  We investigate the numerical values of the low-energy constants in the chiral
effective Lagrangian for the interactions between the charmed mesons and the
lightest pseudoscalar mesons, the Goldstone bosons of the spontaneous breaking
of chiral symmetry for QCD. This problem is tackled from two sides: estimates
using the resonance exchange model, and positivity constraints from the general
properties of the $S$-matrix including analyticity, crossing symmetry and
unitarity. These estimates and constraints are compared with the values
determined from fits to lattice data of the scattering lengths. Tensions are
found, and possible reasons are discussed. We conclude that more data from
lattice calculations and experiments are necessary to fix these constants
better. As a by-product, we also estimate the coupling constant $g_{DDa_2}$,
with $a_2$ the light tensor meson, via the QCD sum rule approach.
