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arXiv 2006.05428hep-phhep-th
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拉普拉斯空间中$B$介子光锥分布振幅的演化

Evolution of the $B$-Meson Light-Cone Distribution Amplitude in Laplace Space

Anne Mareike Galda, Matthias Neubert

摘要:

$B$ -介子光锥分布振幅是控制$B$排斥衰变中非微扰强子动力学的中心量。我们表明,所需的信息来描述这样的过程在领先的权力在$Λ_{\rm QCD}/m_b$是最直接包含在其拉普拉斯变换$\tildeϕ_+(η)$。我们推导出该函数所满足的重整化群(RG)方程,并给出其精确解。我们用$\tildeϕ_+(η)$表示了衰变$B^-\toγ\ell^-\barν$的RG改进的QCD因子分解定理,并证明了它与因子分解标度无关。我们提出了一个无偏参数化的$\tildeϕ_+(η)$的一个小的不相关的强子参数。

英文摘要:

The $B$-meson light-cone distribution amplitude is a central quantity governing non-perturbative hadronic dynamics in exclusive $B$ decays. We show that the information needed to describe such processes at leading power in $Λ_{\rm QCD}/m_b$ is most directly contained in its Laplace transform $\tildeϕ_+(η)$. We derive the renormalization-group (RG) equation satisfied by this function and present its exact solution. We express the RG-improved QCD factorization theorem for the decay $B^-\toγ\ell^-\barν$ in terms of $\tildeϕ_+(η)$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parameterization of $\tildeϕ_+(η)$ in terms of a small set of uncorrelated hadronic parameters.

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