Light quark mass dependence of the $ and $ decay constants

We study the light quark mass dependence of the $ and $ meson decay constants, $ and {D_s}$, using a covariant formulation of chiral perturbation theory ($\chi) at next-to-next-to-leading order (NNLO). Using the HPQCD lattice results for the decay constants as a benchmark we show that covariant $\chi can describe the HPQCD results better than heavy meson $\chi (HM$\chi) at both NLO and NNLO. Within the same framework, taking into account sub-leading (/m_Q$, with $ the heavy quark mass) corrections to the values of the low-energy constants and employing the lattice QCD results for {BB^ \pi}$, we estimate the ratio of {B_s}/f_B$ to be .22^{+0.05}_{-0.04}$, which agrees well with the HPQCD result .226(26)$.