Reaction Operator Approach to Non-Abelian Energy Loss

A systematic expansion of the induced inclusive gluon radiation associated with jet production in a dense QCD plasma is derived using a reaction operator formalism. Analytic expressions for the transverse momentum and light-cone momentum distributions are derived to all orders in powers of the gluon opacity of the medium, $N{\sigma }_g\mathrm{/}A=L\mathrm{/}{\lambda }_g$. The reaction operator approach also leads to a simple algebraic proof of the color triviality'' of single inclusive distributions and to a solvable set of recursion relations. The analytic solution generalizes previous continuum solutions (BDMPS) for applications to mesoscopic QCD plasmas. The solution is furthermore not restricted to uncorrelated geometries and allows for evolving screening scales as well as the inclusion of finite kinematic constraints. The later is particularly important because below LHC energies the kinematic constraints significantly decrease the non-abelian energy loss. Our solution for the inclusive distribution also generalizes the finite order exclusive (tagged) distribution case studied previously (GLV1). The form of the analytic solution is well suited for numerical implementation in Monte Carlo event generators to enable more accurate calculations of jet quenching in ultra-relativistic nuclear collisions. Numerical results illustrating the constributions of the first three orders in opacity are compared to the self-quenching’’ hard radiation intensity. A surprising result is that the induced gluon radiation intensity is dominated by the (quadratic in $L$) first order opacity contribution for realistic geometries and jet energies in nuclear collisions.