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arXiv 0704.3790hep-ph
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$k_T$分解中互斥过程的次首阶修正

Next-to-leading-order corrections to exclusive processes in $k_T$ factorization

Soumitra Nandi, Hsiang-nan Li

摘要:

以$πγ^*\toγ$为例,计算了$k_T$分解定理中互斥过程的次首阶修正.用$k_T^2$计算出的离壳部分子在全量子色动力学的夸克图和π波函数的有效图中都有考虑。当导出$k_T$依赖的硬核作为它们的差时,上述两组图中的规范依赖性取消。然后通过归纳法证明了硬核的所有阶规范不变性。在$k_T$依赖的π波函数的光锥奇点正则化的威尔逊线远离光锥旋转。这种正则化将因子分解方案依赖性引入到硬内核中,其可以以标准方式最小化。大的双光子数$\ln^2k_T$和$\ln^2 x$($x$是一个部分子动量分数)都是由虚光子顶点的环修正引起的,前者被吸收到π介子波函数中,并由$k_T$重算组织,后者被吸收到喷流函数中,并由阈值重算组织。对于$πγ^*\toγ$,如果将因子分解尺度设为虚光子的动量传递,则非线性光学修正仅为几个百分点。

英文摘要:

We calculate next-to-leading-order (NLO) corrections to exclusive processes in $k_T$ factorization theorem, taking $πγ^*\toγ$ as an example. Partons off-shell by $k_T^2$ are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the $k_T$-dependent hard kernel as their difference. The gauge invariance of the hard kernel is then proven to all orders by induction. The light-cone singularities in the $k_T$-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. This regularization introduces a factorization-scheme dependence into the hard kernel, which can be minimized in the standard way. Both the large double logarithms $\ln^2k_T$ and $\ln^2 x$, $x$ being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function and organized by the $k_T$ resummation, and the latter absorbed into a jet function and organized by the threshold resummation. The NLO corrections are found to be only few-percent for $πγ^*\toγ$, if setting the factorization scale to the momentum transfer from the virtual photon.

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