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

Abstract

The ${\eta }^{(\prime )}$-mesons in the quark-flavor basis are mixtures of two mesonic states $|{\eta }_q⟩=|\bar{u}u+\bar{d}d⟩/\sqrt{2}$ and $|{\eta }_s⟩=|\bar{s}s⟩$. 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 ${\varphi }_{2;{\eta }_q}$ at an initial scale ${\mu }_0\sim 1$ GeV are then fixed by using those moments. The sum rules for the $0_{\mathrm{th}}$-order moment can also be used to fix the magnitude of ${\eta }_q$ decay constant, which gives $f_{{\eta }_q}=0.141\pm 0.005$ GeV. As an application of the present derived ${\varphi }_{2;{\eta }_q}$, 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 $B(D{)}^{+}\to {\eta }^{(\prime )}{\ell }^{+}{\nu }_{\ell }$.

Comments: 16 pages, 8 figures, Comments welcome