  We study the jet energy drop, which is the relative difference between the
groomed and ungroomed jet energy or transverse momentum. It is one of the
fundamental quantities that characterizes the impact of grooming on jets
produced in high energy collisions. We consider three different grooming
algorithms i) soft drop, ii) iterated soft drop, and iii) trimming. We carry
out the resummation of large logarithms of the jet energy drop, the jet radius
as well as relevant grooming parameters at next-to-leading logarithmic (NLL$'$)
accuracy. In addition, we account for non-global and clustering logarithms, and
determine the next-to-leading order corrections. For soft drop we perform a
joint resummation of the jet energy drop and the groomed jet radius, which is
necessary to achieve the correct all-order structure of the cross section, in
particular for the Sudakov-safe case of soft drop with $\beta=0$. We present
numerical results for LHC energies and compare to Pythia simulations as well as
CMS data. Our factorization framework predicts the onset of nonperturbative
effects in the jet energy distribution, in line with what we find in Pythia.
The jet energy drop observables stand out because they only probe soft
radiation, making them ideal candidates for the tuning of parton shower Monte
Carlo event generators and for probing medium effects in heavy-ion collisions.
