  Using the framework of soft-collinear effective theory with Glauber gluons
($\SCETG$), we evaluate medium-induced splitting kernels. Because of the power
counting of the effective theory, our results are valid for arbitrary, not
necessarily small values of the energy fraction $x$ taken by the emitted
parton. In this framework we prove the factorization from the hard process and
gauge invariance of the splitting kernels, we also show how nuclear recoil and
the phase space cuts can be implemented into the phenomenology.
