Double parton distributions in the pion in the Nambu–Jona-Lasinio model

Abstract

Two-parton correlations in the pion, a non perturbative information encoded in double parton distribution functions, are investigated in the Nambu and Jona-Lasinio model. It is found that double parton distribution functions expose novel dynamical information on the structure of the pion, not accessible through one-body parton distributions, as it happens in several estimates for the proton target and in a previous evaluation for the pion, in a light-cone framework. Expressions and predictions are given for double parton distributions corresponding to leading-twist Dirac operators in the quark vertices, and to different regularization methods for the Nambu and Jona-Lasinio model. These results are particularly relevant in view of forthcoming lattice data. arXiv:1909.09530v1 [hep-ph]

Sum rule improved double parton distributions in position space

“…It is hence essential to develop realistic models for DPDs. Considerable efforts have been made to compute them in quark models [51][52][53][54][55][56][57][58][59][60][61][62], and lattice calculations of Mellin moments of DPDs are underway [63,64]. In addition, there are important theoretical constraints on DPDs.…”

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

“…Similarly an ansatz relates the dPDFs to the product of two GPDs, and we have analyzed it in the same model in Ref. [24]. Based on our previous experience, we expect a similar contribution for the two current correlation from diagrams of the type shown in Fig.…”

“…A first estimate has been performed using light cone wave functions obtained within the AdS/QCD correspondence [22,23] ; then a calculation within a Nambu-Jona-Lasinio (NJL) framework was presented in Ref. [24]. The latter represents the first evaluation of pion dPDFs in a field theoretical approach, which allowed a systematical study of the different contributions to the pion observables.…”

“…(B.7) can be approximated by the quantities -the relevant expressions are available, e.g. in Ref [24]. 2ig 1 − 2g Π S ((P + q) 2 ) −ig 2 σ qq (P + q) 2 − m 2 σ + i , 2ig 2g Π P S ((P + q) 2 ) −ig 2 πqq (P + q) 2 − m 2 π + i .…”

Applications of the Nambu–Jona-Lasinio model to the partonic structure of the pion

“…These results, amended with the necessary QCD evolution which generates radiatively the gluon degrees of freedom, compares very favorably to the available experimental and lattice data. We briefly review some of these results and then pass to a recent topic of double parton distribution functions (dPDF) in the pion [4][5][6] evaluated in chiral quark models followed with the DGLAP evolution. We discuss the issue of partonic correlations and the proposed measures based on the Mellin moments of dPDFs [6].…”