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We first improve the previous results on the masses of the doublets (0^+,1^+)and (1^+,2^+) with QCD sum rules up to the order of O(1/m_Q) in the frameworkof HQET and calculate the O(1/m_Q) correction to the decay constants f_{-,1/2}and f_{+,3/2}. With the mass matrix of the two 1^+ states, we obtain the mixingangle for the two states and the interpolating currents, which couple to onlyone of the two eigenstates up to the order of O(1/m_Q). Using these results wederive the light-cone sum rules for the amplitudes of the pionic decay of B_1and B_2^* up to the order of O(1/m_Q) in HQET. The O(1/m_Q) correction to thedecay amplitude of B_1 and B_2^* are found to be small. When applied to D_1 andD_2^* the theoretical results are in good agreement with experimental datathough the theoretical uncertainty is sizeable for D system.Comment: Final version to appear in Phys. Rev. D, four references are added,  typos in the references are correcte

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Decay widths of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math>up to the order<mml:math …

Decay widths ofB1andB2*up to the order