Radiative energy loss of high energy quarks in finite-size nuclear matter and quark-gluon plasma

The induced gluon radiation of a high energy quark in a finite-size QCD medium is studied. For a sufficiently energetic quark produced inside a medium we find the radiative energy loss ∆Eq ∝ L, where L is the distance passed by quark in the medium. It has a weak dependence on the initial quark energy Eq. The L 2 dependence turns to L as the quark energy decreases. Numerical calculations are performed for a cold nuclear matter and a hot quark-gluon plasma. For a quark incident on a nucleus we predict ∆Eq ≈ 0.1Eq(L/10 fm), with β close to unity. The radiative energy loss of a high energy parton in a QCD medium is under active investigation nowadays [1-5]. In classical electrodynamics the radiation of a charged particle in a dense medium was first considered long ago by Landau and Pomeranchuk [6]. The quantum treatment of this phenomenon was given by Migdal [7]. In Ref. [4] (see also [8]) we developed a new path integral approach to the bremsstrahlung in a dense medium applicable both in QED and QCD. In the present paper we evaluate within the formalism of Ref. [4] the radiative energy loss of a fast quark, ∆Eq, propagating through a finite-size uniform QCD medium. We consider both a cold nuclear matter and a hot quarkgluon plasma (QGP). Following [2] we model QGP by a system of static scattering centres described by the Debye screened potential∝ exp(−rμD)/r, where μD is the color screening mass. For the screening mass we use perturbative formula μD = (1 + nF/6) gs T [9], where gs = √ 4παs is the QCD coupling constant, T is the temperature of QGP. We assume that a fast quark produced at z = 0 through a hard mechanism propagates in a medium of extent L along z axis. Neglecting the multigluon emission the radiative energy loss can be written as