近日，中国格点合作组The Lattice Parton Collaboration (LPC)与德国雷根斯堡大学的Hai-Tao Shu等人合作，并取得一项新进展。经过不懈努力，他们实现内禀软函数和Collins-Soper核的格点计算。相关研究成果已于2023年8月25日在国际知名学术期刊《高能物理杂志》上发表。

该研究团队在包含单回路微扰贡献的大动量有效理论框架下，利用格点QCD计算了软函数。软函数是确定光锥物体点阵的关键因素，通过横向动量依赖(TMD)分解实现。它由与速度无关的内禀软函数和与速度依赖的Collins-Soper核组成。为确定本征部分所需的伪标量介子形式因子，研究人员采用了适当的归一化方法，并通过Fierz重排抑制了高扭度效应。在计算Collins-Soper核时，研究人员考虑了CLS集成，而不是之前研究中使用的MILC集成。

此外，研究人员比较了使用准TMDWFs和准TMDPDFs确定Collins-Soper内核的适用性。作为一个例子，他们利用确定的软函数获得了介子的物理TMD波函数(WFs)和质子的非极化等矢量TMD部分子分布函数(PDFs)。

附：英文原文

Title: Lattice calculation of the intrinsic soft function and the Collins-Soper kernel

Author: Chu, Min-Huan, He, Jin-Chen, Hua, Jun, Liang, Jian, Ji, Xiangdong, Schfer, Andreas, Shu, Hai-Tao, Su, Yushan, Walter, Lisa, Wang, Wei, Wang, Ji-Hao, Yang, Yi-Bo, Zeng, Jun, Zhang, Qi-An

Issue&Volume: 2023-08-25

Abstract: We calculate the soft function using lattice QCD in the framework of large momentum effective theory incorporating the one-loop perturbative contributions. The soft function is a crucial ingredient in the lattice determination of light cone objects using transverse-momentum-dependent (TMD) factorization. It consists of a rapidity-independent part called intrinsic soft function and a rapidity-dependent part called Collins-Soper kernel. We have adopted appropriate normalization when constructing the pseudoscalar meson form factor that is needed in the determination of the intrinsic part and applied Fierz rearrangement to suppress the higher-twist effects. In the calculation of CS kernel we consider a CLS ensemble other than the MILC ensemble used in a previous study. We have also compared the applicability of determining the CS kernel using quasi TMDWFs and quasi TMDPDFs. As an example, the determined soft function is used to obtain the physical TMD wave functions (WFs) of pion and unpolarized iso-vector TMD parton distribution functions (PDFs) of proton.

DOI: 10.1007/JHEP08(2023)172

Source: https://link.springer.com/article/10.1007/JHEP08(2023)172