在準部份子分布中的重整子效應

Abstract

我們從強子的等矢量準部份子分佈函數（isovector quasi parton distribution function）中的氣泡鏈圖研究了重整子歧義（renormalon ambiguity）。我們確認了 Braun Vladimirov 和 Zhang 的推論，即最具貢獻的紅外區重整子歧義在形式上是具有ΛQCD^2/(xPz)^2等級的效應，其中x表示部份子動量分數，Pz表示強子動量。我們還通過指出具有發散前因子的δ(x)貢獻來闡明在重整子歧義中夸克數守恆是如何被滿足的。為了進一步量化這種來自重整子歧義的效應，我們將氣泡鏈圖的計算展開至三圈費曼圖，並發現這些結果在RI/MOM重整化準部份子分佈與MS部份子分佈的匹配核（matching kernel）中表現了出色的收斂性。這表明在該方案（scheme）中，在三圈圖的等級下，重整子不會導致匹配核的微擾展開緩慢收斂。我們同時還證明了使用R方案（R-scheme）可以改善來自最具貢獻的重整子 歧義所導致的緩慢收斂性。

We investigate the renormalon ambiguity from bubble-chain diagrams in the isovector quasi-parton distribution function of a hadron. We confirm the assertion by Braun, Vladimirov and Zhang that the leading IR renormalon ambiguity is formally a twist-4 effect of order ΛQCD^2/(xPz)^2, with x the parton momentum fraction and Pz the hadron momentum. We also clarify how quark number conservation in the renormalon ambiguity is satisfied by identifying a delta-function-like contribution with a divergent prefactor. To further quantify this effect, we study the bubble-chain diagrams to three-loops and find excellent convergence for the matching kernel between the RI/MOM renormalized quasi-parton distribution and the MS-bar parton distribution. This suggests that renormalons do not cause a slow convergence to the perturbative kernel in this scheme at the three-loop order. The improvement of convergence using the R-scheme to remove the leading renormalon ambiguity is also demonstrated.