Medium-induced splitting kernels from SCETG

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