Multiple Scattering, Parton Energy Loss, and Modified Fragmentation Functions in Deeply InelasticeAScattering

Modified quark fragmentation functions in deeply inelastic $\mathrm{eA}$ collisions and their QCD evolution equations are derived for the first time in the framework of multiple parton scattering. Induced radiation gives rise to additional terms in the evolution equations and thus softens the modified quark fragmentation functions. The results in the next-leading-twist depend on both diagonal and off-diagonal twist-four parton distributions and the combination of which clearly manifests the LPM interference pattern. The predicted modification depends quadratically on the nuclear size ( $A^{2/3}$). Generalization to the case of hot QCD medium is also discussed.