Reaction operator approach to non-abelian energy loss

A systematic expansion of induced gluon radiation associated with jet production in a dense QCD plasma is derived using a reaction operator formalism. Analytic expressions for the induced inclusive gluon transverse momentum and light-cone momentum distributions are derived to all orders in powers of the opacity of the medium for gluons, N sigma (g)/A(perpendicular to) = L/lambda (g) The reaction operator approach leads to a simple algebraic proof of the color triviality of single inclusive distributions and leads to a solvable set of recursion relations. The analytic solution to all orders in opacity generalizes previous continuum solutions (BDMPS) by allowing for arbitrary correlated nuclear geometry and evolving screening scales as well as the inclusion of finite kinematic constraints. The latter is particularly important because below LHC energies the kinematic constraints significantly decrease the non-abelian energy loss. Our solution for the inclusive distribution turns out to have a much simpler structure than the exclusive (tagged) distribution case that we studied previously (GLV1). The analytic expressions are also obtained in a form suitable 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 first three orders in opacity are compared to the self-quenching hard radiation intensity that always accompanies jet production in the vacuum. 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. (C) 2001 Elsevier Science B.V. All rights reserved.