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We investigate the numerical values of the low-energy constants in the chiraleffective Lagrangian for the interactions between the charmed mesons and thelightest pseudoscalar mesons, the Goldstone bosons of the spontaneous breakingof chiral symmetry for QCD. This problem is tackled from two sides: estimatesusing the resonance exchange model, and positivity constraints from the generalproperties of the $S$-matrix including analyticity, crossing symmetry andunitarity. These estimates and constraints are compared with the valuesdetermined from fits to lattice data of the scattering lengths. Tensions arefound, and possible reasons are discussed. We conclude that more data fromlattice calculations and experiments are necessary to fix these constantsbetter. 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.

Aspects of the low-energy constants in the chiral Lagrangian for charmed mesons