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

TL;DR

This paper determines the $ ext{eta}_q$ meson distribution amplitude using QCD sum rules and models its impact on $B/D^+ o ext{eta}^{( ext{prime})}$ semileptonic decays, providing insights into meson structure and decay processes.

Contribution

It fixes the $ ext{eta}_q$ distribution amplitude parameters and applies them to calculate transition form factors and decay widths for $B/D^+$ meson decays, incorporating next-to-leading order QCD corrections.

Findings

The decay constant $f_{ ext{eta}_q}$ is determined as 0.141 GeV.

Transition form factors for $B/D^+ o ext{eta}^{( ext{prime})}$ are calculated with twist-4 accuracy.

Predictions for semileptonic decay widths are provided.

Abstract

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. The sum rules for the $0_{\rm th}$-order moment can also be used to fix the magnitude of $\eta_q$ decay constant, which gives $f_{\eta_q}=0.141\pm0.005$ GeV. As an application of the present derived $\phi_{2;\eta_q}$, we calculate the transition form factors $B(D)^+ \to\eta^{(\prime)}$ by using the QCD light-cone sum rules up to twist-4 accuracy and by including the next-to-leading order QCD corrections to the twist-2 part, and then fix the related CKM matrix element and the decay width for the semi-leptonic decays $B(D)^+ \to\eta^{(\prime)}\ell^+ \nu_\ell$.