  We develop a factorization framework to compute the double differential cross
section in soft drop groomed jet mass and groomed jet radius. We describe the
effective theories in the large, intermediate, and small groomed jet radius
regions defined by the interplay of the jet mass and the groomed jet radius
measurement. As an application we present the NLL$'$ results for the
perturbative moments that are related to the coefficients $C_1$ and $C_2$ that
specify the leading hadronization corrections up to three universal parameters.
We compare our results with Monte Carlo simulations and a calculation using the
coherent branching method.
