Multiple Collisions and Induced Gluon Bremsstrahlung in QCD

Induced soft gluon bremsstrahlung associated with multiple collisions is calculated via perturbative QCD. We derive the non-abelian analog of the Landau-Pomeranchuk effect that suppresses induced soft radiation with formation times exceeding the mean free path, $\lambda$. The dependence of the suppression effect on the $SU(N)$ representation of the jet parton as well as the kinematic variables is expressed through a radiation formation factor. Unlike in QED, the finite contribution from the small $x$ regime in QCD leads to an approximately constant radiative energy loss per unit length, $dE/dz\propto \mu^2$, in the high energy limit that is sensitive to the infrared screening scale, $\mu$, of the medium. As a function of the dimensionless parameter $\zeta=\lambda \mu^2/E$, we show furthermore how the energy dependence of $dE/dz$ evolves from the above constant for $\zeta\ll 1$ to the more familiar (Bethe-Heitler) linear dependence for $\zeta \gg 1$.