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 $\Delta E_{q}\propto L^{2}$, where L is the distance passed by quark in the medium. It has a weak dependence on the initial quark energy $E_{q}$. The $L^{2}$ dependence turns to $L^{1}$ 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 $\Delta E_{q}\approx 0.1 E_{q}(L/10 fm)^{\beta}$, with $\beta$ close to unity.