Pion and kaon valence quark distribution functions from Dyson-Schwinger equations

TL;DR

This paper uses Dyson-Schwinger equations to calculate pion and kaon valence quark distribution functions, revealing valence characteristics, symmetry breaking effects, and comparing results with experimental data, highlighting the role of gluons.

Contribution

It introduces a new precise calculation technique for valence PDFs using Dyson-Schwinger equations and modified impulse approximation.

Findings

Good agreement with pion valence PDF data.

Deviation observed in kaon PDFs, suggesting gluon contributions differ.

Highlights the importance of nonperturbative gluon effects in mesons.

Abstract

Using realistic quark propagators and meson Bethe-Salpeter amplitudes based on the Dyson-Schwinger equations, we calculate the pion and kaon's valence parton distribution functions (PDF) through the modified impulse approximation. The PDFs we obtained at hadronic scale have the purely valence characteristic and exhibit both dynamical chiral symmetry breaking and SU(3) flavor symmetry breaking effects. A new calculation technique is introduced to determine the valence PDFs with precision. Through NLO DGLAP evolution, our result is compared with pion and kaon valence PDF data at experimental scale. Good agreement is found in the case of pion, while deviation emerges for kaon. We point out this situation can be resolved by incorporating gluon contributions into the mesons if the pion hosts more gluons than kaon nonperturbatively.