Signatures of S-wave bound-state formation in finite volume

Details Signatures of S-wave bound-state formation in finite volume Signatures of S-wave bound-state formation in finite volume

2006-10-13

arxiv.org/abs/hep-lat/0610081v3

Phys.Rev.D74:114507,2006

Physics

High Energy Physics

High Energy Physics - Lattice

25 pages, 30 figures; v2: typos corrected and two references added, v3: final version to appear in PRD

Scientific paper

10.1103/PhysRevD.74.114507

We discuss formation of an S-wave bound-state in finite volume on the basis of L\"uscher'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 $L^3$. 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 loosely bound state from the lowest energy level of the scattering state in finite volume simulations.

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