基于 QCD 求和规则的矢量介子领头扭转纵向分布振幅及相关半轻子衰变
Vector mesons leading-twist longitudinal distribution amplitudes and related semi-leptonic decays within QCD sum rules
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中文总结 AI 辅助
研究聚焦于轻矢量介子领头扭转纵向分布振幅，采用新 QCD 求和规则方案，计算$\xi$矩并拟合确定其行为，还重新计算了相关半轻子衰变过程的跃迁形状因子和分支比。
中文摘要 AI 辅助
在这项工作中，我们聚焦于轻矢量介子领头扭转纵向分布振幅$\phi^\parallel_{2;V}(x,\mu)$，其中$V = \rho, K^\ast, \phi$。为获得其精确行为，采用了我们在2021年提出的关于分布振幅的 QCD 求和规则研究新方案。通过改进的求和规则公式计算了直至十阶的$\xi$矩$\langle\xi^n\rangle_{2;V}^\parallel$，并给出了具体数值。用最小二乘法拟合确定了$\rho, K^\ast, \phi$的领头扭转纵向分布振幅行为。此外，重新计算了$D\to(\rho,K^\ast)$、$D_s\to\phi$半轻子衰变过程的跃迁形状因子和分支比。
英文摘要
In this work, we focus on the light vector meson leading-twist longitudinal distribution amplitudes (DAs) $ϕ^\parallel_{2;V}(x,μ)$ with $V = ρ, K^\ast, ϕ$. 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 $\langleξ^n\rangle_{2;V}^\parallel$ up to tenth order are calculated. In which, $\langleξ^2\rangle^\parallel_{2;ρ}=0.225^{+0.013}_{-0.012}$, $\langleξ^1\rangle^\parallel_{2;K^\ast}=-0.0228^{+0.0042}_{-0.0040}$, $\langleξ^2\rangle^\parallel_{2;K^\ast}=0.217^{+0.007}_{-0.007}$, $\langleξ^2\rangle^\parallel_{2;ϕ}=0.209^{+0.020}_{-0.020}$, and the corresponding Gegenbauer moments $a^{2;\parallel}_{2;ρ}=0.074^{+0.039}_{-0.036}$, $a^{1;\parallel}_{2;K^\ast}=-0.038^{+0.007}_{-0.007}$, $a^{2;\parallel}_{2;K^\ast}=0.050^{+0.020}_{-0.019}$, $a^{2;\parallel}_{2;ϕ}=0.027^{+0.058}_{-0.058}$ at the scale $μ= 1~{\rm GeV}$, respectively. By fitting those $\langleξ^n\rangle^\parallel_{2;V}(n = 1,2,\cdots,10)$ with the least squares method, the behaviors of leading-twist longitudinal DAs for $ρ, K^\ast, ϕ$ are determined. Further, we recalculate the transition form factors and branching ratio of the $D\to(ρ,K^\ast)$, $D_s\toϕ$ semi-leptonic decay processes.
