Three-channel uniformized amplitude using Jost function formalism

Abstract

Conventional quark model cannot be used to explain why currently observed hadron states are exotics. Exotic states appear as enhancements in scattering amplitudes which can be analyzed more rigorously in terms of poles in the S-Matrix theory. Considering three-channel scattering, we have 2³ = 8 Riemann sheets due to the thresholds serving as branch points. We show that using the established two-channel and three-channel uniformization of momentum, we construct the S-matrix through the Jost function without using Mittag-Leffler expansion. We apply our uniformized amplitude to the invariant mass of D⁰D⁰π⁺. We found that by placing an isolated pole in the second Riemann sheet produces a peak at exactly the D^*+D⁰. Another peak also emerged below second threshold which could be a consequence of a line shape distortion at the threshold.