We have performed a systematical calculation of the pion ($\pi$, $K$, $\eta$) and heavy pseudoscalar meson $S$-wave scattering lengths up to $\mathcal{O}(p^3)$ in the chiral perturbation theory in the heavy quark symmetry limit. With the three scattering lengths from the lattice simulations as input we estimate the unknown low-energy constants. Then we predict all the other unmeasured scattering lengths. The analytical expressions and predictions may be helpful to future investigations. Especially we note that the $DK$ scattering length is positive. Therefore their interaction is attractive, which helps to lower the mass of the bare charm-strange scalar state in the quark model through the couple-channel effect.

• Received 15 April 2009

DOI:https://doi.org/10.1103/PhysRevD.79.094026