文章基本信息

标题：Identification of shallow two-body bound states in finite volume
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作者：S. Sasaki
期刊名称：PoS - Proceedings of Science
印刷版ISSN：1824-8039
出版年度：2007
出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We discuss signatures of bound-state formation in finite volume via the L¨uscher 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 L¨uscher’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.