Zhang Kuan, Ji Xiangdong, Yang Yi-Bo, Yao Fei, Zhang Jian-Hui
University of Chinese Academy of Sciences, School of Physical Sciences, Beijing 100049, China.
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Phys Rev Lett. 2022 Aug 19;129(8):082002. doi: 10.1103/PhysRevLett.129.082002.
To calculate the transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice QCD, an important goal yet to be realized, it is crucial to establish a viable nonperturbative renormalization approach for linear divergences in the corresponding Euclidean quasi-TMDPDF correlators in large-momentum effective theory. We perform a first systematic study of the renormalization property of the quasi-TMDPDFs by calculating the relevant matrix elements in a pion state at five lattice spacings ranging from 0.03 fm to 0.12 fm. We demonstrate that the square root of the Wilson loop combined with the short distance hadron matrix element provides a successful method to remove all ultraviolet divergences of the quasi-TMD operator, and thus provides the necessary justification to perform a continuum limit calculation of TMDPDFs. In contrast, the popular regularization independent momentum subtraction renormalization (RI/MOM) scheme fails to eliminate all linear divergences.
要从格点量子色动力学计算横动量依赖的部分子分布函数（TMDPDFs），这一重要目标尚未实现，关键在于为大动量有效理论中相应欧几里得准TMDPDF关联函数的线性发散建立一种可行的非微扰重整化方法。我们通过计算在从0.03飞米到0.12飞米的五个格距下π介子态的相关矩阵元，对准TMDPDFs的重整化性质进行了首次系统研究。我们证明，威尔逊圈的平方根与短程强子矩阵元相结合，提供了一种成功的方法来消除准TMD算符的所有紫外发散，从而为进行TMDPDFs的连续极限计算提供了必要的依据。相比之下，流行的与正则化无关的动量减法重整化（RI/MOM）方案未能消除所有线性发散。
