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arXiv · 2506.13214

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

Yu-Jie Zhang·Xing-Gang Wu·Dan-Dan Hu·Long Zeng
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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.

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Yu-Jie Zhang, Xing-Gang Wu, Dan-Dan Hu, Long Zeng. 2025-06-16. $\eta$-$\eta'$ mixing and its application in the $B^+/D^+/D_s^+\to\eta^{(\prime)}\ell^+ \nu_\ell$ decays. https://arxiv.org/abs/2506.13214

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