TY - JOUR

T1 - Identification of shallow two-body bound states in finite volume

AU - Sasaki, Shoichi

AU - Yamazaki, Takeshi

N1 - Funding Information:
∗Speaker. †The results of calculations were performed by using of RIKEN Super Combined Cluster (RSCC). S.S. is supported by the JSPS for a Grant-in-Aid for Scientific Research (C) (No. 19540265).
Publisher Copyright:
© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

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M3 - Conference article

AN - SCOPUS:85055430626

SN - 1824-8039

VL - 42

JO - Proceedings of Science

JF - Proceedings of Science

M1 - 131

T2 - 25th International Symposium on Lattice Field Theory, LATTICE 2007

Y2 - 30 July 2007 through 4 August 2007

ER -