Spectra and Time Evolution of Near-Threshold Structures in Coupled-Channeled Systems: An Approach by Uniformization and the Mittag-Leffler Expansion*

Many candidates of exotic hadrons have been found near the two-body threshold of hadronic channels. However, due to the non-trivial structure of the S-matrix in the energy plane, model-independent extraction of the pole positions in the near-threshold domain is a rather challenging task.

In this talk, we focus on the analytic structure of the multi-channel S-matrix and introduce the notion of uniformization, an idea to use a variable where the S-matrix is single-valued. Combining uniformization with a pole expansion called the Mittag-Leffler Expansion, we obtain a simple expression applicable to near-threshold hadronic spectra. We present the Mittag-Leffler Expansion for the 2- and 3-channel case and show that in addition to ordinary resonance poles lying on the lower-half energy plane, poles on the upper-half energy plane, when positioned near the threshold, can manifest themselves as a prominent structure in the spectra.

Also, we extend "survival probability" discussed in single-channel systems to the 2-channel case and demonstrate that "threshold cusps" which correspond to near-threshold poles in the upper-half energy plane decay non-exponentially in time.