Light pseudoscalar meson and heavy meson scattering lengths to $\mathcal{O}(p^4)$ in heavy meson chiral perturbation theory

Abstract: We calculate the threshold $T$ matrices of the light pseudoscalar meson and heavy meson scattering to fourth order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting to the lattice QCD data points through both the perturbative and iterated methods and obtain the physical scattering lengths in both formalisms. The values of the scattering lengths tend to be convergent at fourth order for most of the channels in the perturbative method. The value of the scattering length for the channel $DK (I=0)$, which involves the bound state $D_{s0}^{*}(2317)$, is obtained correctly in the iterated method. Based on the heavy diquark-antiquark symmetry, we also estimate the meson and doubly charmed (bottom) baryon scattering lengths, and find that the bound states can be generated with high probability in the channels $\bar{K}\Xi_{cc}(I=0)$ and $\bar{K}\Xi_{bb}(I=0)$. We strongly urge the LHCb Collaboration to look for the very narrow $\bar{K}\Xi_{cc}$ state with $IJ^P=0{1\over 2}^-$ through either the electromagnetic decay or the iso-spin violating strong decay $\Omega_{cc} \pi$.