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

TL;DR

This paper refines the understanding of $ ext{eta}$ and $ ext{eta'}$ meson mixing by including intrinsic charm and gluonic components, and applies this to predict semi-leptonic decay rates consistent with experimental data.

Contribution

It introduces a tetramixing scheme for $ ext{eta}$, $ ext{eta'}$, gluonic, and charm components, and calculates transition form factors and decay widths using QCD sum rules.

Findings

Mixing parameters align with recent experimental results.

Predicted decay widths match Belle and BES-III measurements.

Enhanced understanding of meson structure and decay processes.

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.