Speaker
Description
In a series of papers we have proposed and developed the idea of the pole expansion as a model-independent method to analyze the results of experiments and/or lattice QCD simulations, in particular for unstable states, that are more general than resonances.
In the talk we report on the pole expansion of the two-hadron imaginary-time correlation function in the infinite volume and its finite-volume correction.
First, in the infinite volume, by the Mittag-Leffler theorem, we express the imaginary-time correlation function as a sum of pole terms in terms of the uniformization variable, which makes the correlation function single-valued.
Secondly, in a finite volume, identifying unstable states as poles on the newly defined unphysical complex-energy sheet, we demonstrate that the finite-volume correction to the complex energy of unstable states (and the pole expansion of the correlation function) decreases exponentially as the volume size increases.
Also, we find that $(\text {imaginary time})/(\text {volume size})^2 \rightarrow 0$ is the infinite-volume limit while $(\text {imaginary time})/(\text {volume size})^2 \rightarrow \infty$ is the lowest-mode-dominant limit.
Therefore, in the former region we can obtain the pole positions and residues of unstable states by fitting the pole expansion of the imaginary-time correlation function to the results of lattice QCD simulations.