标题： 介子广义部分子分布和横向动量依赖部分子分布的非壳上修正 显示英文标题

标题： Off-shell modifications of the pion generalized parton distributions and transverse momentum dependent parton distributions

摘要： 介子广义部分子分布（GPDs）和与横动量相关的部分子分布（TMDs）的非壳特性在Nambu-Jona-Lasinio模型框架内被研究。 在我们之前的论文中，我们分别研究了壳上介子GPDs和轻子面波函数的性质。 特别引人注目的是比较壳上和非壳上介子GPDs之间的差异，这使我们能够探索与非壳性相关的效应。 由于缺乏交叉对称性，GPDs的矩也包含偏斜参数的奇次幂，导致新的非壳形式因子。 通过我们的计算，我们推导出校正函数，这些函数考虑了由于非壳效应导致的介子GPDs的变化。 与它们的壳上对应物不同，在非壳情况下某些性质会失效；例如，对称性性质和多项式条件可能不再成立。 此外，我们评估了非壳TMDs，并将它们与对应的壳上版本进行比较，同时研究了它们对$\bm{k}_{\perp}$的依赖性。 显示英文摘要

摘要： The off-shell characteristics of pion generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) are examined within the framework of the Nambu-Jona-Lasinio model. In our previous papers, we separately investigated the properties of on-shell pion GPDs and light-front wave functions. It is particularly intriguing to compare the differences between on-shell and off-shell pion GPDs, which allows us to explore the effects associated with off-shellness. Due to the absence of crossing symmetry, the moments of GPDs also incorporate odd powers of the skewness parameter, resulting in new off-shell form factors. Through our calculations, we derived correction functions that account for modifications in pion GPDs due to off-shell effects. Unlike their on-shell counterparts, certain properties break down in the off-shell scenario; for instance, symmetry properties and polynomiality conditions may no longer hold. Additionally, we evaluate off-shell TMDs and compare them with their on-shell equivalents while also investigating their dependence on $\bm{k}_{\perp}$.