Medium-induced parton splitting kernels from Soft Collinear Effective Theory with Glauber gluons

We derive the splitting kernels for partons produced in large Q2 scattering processes that subsequently traverse a region of strongly-interacting matter using a recently-developed effective theory SCETG. We include all corrections beyond the small-x approximation, consistent with the power counting of SCETG. We demonstrate how medium recoil, geometry and expansion scenarios, and phase space cuts can be implemented numerically for phenomenological applications. For the simplified case of infinite transverse momentum kinematics and a uniform medium, we provide closed-form analytic results that can be used to validate the numerical simulations.