Phase shifts of the light pseudoscalar meson and heavy meson scattering in heavy meson chiral perturbation theory

TL;DR

This paper calculates scattering phase shifts of light pseudoscalar and heavy mesons using heavy meson chiral perturbation theory, fitting lattice QCD data to predict bound states, resonances, and scattering parameters at physical masses.

Contribution

It provides a comprehensive third-order calculation of scattering matrices and predicts exotic states like $D_{s0}^{*}(2317)$ through combined lattice QCD data fitting.

Findings

Strong phase shifts suggest possible bound states or resonances.

Predicted scattering lengths and volumes show good convergence.

Identified channels corresponding to known exotic states.

Abstract

We calculate the complete $T$ matrices of the elastic light pseudoscalar meson and heavy meson scattering to the third order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting the phase shifts and scattering lengths from lattice QCD simulations simultaneously and predict the phase shifts at the physical meson masses. The phase shifts in the $D\pi(I=1/2)$, $DK(I=0)$, $D\bar{K}(I=0)$, $D_s\bar{K}$, $D\eta$ and $D_s\eta$ $S$ waves are so strong that bound states or resonances may be generated dynamically in all these channels. The $DK(I=0)$ channel corresponds to the well-known exotic state $D_{s0}^{*}(2317)$. The $DK(I=0)$ channel corresponds to the well-known exotic state $D_{s0}^{*}(2317)$. The coupled-channel $D\pi$, $D\eta$ and $D_s\bar{K}$ scattering corresponds to $D_{0}^{*}(2400)$. The coupled-channel $D\pi$, $D\eta$ and $D_s\bar{K}$ scattering corresponds to $D_{0}^{*}(2400)$. We also predict the scattering lengths and scattering volumes and observe good convergence in the scattering volumes. Our calculations provide a possibility to accurately investigate the exotic state in the light pseudoscalar meson and heavy meson interactions.