The parton distribution function in a pion with Minkowskian dynamics

TL;DR

This paper derives the pion's parton distribution function directly from Minkowski space dynamics using a Bethe-Salpeter equation, providing new insights into the pion's internal structure and Fock component contributions.

Contribution

First calculation of the pion's parton distribution from Minkowski space dynamics with a Bethe-Salpeter approach, including higher Fock components and comparison with experimental data.

Findings

Higher Fock components significantly contribute at low momentum fractions.

Valence component dominates at high momentum fractions.

Tail behavior of the distribution fits an exponent of ~3 at 5.2 GeV.

Abstract

The parton distribution of the pion is obtained for the first time from the solution of a dynamical equation in Minkowski space. The adopted equation is the homogeneous Bethe-Salpeter one with a ladder kernel, described in terms of i) constituent quarks and gluons degrees of freedom, and ii) an extended quark-gluon vertex. The masses of quark and gluon as well as the interaction-vertex scale have been chosen in a range suggested by lattice QCD calculations, and calibrated to reproduce both pion mass and decay constant. Beside the full parton distribution, we have also calculated the contribution from the light-front valence wave function, corresponding to the lowest Fock component in the expansion of the pion state. After applying an evolution with an effective charge and a LO splitting function, a detailed and inspiring comparison with both the extracted experimental data ( with and without resummation effects) and other recent calculations obtained in different frameworks is presented. Interestingly, in a wide region of longitudinal-momentum fraction, the parton distribution function receives sizable contributions from the higher Fock-components of the pion state at the initial scale, while approaching the tail the light-front valence component dominates, as expected. Moreover, an exponent $\sim$ 3 is found suitable for describing the tail at the scale 5.2 GeV.