  We compute the strong coupling constant $G_{B^{**} B \pi} \; (G_{D^{**} D
\pi})$, where $B^{**}$ ($D^{**}$) is the $0^+$ $P-$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 $m_Q \to \infty$, 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 $f_{D_s}/f_D$.
