2026/07/20 by Wan-Bing Luo, Ru-Meng Pan, Ya-Xiong Wang +1
#hep-ph
In this work, we focus on the light vector meson leading-twist longitudinal distribution amplitudes (DAs) ϕ^∥2;V(x,μ) with V = ρ, K^∗, ϕ. In order to obtain their accurate behaviors, a new scheme of QCD sum rule research with respect to DA suggested in 2021 by us is adopted. With an improved sum rule formula, the ξ-moments ⟨ξn⟩2;V^∥ up to tenth order are calculated. In which, ⟨ξ2⟩^∥2;ρ=0.225+0.013-0.012, ⟨ξ1⟩^∥2;K^∗=-0.0228+0.0042-0.0040, ⟨ξ2⟩^∥2;K^∗=0.217+0.007-0.007, ⟨ξ2⟩^∥2;ϕ=0.209+0.020-0.020, and the corresponding Gegenbauer moments a2;∥2;ρ=0.074+0.039-0.036, a1;∥2;K^∗=-0.038+0.007-0.007, a2;∥2;K^∗=0.050+0.020-0.019, a2;∥2;ϕ=0.027+0.058-0.058 at the scale μ= 1~\rm GeV, respectively. By fitting those ⟨ξn⟩^∥2;V(n = 1,2,⋯,10) with the least squares method, the behaviors of leading-twist longitudinal DAs for ρ, K^∗, ϕ are determined. Further, we recalculate the transition form factors and branching ratio of the D→(ρ,K^∗), Ds→ϕ semi-leptonic decay processes.