Phase space description of the leading order quark and gluon production from a space-time dependent chromofield

Abstract

We derive source terms for the production of quarks and gluons from the QCD vacuum in the presence of a space-time dependent external chromofield ${A}_{\mathrm{cl}}$ to the order of ${S}^{(1)}.$ We find that the source terms for the parton production processes ${A}_{\mathrm{cl}}\ensuremath{\rightarrow}q\overline{q}$ and ${A}_{\mathrm{cl}}{,A}_{\mathrm{cl}}{A}_{\mathrm{cl}}\ensuremath{\rightarrow}\mathrm{gg}$ also include the annihilation processes $q\overline{q}\ensuremath{\rightarrow}{A}_{\mathrm{cl}}$ and $g\stackrel{\ensuremath{\rightarrow}}{g}{A}_{\mathrm{cl}}{,A}_{\mathrm{cl}}{A}_{\mathrm{cl}}.$ The source terms we derive are applicable for the description of the production of partons with momentum p larger than $\mathrm{gA}$ which itself must be larger than ${\ensuremath{\Lambda}}_{\mathrm{QCD}}.$ We observe that these source terms for the production of partons from a space-time dependent chromofield can be used to study the production and equilibration of the quark-gluon plasma during the very early stages of an ultrarelativistic heavy-ion collision.