We present an analysis of two-current correlations for the pion in the Nambu–Jona-Lasinio model, with Pauli–Villars regularization. We provide explicit expressions in momentum space for two-current correlations corresponding to the zeroth component of the vector Dirac bilinear in the quark vertices, which has been evaluated on the lattice, thinking to applications in a high energy framework, as a step towards the calculation of pion double parton distributions. The numerical results show a remarkable qualitative agreement with recent lattice data. The factorization approximation into one-body currents is discussed based on previous evaluation of the relevant low energy matrix elements in the Nambu–Jona-Lasinio model, confirming the lattice result.

我们用Pauli-Villars正则化方法对Nambu–Jona-Lasinio模型中介子的两个电流相关性进行了分析。我们提供了动量空间中与夸克顶点中矢量Dirac双线性的零分量相对应的二次电流相关性的显式表达式，该表达式已在晶格上进行了评估，并考虑了在高能框架中的应用，作为迈向计算的一步pion double parton分布。数值结果表明，其与最近的晶格数据具有明显的定性一致性。基于先前对Nambu–Jona-Lasinio模型中的相关低能矩阵元素的评估，讨论了针对单体电流的分解近似，从而确认了晶格结果。