标题： 横动量矩 显示英文标题

标题： Transverse momentum moments

摘要： 我们建立了横向动量依赖分布（TMDs）与collinear分布之间的稳健关系。 我们定义了TMD的加权积分，称之为横向动量矩（TMMs），并证明TMMs等于在某种极小减除方案下评估的collinear分布。 转换到修正的极小减除（$\bar{MS}$）方案可以通过一个可计算因子完成，对于某些情况，我们推导出该因子直至三圈。 我们详细讨论了零阶、一阶和二阶TMM，并基于当前TMD的提取结果提供了它们的经验结果。 本文的结果为三维和collinear强子结构的理论与经验研究开辟了新的途径。 显示英文摘要

摘要： We establish robust relations between Transverse Momentum Dependent distributions (TMDs) and collinear distributions. We define weighted integrals of TMDs that we call Transverse Momentum Moments (TMMs) and prove that TMMs are equal to collinear distributions evaluated in some minimal subtraction scheme. The conversion to the modified minimal subtraction ($\bar{MS}$) scheme, can be done by a calculable factor, which we derive up to three loops for some cases. We discuss in detail the zeroth, the first, and the second TMMs and provide phenomenological results for them based on the current extractions of TMDs. The results of this paper open new avenues for theoretical and phenomenological investigation of the three-dimensional and collinear hadron structures.