Study of the analytic structure of the S-matrix in coupled-channels applied to the X(3872) meson

Abstract

This project aims at investigating the analytic structure of the two-body scattering S matrix with coupled-channels applied to the exotic meson X(3872). We start with an exercise about the S-matrix poles using a separable potential with a single channel, related to the threshold D0-D*0/D0-D*0, extremely close to the X(3872) mass. Afterwards, we will use a two coupled-channels separable potential, the second channel related to the threshold D±D*, located at < 8 MeV above the first one. We will explore the complexity of the analytic structure of the S matrix with the introduction of this second threshold, and how it affects observables like phase shifts and cross section, and even interpretations of the X(3872) state. This exploratory study will later be systematized through effective quantum field theories.