SU(3) breaking corrections to the $D$, $D^{\ast }$, $B$, and $B^{\ast }$ decay constants

We report on a first next-to-next-to-leading order calculation of the decay constants of the $D$ ($D^{\ast }$) and $B$ ($B^{\ast }$) mesons using a covariant formulation of chiral perturbation theory. It is shown that, using the state-of-the-art lattice QCD results on $f_{D_s}\mathrm{/}{f}_D$ as input, one can predict quantitatively the ratios of $f_{D_s^{\ast }}\mathrm{/}{f}_{D^{\ast }}$, $f_{B_s}\mathrm{/}{f}_B$, and $f_{B_s^{\ast }}\mathrm{/}{f}_{B^{\ast }}$ taking into account heavy-quark spin-flavor symmetry breaking effects on the relevant low-energy constants. The predicted relations between these ratios, $f_{D_s^{\ast }}\mathrm{/}{f}_{D^{\ast }}<f_{D_s}\mathrm{/}{f}_D$ and $f_{B_s}\mathrm{/}{f}_B>f_{D_s}\mathrm{/}{f}_D$, and their light-quark mass dependence should be testable in future lattice QCD simulations, providing a stringent test of our understanding of heavy quark spin-flavor symmetry, chiral symmetry and their breaking patterns.