Scale dependencies of proton spin constituents with a nonperturbative αs

By introducing the contribution from dynamically generated gluon mass, we present a brand new parametrized form of QCD beta function to get an inferred limited running behavior of QCD coupling constant alpha(s). This parametrized form is regarded as an essential factor to determine the scale dependencies of the proton spin constituents at the very low scale. In order to compare with experimental results directly, we work within the gauge-invariant framework to decompose the proton spin. Utilizing the updated next-to-next-leading-order evolution equations for angular momentum observables within a modified minimal subtraction scheme, we indicate that gluon contribution to proton spin cannot be ignored. Specifically, by assuming asymptotic limits of the total quark/gluon angular momentum valid, respectively, the scale dependencies of quark angular momentum J(q) and gluon angular momentum J(g) down to Q(2) similar to 1 GeV2 are presented, which are comparable with the preliminary analysis of deeply virtual Compton scattering experiments by HERMES and JLab. After solving scale dependencies of quark spin Delta Sigma(q), orbital angular momenta of quarks L-q are given by subtraction, presenting a holistic picture of proton spin partition within up and down quarks at a low scale.