  To deepen the search for beyond the Standard Model physics, the Large Hadron
Collider is pushing to higher and higher luminosity. At high luminosity,
precision physics becomes increasingly difficult due to contamination from
additional proton collisions per bunch crossing called pile-up. In recent
years, many methods have been developed to cull this excess mostly low-energy
radiation away from important signal regions, but it has been unclear if these
methods were amenable to systematically-improvable theoretical understanding.
In this paper, it is shown that one such method, soft drop jet grooming, has
excellent theoretical properties: it is ultra-local, depending on only
radiation within a jet, and it is free of non-global logarithms. Calculations
of the soft drop jet mass and related observables are presented at
next-to-next-to-leading logarithmic accuracy matched to next-to-next-to-leading
fixed-order in perturbative Quantum Chromodynamics. Once measured at the Large
Hadron Collider, precision comparisons between theory and data can be made,
essentially independent of the amount of pile-up contamination.
