Properties of the _q leading-twist distribution amplitude and its effects to the B/D⁺ ()l_l⁺ decays

The eta(('))-mesons in the quark-flavor basis aremixtures of two mesonic states vertical bar eta(q)> = vertical bar(u) over baru + (d) over bard >/ root 2 and vertical bar eta(s)> = vertical bar(s) over bars >. In previous work, we have made a detailed study on the eta(s) leading-twist distribution amplitude by using the D-s(+) meson semileptonic decays. 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 forits 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 the initial scale mu(0) similar to 1 GeV are fixed by using those moments. The QCD sum rules for the 0th-order moment can also be used to fix the magnitude of eta(q) decay constant, giving f(eta q) = 0.141 +/- 0.005 GeV. As an application of phi(2;eta q), we calculate the transition form factors B(D)(+) -> eta(') 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 leading-twist part, and then fix the related CKM matrix element and the decay width for the semi-leptonic decaysB(D)(+) -> eta(('))+nu(l).