Heavy quark symmetry, chiral symmetry, and parity doublets of heavy mesons in the Bethe-Salpeter approach

It is shown that there must exist degenerate parity doublets of heavy mesons with arbitrary spin if QCD possesses both heavy quark and chiral symmetries. The chiral symmetric pahase and chiral broken phase can be dynamically turned in the Bethe-Salpeter approach. In the chiral broken phase the mass splittings of the parity doublets can be calculated and they are proportional to the constituent mass m of the light quark to order m/${\mathrm{\Lambda }}_{\mathrm{\chi }}$.