Strong coupling of excited heavy mesons.

We compute the strong coupling constant ${\mathit{G}}_{\mathit{B}}^{\mathrm{*}\mathrm{*}}$B\ensuremath{\pi} (${\mathit{G}}_{\mathit{D}}^{\mathrm{*}\mathrm{*}}$D\ensuremath{\pi}), where ${\mathit{B}}^{\mathrm{*}\mathrm{*}}$ (${\mathit{D}}^{\mathrm{*}\mathrm{*}}$) is the ${0}^{+}$ P-wave bq\ifmmode\bar\else\textasciimacron\fi{} (cq\ifmmode\bar\else\textasciimacron\fi{}) state, by QCD sum rules and by light-cone sum rules. The two methods give compatible results in the limit ${\mathit{m}}_{\mathit{Q}}$\ensuremath{\rightarrow}\ensuremath{\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 ${\mathit{f}}_{\mathit{D}\mathit{s}}$/${\mathit{f}}_{\mathit{D}}$.