AI 中文总结
该研究利用四组扭质量三叶草改进费米子系综，通过调整夸克质量接近物理值并取连续统极限，计算核子能量 - 动量张量矩阵元及相关贡献，提取引力形状因子，评估夸克和胶子对质子动量和角动量的贡献并确定夸克轨道角动量。
AI 中文摘要
我们使用四组扭质量三叶草改进费米子系综来计算核子能量 - 动量张量的矩阵元，其中上、下、奇和粲夸克质量被调整到接近其物理值。这四组系综具有相似的物理体积且格点间距分别为\(a = 0.080\) fm、\(0.068\) fm、\(0.057\) fm 和\(0.049\) fm，使我们能在物理π介子质量点直接取连续统极限。我们计算了连接和非连接夸克贡献以及胶子贡献，所有重整化函数包括夸克单态与胶子的混合都是非微扰确定的。我们在\(Q^2 = 0\)的连续统极限下提取引力形状因子，并评估夸克和胶子对质子数和角动量的贡献。利用相同规范系综计算出的内禀夸克自旋值，我们还确定了每种夸克味的轨道角动量。
英文摘要
We compute the matrix elements of the energy-momentum tensor of the nucleon using four ensembles of twisted mass clover-improved fermions with the up, down, strange and charm quark masses tuned to approximately their physical values. The four ensembles have similar physical volume and lattice spacings $a=0.080$~fm, $0.068$~fm, $0.057$~fm, and $0.049$ fm, allowing us to take the continuum limit directly at the physical pion mass point. We compute both connected and disconnected quark contributions as well as gluon contributions. All renormalization functions, including the mixing of the quark singlet with the gluon, are determined non-perturbatively. We extract the gravitational form factors in the continuum limit at $Q^2=0$ and evaluate the contribution of quarks and gluons to the momentum and angular momentum of the proton. Using the values of the intrinsic quark spin computed using the same gauge ensembles we also determine the orbital angular momentum for each quark flavor.
Comments33 pages, 34 figures
