论文标题
大型摩托车有效理论与短途操作员的扩展：对比度和互补性
Large-Momentum Effective Theory vs. Short-Distance Operator Expansion: Contrast and Complementarity
论文作者
论文摘要
尽管在无限摩托车极限上等效，但大型摩肌有效理论（lamet）和短距离运算符产品扩展（SD-ope）是从大型摩尔植物中提取Parton分布函数（PDF）的两种不同方法。 Lamet在$λ_ {\ rm qcd}/[x（1-x）p^z] $中实现动量空间的扩展，以直接在[x _ {x _ {\ rm min} max} \ sim 1-x _ {\ min}] $。 SD-OPE在小欧几里得距离上应用扰动QCD $ z $提取范围$ [0，λ_{\ rm max}] $的领先相关相关性，$ h（λ= zp^z）$，对应于PDF的傅立叶变换。与量子机械不确定性原理类似，不完整的领先扭转相关性不能容易转换为动量空间的局部分布，而解决``反向问题''的方法基本上涉及对$λ_{\ rm max} $ yest of $λ__{\ rm max} $的缺失信息建模。另一方面，短途相关性以及预期的终点渐进剂可用于现象学上适合板条平均区域中的pdf：$ x \ in [0，x _ {\ rm min}] $和$ [x _ {\ rm min}] $和$ [x _ {x _ {\ rm max max}，1] $。我们使用来自ANL/BNL协作的Pion Valence Quark分布的最新结果来证明这一点。
Although equivalent in the infinite-momentum limit, large-momentum effective theory (LaMET) and short-distance operator product expansion (SD-OPE) are two different approaches to extract parton distribution functions (PDFs) from coordinate-space correlation functions in large-momentum hadrons. LaMET implements a momentum-space expansion in $Λ_{\rm QCD}/[x(1-x)P^z]$ to directly calculate PDFs $f(x)$ in a middle region of Bjorken $x\in [x_{\rm min}\sim Λ_{\rm QCD}/P^z, x_{\rm max}\sim 1-x_{\min}]$. SD-OPE applies perturbative QCD at small Euclidean distances $z$ to extract a range $[0,λ_{\rm max}]$ of leading-twist correlations, $h(λ=zP^z)$, corresponding to the Fourier transformation of PDFs. Similar to the quantum mechanical uncertainty principle, an incomplete leading-twist correlation cannot be readily converted to a momentum-space local distribution, and the methods to solve the ``inverse problem'' involve essentially modelling of the missing information beyond $λ_{\rm max}$. On the other hand, short-distance correlations, along with the expected end-point asymptotics, can be used to phenomenologically fit the PDFs in the LaMET-complementary regions: $x\in [0,x_{\rm min}]$ and $[x_{\rm max}, 1]$. We use the recent results of the pion valence quark distribution from the ANL/BNL collaboration to demonstrate this point.
