準部分分佈的一階混合重整化匹配核

Abstract

大動量有效理論 (Large momentum effective theory) 允許藉由使用大動量匹配夸克雙線性強子矩陣元素來提取晶格量子色動力學中的強子部分子分佈函數。我們計算了混合-RI/MOM 方案 (scheme) 下的未極化、螺旋性和橫向等矢量部份子分佈函數 (isovector parton distribution function) 和無偏斜廣義部分子分佈的匹配核(matching kernel)。此重整化方案在 Wilson 線長度小於 z_s 時使用 RI/MOM，否則使用質量減法方案。根據混合方案之設計，其在 zs → ∞ 之極限恢復為非混合方案。在相反的極限 z→0，得到自重整化方案。當參數 p^z_R = 0 和 µ_R*z_s ≪ 1 時，混合-RI/MOM 方案與混合-比率方案乘以分佈函數的電荷相符。我們還討論了改進的最小減法方案 (modified minimal subtraction scheme) 中傅里葉變換和 ε 展開的可交換性。

Large momentum effective theory allows extraction of hadron parton distribution functions in lattice QCD by matching them to quark bilinear matrix elements of hadrons with large momenta. We calculate the matching kernels for the unpolarized, helicity, and transversity isovector parton distribution functions and skewless generalized parton distributions of all hadrons in the hybrid-RI/MOM scheme. This renormalization scheme uses RI/MOM when the Wilson line length is less then zs, otherwise a mass subtraction scheme is used. By design, the non-hybrid scheme is recovered as zs → ∞. In the opposite limit, zs → 0, the self renormalization scheme is obtained. When the parameters p^z_R = 0 and µ_R*z_s ≪ 1, the hybrid-RI/MOM scheme coincides with the hybrid-ratio scheme times the charge of the PDF. We also discuss the subtlety related to the commutativity of Fourier transform and ϵ expansion in the MS scheme.