We discuss signatures of bound-state formation in finite volume via the Lüscher finite size method. Assuming that the phase-shift formula in this method inherits all aspects of the quantum scattering theory, we may expect that the bound-state formation induces the sign of the scattering length to be changed. If it were true, this fact provides us a distinctive identification of a shallow bound state even in finite volume through determination of whether the second lowest energy state appears just above the threshold. We also consider the bound-state pole condition in finite volume, based on Lüscher’s phase-shift formula and then find that the condition is fulfilled only in the infinite volume limit, but its modification by finite size corrections is exponentially suppressed by the spatial lattice size L. These theoretical considerations are also numerically checked through lattice simulations to calculate the positronium spectrum in compact scalar QED, where the short-range interaction between an electron and a positron is realized in the Higgs phase.
|Journal||Proceedings of Science|
|Publication status||Published - 2007|
|Event||25th International Symposium on Lattice Field Theory, LATTICE 2007 - Regensburg, Germany|
Duration: 2007 Jul 30 → 2007 Aug 4
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