Based on the method of solving the complete Salpeter equation, we study the semileptonic decays of a 0− heavy meson to 1P, 2P, or 3P heavy-tensor mesons, Bq→(c¯q)(nP)ℓ+νℓ (q=u,d,s,c;n=1,2,3). The obtained branching ratio of B(B→D2⋆(2460)ℓ+νℓ) agrees with the experimental data. We predict B(Bs0→Ds2⋆−(1P)ℓ+νℓ)=3.76×10−3 and B(Bc+→χc2(1P)ℓ+νℓ)=1.82×10−3. The branching ratios of decays to 2P and 3P final states are found to be very small. The ratios R(D¯2⋆0)=0.045, R(Ds2⋆)=0.048 and R(χc2)=0.059 are also obtained. This study focuses on the contribution of relativistic corrections. The wave function of the pseudoscalar includes nonrelativistic S-wave and relativistic P-wave. While for a tensor, it contains nonrelativistic P-wave and relativistic P-, D-, and F-waves in its wave function. We find the individual contributions of relativistic partial waves are significant in the decay B→D2⋆(2460)ℓ+νℓ, but the overall contribution of the relativistic effect is 24.4%, which is small due to cancellation. Similarly, for the decay Bs0→Ds2⋆−(1P)ℓ+νℓ, the contribution of the relativistic effect is 28.8%. While for Bc+→χc2(1P)ℓ+νℓ, the individual contributions of relativistic partial waves and the overall relativistic correction are both small, the later of which is 22.1%. Published by the American Physical Society 2024
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