η(′)-meson twist-2 distribution amplitude within QCD sum rule approach and its application to the semi-leptonic decay Ds+→η(′)ℓ+νℓ.

In this paper, we make a detailed discussion on the η and η ′ -meson leading-twist light-cone distribution amplitude ϕ 2 ; η (′) (u , μ) by using the QCD sum rules approach under the background field theory. Taking both the non-perturbative condensates up to dimension-six and the next-to-leading order (NLO) QCD corrections to the perturbative part, its first three moments ⟨ ξ 2 ; η (′) n ⟩ | μ 0 with n = (2 , 4 , 6) can be determined, where the initial scale μ 0 is set as the usual choice of 1 GeV. Numerically, we obtain ⟨ ξ 2 ; η 2 ⟩ | μ 0 = 0. 231 - 0.013 + 0.010 , ⟨ ξ 2 ; η 4 ⟩ | μ 0 = 0. 109 - 0.007 + 0.007 , and ⟨ ξ 2 ; η 6 ⟩ | μ 0 = 0. 066 - 0.006 + 0.006 for η -meson, ⟨ ξ 2 ; η ′ 2 ⟩ | μ 0 = 0. 211 - 0.017 + 0.015 , ⟨ ξ 2 ; η ′ 4 ⟩ | μ 0 = 0. 093 - 0.009 + 0.009 , and ⟨ ξ 2 ; η ′ 6 ⟩ | μ 0 = 0. 054 - 0.008 + 0.008 for η ′ -meson. Next, we calculate the D s → η (′) transition form factors (TFFs) f + η (′) (q 2) within QCD light-cone sum rules approach up to NLO level. The values at large recoil region are f + η (0) = 0. 476 - 0.036 + 0.040 and f + η ′ (0) = 0. 544 - 0.042 + 0.046 . After extrapolating TFFs to the allowable physical regions within the series expansion, we obtain the branching fractions of the semi-leptonic decay, i.e. D s + → η (′) ℓ + ν ℓ , i.e. B (D s + → η (′) e + ν e) = 2. 346 - 0.331 + 0.418 (0. 792 - 0.118 + 0.141) × 10 - 2 and B (D s + → η (′) μ + ν μ) = 2. 320 - 0.327 + 0.413 (0. 773 - 0.115 + 0.138) × 10 - 2 for ℓ = (e , μ) channels respectively. And in addition to that, the mixing angle for η - η ′ with φ and ratio for the different decay channels R η ′ / η ℓ are given, which show good agreement with the recent BESIII measurements. [ABSTRACT FROM AUTHOR]