有限体积中浅二体束缚态的识别
Identification of shallow two-body bound states in finite volume
摘要：
我们讨论了通过Luscher有限尺寸方法在有限体积中形成束缚态的签名。假设这种方法中的相移公式继承了量子散射理论的所有方面，我们可以预期，束缚态的形成导致散射长度的符号发生变化。如果这是真的，这一事实为我们提供了一个独特的识别浅的束缚态，即使在有限的体积，通过确定是否第二低的能量状态出现刚刚超过阈值。基于Luscher的相移公式，我们还考虑了有限体积下的束缚态极点条件，发现该条件仅在无限体积极限下才满足，但有限尺寸修正对该条件的修正受空间晶格尺寸L的指数抑制.这些理论的考虑也数值检查通过晶格模拟计算的正电子偶素谱在紧凑的标量QED，其中电子和正电子之间的短程相互作用是在希格斯相实现。
英文摘要：
We discuss signatures of bound-state formation in finite volume via the Luscher 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 Luscher'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.
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