Two-current correlations in the pion in the Nambu and Jona-Lasinio model

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.