  We present results for the soft drop groomed jet radius $R_g$ at
next-to-leading logarithmic accuracy. The radius of a groomed jet which
corresponds to the angle between the two branches passing the soft drop
criterion is one of the characteristic observables relevant for the precise
understanding of groomed jet substructure. We establish a factorization
formalism that allows for the resummation of all relevant large logarithms,
which is based on demonstrating the all order equivalence to a jet veto in the
region between the boundaries of the groomed and ungroomed jet. Non-global
logarithms including clustering effects due to the Cambridge/Aachen algorithm
are resummed to all orders using a suitable Monte Carlo algorithm. We perform
numerical calculations and find a very good agreement with Pythia 8
simulations. We provide theoretical predictions for the LHC and RHIC.
