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

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 $D_{s0}^{\ast }(2317)$. The $DK(I=0)$ channel corresponds to the well-known exotic state $D_{s0}^{\ast }(2317)$. The coupled-channel $D\pi$, $D\eta$ and $D_s\bar{K}$ scattering corresponds to $D_0^{\ast }(2400)$. The coupled-channel $D\pi$, $D\eta$ and $D_s\bar{K}$ scattering corresponds to $D_0^{\ast }(2400)$. 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.

Comments: 22 pages, 7 figures, 4 tables