  We derive the scattering amplitude for Goldstone bosons of chiral symmetry
off the pseudoscalar charmed mesons up to leading one-loop order in a covariant
chiral effective field theory, using the so-called extended-on-mass-shell
renormalization scheme. Then we use unitarized chiral perturbation theory to
fit to the available lattice data of the S-wave scattering lengths. The lattice
data are well described. However, most of the low-energy constants determined
from the fit bear large uncertainties. Lattice simulations in more channels are
necessary to pin down these values which can then be used to make predictions
in other processes related by chiral and heavy quark symmetries.
