Properties of the η _q leading-twist distribution amplitude and its effects to the B/D^+ →η ^(' )ℓ ^+ ν _ℓ decays

The η ^(' ) -mesons in the quark-flavor basis are mixtures of two mesonic states |η _q⟩ =|u̅ u+d̅ d⟩ /√(2) and |η _s⟩ =|s̅ s⟩ . In previous work, we have made a detailed study on the η _s leading-twist distribution amplitude by using the D^+_s meson semileptonic decays. As a sequential work, in the present paper, we fix the η _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 η _q leading-twist distribution amplitude ϕ _2;η _q at the initial scale μ _0∼ 1 GeV are fixed by using those moments. The QCD sum rules for the 0_th -order moment can also be used to fix the magnitude of η _q decay constant, giving f_η _q=0.141± 0.005 GeV. As an application of ϕ _2;η _q, we calculate the transition form factors B(D)^+ →η ^(' ) 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 decays B(D)^+ →η ^(' )ℓ ^+ ν _ℓ .