重加化及其應用

Abstract

在本論文中我們即將展示：根據Collins及Soper(CS)所發展的重加化技巧， 將對現行微擾量子色動力學中已知的各種單一或雙重指數發散，指出期間的關 係並形成整體的觀點。對部分子分佈函數的kT重加化 與閥值重加化而言，將可 以視為將實膠子發射的貢獻做軟近似的結果。同時，我們也將展示CS的重加 化技巧提供一個簡單而統一的觀點來重新組織各種不同形式的指數發散，進而 在不同的運動區間，化約成著名的DGLAP, BFKL 與CCFM等演化方程式，各 方程式之間的關係將因此顯得清楚透明。我們也將用由不同的演化方程式所解 出的膠子分佈函數，來計算結構函數F2及FL，同時觀察到由修正BFKL方程式 與CCFM方程式所得到的結果，可以吻合實驗數據。在CS的架構下，我們同 時可以推導一個新的統一演化方程式，它將加整ln Q 和 ln (1/x) 等指數發散的 貢獻，改善CCFM方程式的結果。

In this article we demonstrated the relation among all known single- and double-logarithm summations by means of the CS technique. For the kT and threshold resummations for parton distribution functions, it has been understood that the summations of the different logarithms are determined by the soft approximations for the real gluon emissions, respectively. Also, we have shown that the resummation technique provides a unified and simple viewpoint to the organization of the various large logarithms, and reduces to the DGLAP, BFKL and CCFM equation in different kinematic regions. By means of the resummation technique, the connection among the evolution equations becomes transparent. We have calculated the structure functions F2 , F,L using gluon distribution functions solved from different evolution equations. It has been observed that the predictions from the modified BFKL equation and from the CCFM equations are consistent with the data of experiments. Within the CS approach, we can also derive a new unified evolution equation for the ln Q and ln (1/x) summations, which improves the CCFM equation.