Speaker
Description
We evaluate the quark double parton distribution (dPDF) function of the pion in the Nambu-Jona-Lasinio model, previously used to successfully obtain related quantities such as PDF, PDA, GPD, TMD, etc. In this model the pion appears as a Goldstone boson of the spontaneously broken chiral symmetry and as a fully relativistic q qbar bound state of the Bethe-Salpeter equation. We show that at the quark model scale the model reproduces dPDF in the valon form, namely, constant times delta(1-x1-x2), where x1 and x2 are the longitudinal momentum fractions of the constituent quark and antiquark. Our analysis provides a nontrivial example of a dynamical calculation in a simple field-theoretic model, where all the required formal features are satisfied. In particular, the valon form satisfies the Gaunt-Stirling sum rules. Subsequent DGLAP evolution to higher momentum scales, achieved via Mellin moments, preserves these features. It results in a correlated partonic system, where the departure from the frequently used product ansatz is substantial.
