从twist-3广义部分子分布计算质子中的夸克轨道角动量
Quark orbital angular momentum in the proton from a twist-3 generalized parton distribution
AI总结：
本文基于Lattice QCD计算twist-3广义部分子分布$\widetilde{E}_{2T}$的第二个Mellin矩，评估了质子中的夸克轨道角动量，验证了该方法与既有替代方法结果的一致性。
摘要：
通过在向前极限下计算twist-3广义部分子分布$\widetilde{E}_{2T}$的第二个Mellin矩，评估了质子中的夸克轨道角动量，该计算基于Lattice QCD。本文回顾了这种夸克轨道角动量方法与Lattice QCD计算中先前使用的方法（即通过广义横向动量依赖部分子分布和Ji求和规则）之间的联系。这种联系可以通过洛伦兹不变性和运动方程关系来给出。$\widetilde{E}_{2T}$的第二个Mellin矩的计算，是通过具有直线路径规范连接且在纵向和横向均存在分离的夸克双局域算符的有限动量质子矩阵元进行的。对前一分量的依赖性用于提取第二个Mellin矩，而对后一分量的依赖性为矩阵元提供了横向动量截断。此外，需要矩阵元在向前极限下对动量转移的导数，这是使用直接求导法获得的。该计算利用了在317 MeV pion质量下的clover费米子系综。所得的夸克轨道角动量与先前通过替代方法的评估结果一致，尽管在使用可比数量的样本时具有更大的统计不确定性。
英文摘要：
Quark orbital angular momentum in the proton is evaluated via a Lattice QCD calculation of the second Mellin moment of the twist-3 generalized parton distribution $\widetilde{E}_{2T} $ in the forward limit. The connection between this approach to quark orbital angular momentum and approaches previously utilized in Lattice QCD calculations, via generalized transverse momentum-dependent parton distributions and via Ji's sum rule, is reviewed. This connection can be given in terms of Lorentz invariance and equation of motion relations. The calculation of the second Mellin moment of $\widetilde{E}_{2T} $ proceeds via a finite-momentum proton matrix element of a quark bilocal operator with a straight-line gauge connection and separation in both the longitudinal and transverse directions. The dependence on the former component serves to extract the second Mellin moment, whereas the dependence on the latter component provides a transverse momentum cutoff for the matrix element. Furthermore, a derivative of the matrix element with respect to momentum transfer in the forward limit is required, which is obtained using a direct derivative method. The calculation utilizes a clover fermion ensemble at pion mass 317 MeV. The resulting quark orbital angular momentum is consistent with previous evaluations through alternative approaches, albeit with greater statistical uncertainty using a comparable number of samples.
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