We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function $g_T(x)=g_1(x)+g_2(x)$, the less-studied but known transverse gluon polarization density $\mathrm{\Delta }{G}_T(x)$, and quark and gluon canonical orbital angular momentum densities associated with transverse polarization. This is the counter part of the sum rule for the longitudinal spin of the proton derived by Jaffe and Manohar previously. We relate the partonic canonical orbital angular momentum densities to a new class of twist-3 generalized parton distribution functions which are potentially measurable in deep-virtual exclusive processes. We also discuss in detail an important technicality related to the transverse polarization in the infinite momentum frame, i.e., separation of intrinsic contributions from the extrinsic ones. We apply our finding to the transverse-space distributions of partons, angular momentum, and magnetic moment, respectively, in a transversely polarized proton.

我们为质子的横向自旋推导出了一个新的扭曲 3 部分和规则，它涉及众所周知的夸克自旋结构函数 $G_{吨}(X)=G_1(X)+G_2(X)$，研究较少但已知的横向胶子极化密度 $\mathrm{\Delta }{G}_{吨}(X)$，以及与横向极化相关的夸克和胶子规范轨道角动量密度。这是先前由 Jaffe 和 Manohar 推导出的质子纵向自旋求和规则的对立部分。我们将partonic 规范轨道角动量密度与一类新的twist-3 广义parton 分布函数联系起来，这些函数在深度虚拟独占过程中可能是可测量的。我们还详细讨论了与无限动量框架中的横向极化相关的一个重要技术问题，即内在贡献与外在贡献的分离。我们将我们的发现分别应用于横向极化质子中部分子、角动量和磁矩的横向空间分布。