$\eta$-${\eta }^{\prime }$ mixing and its application in the $B^{+}/D^{+}/D_s^{+}\to {\eta }^{(\prime )}{\ell }^{+}{\nu }_{\ell }$ decays

Abstract

In this paper, we take into account the intrinsic charm and gluonic contents into the $\eta -{\eta }^{\prime }$ mixing scheme and formulate the tetramixing $\eta -{\eta }^{\prime }-G-{\eta }_c$ to study the mixing properties of ${\eta }^{(\prime )}$ mesons. Using the newly derived mixing parameters, we calculate the transition form factors (TFFs) of $B^{+}/D^{+}/D_s^{+}\to {\eta }^{(\prime )}$ within the QCD light-cone sum rules up to next-to-leading order QCD corrections and twist-4 contributions. Using the extrapolated TFFs, we then calculate the decay widths and branching fractions of the semi-leptonic decays $B^{+}/D^{+}/D_s^{+}\to {\eta }^{(\prime )}{\ell }^{+}{\nu }_{\ell }$. Our results are consistent with the recent Belle and BES-III measurements within reasonable errors.