  Grooming techniques, such as soft drop, play a central role in reducing
sensitivity of jets to e.g. underlying event and hadronization at current
collider experiments. The momentum sharing fraction $z_g$, of the two branches
in a jet that pass the soft drop condition, is one of the most important
observables characterizing a collinear splitting inside the jet, and directly
probes the QCD splitting functions. In this work, we present a factorization
framework that enables a systematic calculation of the corresponding cross
section beyond leading-logarithmic (LL) accuracy, showing that this measurement
is not only sensitive to the QCD charge but also the spin of the parton that
initiates the jet. Our results at next-to-leading logarithmic (NLL$'$) accuracy
include non-global logarithms, and provide a first meaningful assessment of the
perturbative uncertainty. We present a comparison to the available experimental
data from ALICE, ATLAS, and STAR and find excellent agreement.
