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°$, $ {\theta }_{2}=26.6\pm 0.6°$, $ {\theta }_{3}=38.6\pm 0.1°$, and $ {\theta }_{4}=38.5\pm 0.1°$. These values are in good agreement with the predictions of heavy quark effective theory, particularly for the mixing angle $ \theta =35.3°$, 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.