Abstract
Gluon dressing of the light quarks within hadrons is very strong and extremely important in that it dynamically generates most of the observable mass through the breaking of chiral symmetry. The quark and gluon parton densities, q(x) and g(x), are necessarily interrelated since any gluon emission and absorption process, especially dressing of a quark, contributes to g(x) and modifies q(x). Guided by long-established results for the parton-in-parton distributions from a strict 1-loop perturbative analysis of a quark target, we extend the non-perturbative QCD approach based on the Rainbow-Ladder truncation of the Dyson-Schwinger equations to describe the interrelated valence qv(x) and the dressing-gluon g(x) for a hadron at its intrinsic model scale. We employ the pion description from previous DSE work that accounted for the gluon-in-quark effect, and introduce a simple model of the nucleon for exploratory purposes. We find typically 〈x〉g∼0.20 for both pion and nucleon at the model scale, and the valence quark helicity contributes 52% of nucleon spin. We deduce both qv(x) and g(x) from 30 calculated Mellin moments, and after adopting existing data analysis results for qsea(x), we find that NLO scale evolution produces g(x) in good agreement with existing data analysis results for the pion at 1.3 GeV and the nucleon at 5 GeV2. At the scale 2 GeV typical of lattice-QCD calculations, we obtain 〈x〉gN=0.42 in good agreement with 0.38 from the average of recent lattice-QCD calculations.
Highlights
Outlook: We extend the DSE-RL approach to enable the calculation of the gluon parton distribution functions (PDFs) a ributable to the dressing of quarks
We nd the dressing gluon carries about 20% of the lightcone momentum fraction for both hadrons
Due to the strength of dynamical chiral symmetry breaking, this quark dressing mechanism is expected to produce most of the gluon PDF of light-quark hadrons
Summary
Gluon dressing of the light quarks within hadrons is very strong and extremely important in that it dynamically generates most of the observable mass through the breaking of chiral symmetry. e quark and gluon parton densities, q(x) and g(x), are necessarily interrelated since any gluon emission and absorption process, especially dressing of a quark, contributes to g(x) and modi es q(x). Guided by long-established results for the parton-in-parton distributions from a strict 1-loop perturbative analysis of a quark target, we extend the non-perturbative QCD approach based on the Rainbow-Ladder truncation of the Dyson-Schwinger equations to describe the interrelated valence qv(x) and the dressing-gluon g(x) for a hadron at its intrinsic model scale. We nd typically x g ∼ 0.20 for both pion and nucleon at the model scale, and the valence quark helicity contributes 52% of nucleon spin. We deduce both qv(x) and g(x) from 30 calculated Mellin moments, and a er adopting existing data analysis results for qsea(x), we nd that NLO scale evolution produces g(x) in good agreement with existing data analysis results for the pion at 1.3 GeV and the nucleon at 5 GeV2. 0.38 from the average of recent la ice-QCD calculations
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