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Abstract: We discuss signatures of bound-state formation in finite volume via theLuscher finite size method. Assuming that the phase-shift formula in thismethod inherits all aspects of the quantum scattering theory, we may expectthat the bound-state formation induces the sign of the scattering length to bechanged. If it were true, this fact provides us a distinctive identification ofa shallow bound state even in finite volume through determination of whetherthe second lowest energy state appears just above the threshold. We alsoconsider the bound-state pole condition in finite volume, based on Luscher-sphase-shift formula and then find that the condition is fulfilled only in theinfinite volume limit, but its modification by finite size corrections isexponentially suppressed by the spatial lattice size L. These theoreticalconsiderations are also numerically checked through lattice simulations tocalculate the positronium spectrum in compact scalar QED, where the short-rangeinteraction between an electron and a positron is realized in the Higgs phase.



Autor: Shoichi Sasaki Univ. of Tokyo, Takeshi Yamazaki Univ. of Connecticut

Fuente: https://arxiv.org/







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