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Identification of shallow two-body bound states in finite volume

Presenter: Shoichi Sasaki — University of Tokyo

Shoichi Sasaki and Takeshi Yamazaki

We discuss formation of an S-wave bound-state in finite volume on the basis of Lüscher's phase-shift formula. It is found that although a bound-state pole condition is fulfilled only in the infinite volume limit, its modification by the finite size corrections is exponentially suppressed by the spatial extent L in a finite box L3. We also confirm that the appearance of the S-wave bound state is accompanied by an abrupt sign change of the S-wave scattering length even in finite volume through numerical simulations. This distinctive behavior may help us to discriminate the shallow bound state from the lowest energy level of the scattering state in finite volume simulations.