (2004), arXiv:cond-mat/0404313.

[2]Deltuva, Efimov physics in bosonic atom-trimer scattering, Phys. Rev. A 82, 040701 (2010), arXiv:1009.1295 [physics.atm-clus].