Strong coupling of excited heavy mesons

We compute the strong coupling constant $G_{B^{} B \pi} ; (G_{D^{} D \pi})$,where$B^{}$($D^{}$)isthe$0^+$ $P-$wave $b \bar q ; (c \bar q)$ state, by QCD sum rules and by light-cone sum rules. The two methods give compatible results in the limit $m_Q\to \mathrm{\infty }$, with a rather large value of the coupling constant. We apply the results to the calculation of the hadronic widths of the positive parity $B$ and $D$ states and to the chiral loop contribution to the ratio $f_{D_s}\mathrm{/}{f}_D$.