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

Abstract

AbstractThe $$\eta ^{(\prime )}$$ η ( ′ ) -mesons in the quark-flavor basis are mixtures of two mesonic states $$|\eta _{q}\rangle =|{\bar{u}} u+{\bar{d}} d\rangle /\sqrt{2}$$ | η q ⟩ = | u ¯ u + d ¯ d ⟩ / 2 and $$|\eta _{s}\rangle =|{\bar{s}} s\rangle .$$ | η s ⟩ = | s ¯ s ⟩ . In previous work, we have made a detailed study on the $$\eta _{s}$$ η s leading-twist distribution amplitude by using the $$D^+_s$$ D s + meson semileptonic decays. As a sequential work, in the present paper, we fix the $$\eta _q$$ 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 $$\eta _q$$ η q leading-twist distribution amplitude $$\phi _{2;\eta _q}$$ ϕ 2 ; η q at the initial scale $$\mu _0\sim 1$$ μ 0 ∼ 1  GeV are fixed by using those moments. The QCD sum rules for the $$0_{\textrm{th}}$$ 0 th -order moment can also be used to fix the magnitude of $$\eta _q$$ η q decay constant, giving $$f_{\eta _q}=0.141\pm 0.005$$ f η q = 0.141 ± 0.005  GeV. As an application of $$\phi _{2;\eta _q},$$ ϕ 2 ; η q , we calculate the transition form factors $$B(D)^+ \rightarrow \eta ^{(\prime )}$$ 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 $$B(D)^+ \rightarrow \eta ^{(\prime )}\ell ^+ \nu _\ell .$$ B ( D ) + → η ( ′ ) ℓ + ν ℓ .