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arXiv 1002.1177hep-ph
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坐标空间重夸克有效理论中B介子分布振幅的演化方程

Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space

Hiroyuki Kawamura, Kazuhiro Tanaka

摘要:

B介子分布振幅(DA)是重夸克有效理论中夸克-反夸克双局域光锥算符的矩阵元,对应于B介子衰变因子分解公式中的长距离分量. B介子DA的演化方程受尖点反常维数和Dokshitzer-Gribov-Lipatov-Altarelli-Parisi型反常维数的支配,这些反常维数给出了坐标空间表象中的“准定域”核.我们表明,这个演化方程可以解析地解决在坐标空间中,完成相关的Sudakov重积在下一个领先的对数精度。准定域性质导致我们的解的一个非常简单的形式,它确定了具有夸克-反夸克光锥分离$t$的B介子DA在较低的重整化尺度$μ$与较小的夸克间分离$zt$($z \leq 1$)。这个公式使我们能够在因子分解标度$\sim \sqrt{m_b Λ_{\rm QCD}}$下对$t$小于$\sim 1$ ^{-1}的B介子DA进行严格的计算,使用最近获得的DA的算子乘积展开作为$μ\sim 1$ GeV的输入。我们还推导了主公式,它重新表示的积分的DA在$μ\sim \sqrt{m_b Λ_{\rm QCD}}$的因式分解公式的紧凑积分的DA在$μ\sim 1$ GeV。

英文摘要:

The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the "quasilocal" kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate-space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation $t$ in terms of the DA at a lower renormalization scale $μ$ with smaller interquark separations $zt$ ($z \leq 1$). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale $\sim \sqrt{m_b Λ_{\rm QCD}}$ for $t$ less than $\sim 1$ GeV^{-1}, using the recently obtained operator product expansion of the DA as the input at $μ\sim 1$ GeV. We also derive the master formula, which reexpresses the integrals of the DA at $μ\sim \sqrt{m_b Λ_{\rm QCD}}$ for the factorization formula by the compact integrals of the DA at $μ\sim 1$ GeV.

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