  This paper presents the first study of mesons with a quark and an antiquark
with different and finite masses, in a simple confining and chiral invariant
quark-antiquark interaction, leading to spontaneous chiral symmetry breaking
and to constituent quarks. In the false chiral invariant vacuum, the chiral
partners are degenerate, and tachyons occur in the light-light spectrum. In the
true vacuum, most of the standard non-relativistic quark model spectra should
be recovered except for the pion and other particular constraints. The
calibration problem of chiral quark models is also addressed here. The detailed
inspection of the different contributions to the D and Ds masses suggests that
the challenging recently observed Ds*(2317) and Ds*(2460) mesons might not fit
as global chirally rotated quark-antiquark Ds mesons.
