Deriving the QCD evolution equations under the Abelian decomposition scheme

Abstract

The Abelian decomposition of QCD reveals two types of gluons: color-neutral ``neurons" and color-carrying ``chromons". This classification does not alter the overall properties of QCD, but the investigation of different types of gluon dynamics is necessary. By employing the Cho-Duan-Ge decomposition theorem, we have derived dynamic evolution equations for two types of gluons by using the time-ordered perturbation theory. We propose that the new equations are compatible with the DGLAP equations, requiring only the separate contributions of neurons and chromons to be summed. Surprisingly, with the evolution to high $Q^2$, the ratio of the number of chromons to neurons is approximately 3:1 in small-$x$ region regardless of the inputs at evolution starting point. The new gluon dynamic equations reevaluate the gluon distribution functions and allow for a elaborate inverstigation of the distinct contributions of gluons in high-energy collisions.