由于半轻子衰变$B\to D\ell\barν_{\ell}$的$\mathcal{R}(D)$值在实验测量与标准模型（SM）理论预测之间存在显著差异，人们推测这可能是超出SM的新物理的证据。通常，在使用微扰QCD因子化和光锥QCD求和规则研究$B\to D\ell\barν_{\ell}$时，$D$介子twist-2, 3分布振幅（DAs）$ϕ_{2;D}(x,μ)$、$ϕ_{3;D}^p(x,μ)$和$ϕ_{3;D}^σ(x,μ)$是主要的误差来源。因此，获得这些DAs更合理和准确的行为非常重要。受我们之前关于π介子leading-twist DA的工作[Phys. Rev. D 104, no.1, 016021 (2021)]的启发，我们重新审视了$D$介子twist-2, 3 DAs $ϕ_{2;D}(x,μ)$、$ϕ_{3;D}^p(x,μ)$和$ϕ_{3;D}^σ(x,μ)$。提出了这三种DAs的$ξ$-矩的新求和规则公式，以获得更准确的值。改进了这些DAs的光锥谐振子模型，并通过用最小二乘法拟合$ξ$-矩的值确定了其模型参数。
英文摘要：
Due to the significant difference between the experimental measurements and the theoretical predictions of standard model (SM) for the value of $\mathcal{R}(D)$ of the semileptonic decay $B\to D\ell\barν_{\ell}$, people speculate that it may be the evidence of new physics beyond the SM. Usually, the $D$-meson twist-2, 3 distribution amplitudes (DAs) $ϕ_{2;D}(x,μ)$, $ϕ_{3;D}^p(x,μ)$ and $ϕ_{3;D}^σ(x,μ)$ are the main error sources when using perturbative QCD factorization and light-cone QCD sum rules to study $B\to D\ell\barν_{\ell}$. Therefore, it is important to get more reasonable and accurate behaviors for those DAs. Motivated by our previous work [Phys. Rev. D 104, no.1, 016021 (2021)] on pionic leading-twist DA, we revisit $D$-meson twist-2, 3 DAs $ϕ_{2;D}(x,μ)$, $ϕ_{3;D}^p(x,μ)$ and $ϕ_{3;D}^σ(x,μ)$. New sum rules formulae for the $ξ$-moments of these three DAs are suggested to obtain more accurate values. The light-cone harmonic oscillator models for those DAs are improved, and whose model parameters are determined by fitting the values of $ξ$-moments with the least squares method.
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