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

Bo-Lin Huang, Zi-Yang Lin, Kan Chen, Shi-Lin Zhu

Published 2022-05-05Version 1

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 to the phase shifts and scattering lengths from the 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 coupled-channel $D\pi$, $D\eta$ and $D_s\bar{K}$ scattering corresponds to the $D_{0}^{*}(2400)$. We also predict the scattering lengths and scattering volumes and observe a good convergence in the $P$ waves and scattering volumes. Our calculations provide a possibility to accurately investigate the exotic state in the light pseudoscalar meson and heavy meson interactions.