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We present the method and compute the strong couplings of the lowest and first orbitally excited heavy-light mesons to a soft pion in the static heavy quark limit on the lattice. Besides the usual g^ and ~g couplings, we were able to make the first computation of the coupling h using the relevant radial distributions. Our results are obtained from the simulations of QCD with Nf=2 light Wilson-Clover quarks, combined with the improved static quark actions. The hierarchy among couplings that emerges from our study is ~g < g^ < h.

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