标题： Collins-Soper 核与格点 QCD 中的简化软函数 显示英文标题

标题： Collins-Soper Kernel and Reduced Soft Function in Lattice QCD

摘要： 我们评估了Collins-Soper核和约简的软函数，在格点QCD中结合了$\mathcal{O}(\alpha_s)$匹配修正。 该计算依赖于使用非对称的“十字形”夸克双线性算符和四点介子形式因子来评估准横动量依赖的波函数。 这些量是通过使用两个$N_f=2+1+1$扭曲质量费米子系综非微扰地计算的，具有相同的格点间距$a=0.093$fm：第一个系综的格点尺寸为$24^3 \times 48$，介子质量为346 MeV；第二个系综的格点尺寸为$32^3 \times 64$，介子质量为261 MeV。 Collins-Soper核和软函数用于确定横动量依赖的强子分布函数。 显示英文摘要

摘要： We evaluate the Collins-Soper kernel and the reduced soft function in lattice QCD, incorporating $\mathcal{O}(\alpha_s)$ matching corrections. The calculation relies on the evaluation of the quasi-transverse momentum-dependent wave function with asymmetric staple-shaped quark bilinear operators and four-point meson form factors. These quantities are computed non-perturbatively using two $N_f=2+1+1$ twisted-mass fermion ensembles with the same lattice spacing of $a=0.093$ fm: the first ensemble has a lattice size of $24^3 \times 48$ and a pion mass of 346 MeV; the second one has a lattice size of $32^3 \times 64$ and a pion mass of 261 MeV. The Collins-Soper kernel and the soft function are needed for the determination of the transverse momentum-dependent parton distribution functions.