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In this paper, we study the OZI-allowed two-body strong decays of \(3^-\) heavy–light mesons. Experimentally the charmed \(D_{3}^{*}(2760)\) and the charm–strange \(D_{s3}^{*}(2860)\) states with these quantum numbers have been discovered. For the bottomed B(5970) state, which was found by the CDF Collaboration recently, its quantum number has not been decided yet and we assume it is a \(3^-\) meson in this paper. The theoretical prediction for the strong decays of bottom–strange state \(B_{s3}^*\) is also given. The relativistic wave functions of \(3^-\) heavy mesons are constructed and their numerical values are obtained by solving the corresponding Bethe–Salpeter equation with instantaneous approximation. The transition matrix is calculated by using the PCAC and low energy theorem, following which the decay widths are obtained. For \(D_{3}^*(2760)\) and \(D_{s3}^*(2860)\), the total strong decay widths are 72.6 and 47.6 MeV, respectively. For \(B_3^*\) with \(M=5978\) MeV and \(B_{s3}^*\) with \(M=6178\) MeV, their strong decay widths are 22.9 and 40.8 MeV, respectively.

Strong decays of $$D_{3}^{*}(2760)$$ D 3 ∗ ( 2760 ) , $$D_{s3}^{*}(2860)$$ D s 3 ∗ ( 2860 ) , $$B_{3}^{*}$$ B 3 ∗ , and $$B_{s3}^{*}$$ B s 3 ∗

Strong decays of $$D_{3}^{}(2760)$$ D 3 ∗ ( 2760 ) , $$D_{s3}^{}(2860)$$ D s 3 ∗ ( 2860 ) , $$B_{3}^{}$$ B 3 ∗ , and $$B_{s3}^{}$$ B s 3 ∗