  Jet substructure is playing a central role at the Large Hadron Collider (LHC)
probing the Standard Model in extreme regions of phase space and providing
innovative ways to search for new physics. Analytic calculations of
experimentally successful observables are a primary catalyst driving
developments in jet substructure, allowing for a deeper understanding of
observables and for the exploitation of increasingly subtle features of jets.
In this paper we present a field theoretic framework enabling systematically
improvable calculations of groomed multi-prong substructure observables, which
builds on recent developments in multi-scale effective theories. We use this
framework to compute for the first time the full spectrum for groomed tagging
observables at the LHC, carefully treating both perturbative and
non-perturbative contributions in all regions. Our analysis enables a precision
understanding which we hope will improve the reach and sophistication of jet
substructure techniques at the LHC.
