A Lattice QCD approach to quark orbital angular momentum in the proton based on generalized transverse momentum-dependent parton distributions (GTMDs) is enhanced methodologically by incorporating a direct derivative technique. This improvement removes a significant numerical bias that had been seen to afflict results of a previous study. In particular, the value obtained for Ji quark orbital angular momentum is reconciled with the one obtained independently via Ji’s sum rule, validating the GMTD approach. Since GTMDs simultaneously contain information about the quark impact parameter and transverse momentum, they permit a direct evaluation of the cross product of the latter. They are defined through proton matrix elements of a quark bilocal operator containing a Wilson line; the choice in Wilson line path allows one to continuously interpolate from Ji to Jaffe-Manohar quark orbital angular momentum. The latter is seen to be significantly enhanced in magnitude compared to Ji quark orbital angular momentum, confirming previous results.

中文翻译：

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直接导数法从Qi到Qaffe的Jaffe-Manohar轨道角动量

通过并入直接导数技术，从方法上增强了基于广义横向动量相关性parton分布（GTMDs）的质子夸克轨道角动量的格子QCD方法。这种改进消除了以前的研究结果受到影响的明显的数值偏差。特别是，将通过夸克求和规则独立获得的吉夸克轨道角动量值与吉夸克轨道角动量相一致，从而验证了GMTD方法。由于GTMD同时包含有关夸克冲击参数和横向动量的信息，因此它们可以直接评估后者的叉积。通过包含威尔逊线的夸克双局部算子的质子矩阵元素定义它们；威尔逊线路径的选择允许人们连续地从Ji到Jaffe-Manohar夸克轨道角动量进行插值。与吉夸克轨道角动量相比，后者的强度明显提高，证实了先前的结果。