We present first analytic, resummed calculations of the rates at which widespread jet substructure tools tag QCD jets. As well as considering trimming, pruning and the mass-drop tagger, we introduce modified tools with improved analytical and phenomenological behaviours. Most taggers have double logarithmic resummed structures. The modified mass-drop tagger is special in that it involves only single logarithms, and is free from a complex class of terms known as non-global logarithms. The modification of pruning brings an improved ability to discriminate between the different colour structures that characterise signal and background. As we outline in an extensive phenomenological discussion, these results provide valuable insight into the performance of existing tools and help lay robust foundations for future substructure studies.

In this paper, we review recent theoretical progress and the latest experimental results in jet substructure from the Tevatron and the LHC. We review the status of and outlook for calculation and simulation tools for studying jet substructure. Following up on the report of the Boost 2010 workshop, we present a new set of benchmark comparisons of substructure techniques, focusing on the set of variables and grooming methods that are collectively known as 'top taggers'. To facilitate further exploration, we have attempted to collect, harmonize and publish software implementations of these techniques.

We consider the mass distribution of QCD jets after the application of jet substructure methods, specifically the mass-drop tagger, pruning, trimming and their variants. In contrast to most current studies employing Monte Carlo methods, we carry out analytical calculations at the next-to-leading order level, which are sufficient to extract the dominant logarithmic behaviour for each technique, and compare our findings to exact fixed-order results. Our results should ultimately lead to a better understanding of these jet substructure methods which in turn will influence the development of future substructure tools for LHC phenomenology.