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

Aurore Courtoy,Sergio Scopetta,Santiago Noguera

doi:10.1140/epjc/s10052-020-08470-1

Abstract

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.

Highlights

The double Parton Distribution Functions (PDFs) of the pion have attracted considerable attention
The latter represents the first evaluation of pion double parton distribution functions (dPDFs) in a field theoretical approach, which allowed a systematical study of the different contributions to the pion observables
Since similar considerations are premature for multi parton PDFs, it seems opportune to consider the two-current correlations in the pion – quantities that could be related to dPDFs through moments – with current operators evaluated at different space points but at equal time, from a model point of view

Summary

Introduction

The double PDFs of the pion have attracted considerable attention. A first estimate has been performed using light cone wave functions obtained within the AdS/QCD correspondence [22,23] ; a calculation within a Nambu– Jona-Lasinio (NJL) framework was presented in Ref. [24]. Since similar considerations are premature for multi parton PDFs, it seems opportune to consider the two-current correlations in the pion – quantities that could be related to dPDFs through moments – with current operators evaluated at different space points but at equal time, from a model point of view. Such correlations have been calculated on the lattice, e.g., in Ref.

Definitions and isospin decomposition

Leading order

Dressing the vertex and other contributions

Conclusions