Properties of the $\eta_q$ leading-twist distribution amplitude and its effects to the $B/D^+ \to\eta^{(\prime)}\ell^+ \nu_\ell$ decays

Understand

The $\eta^{(\prime)}$-mesons in the quark-flavor basis are mixtures of two mesonic states $|\eta_{q}\rangle=|\bar u u+\bar d d\rangle/\sqrt 2$ and $|\eta_{s}\rangle=|\bar s s\rangle$.

• In the previous work, we have made a detailed study on the $\eta_{s}$ leading-twist distribution amplitude.
• As a sequential work, in the present paper, we fix the $\eta_q$ leading-twist distribution amplitude by using the light-cone harmonic oscillator model for its wave function and by using the QCD sum rules within the QCD background field to calculate its moments.
• The input parameters of $\eta_q$ leading-twist distribution amplitude $\phi_{2;\eta_q}$ at an initial scale $\mu_0\sim 1$ GeV are then fixed by using those moments.