Mixing angle between $^{3}P_1$ and $^{1}P_1$ states in heavy axial vector mesons within the QCD sum rules framework

In this study, we calculate the mixing angles between the axial-vector mesons $D_{1(s1)} - D_{1(s1)}^\prime$ and $B_{1(s1)} - B_{1(s1)}^\prime$ using the QCD sum rules approach. Our results are $\theta_1 = 28.2 \pm 0.6^\circ$, $\theta_2 = 26.6 \pm 0.6^\circ$, $\theta_3 = 38.6 \pm 0.1^\circ$, and $\theta_4 = 38.5 \pm 0.1^\circ$. These values are in good agreement with the predictions of Heavy Quark Effective Theory, particularly for the mixing angle $\theta = 35.3^\circ$, and are compatible with several existing results in the literature. The predicted mixing angles can be tested through the analysis of semileptonic decays such as $B_c \to B_1 \ell \nu$, $B_c \to B_{s1}^0 \ell \nu$, $B_s \to D_{s1} \ell \nu$, and $B_s \to D_{s1}^\prime \ell \nu$, which can be investigated at experimental facilities such as LHCb and Belle II.