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

Precision physics with pile-up insensitive observables