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  1. Even though jet substructure was not an original design consideration for the Large Hadron Collider (LHC) experiments, it has emerged as an essential tool for the current physics program. We examine the role of jet substructure on the motivation for and design of future energy Frontier colliders. In particular, we discuss the need for a vibrant theory and experimental research and development program to extend jet substructure physics into the new regimes probed by future colliders. Jet substructure has organically evolved with a close connection between theorists and experimentalists and has catalyzed exciting innovations in both communities. We expect such developments will play an important role in the future energy Frontier physics program. 
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  2. Abstract In this work, we consider the case of a strongly coupled dark/hidden sector, which extends the Standard Model (SM) by adding an additional non-Abelian gauge group. These extensions generally contain matter fields, much like the SM quarks, and gauge fields similar to the SM gluons. We focus on the exploration of such sectors where the dark particles are produced at the LHC through a portal and undergo rapid hadronization within the dark sector before decaying back, at least in part and potentially with sizeable lifetimes, to SM particles, giving a range of possibly spectacular signatures such as emerging or semi-visible jets. Other, non-QCD-like scenarios leading to soft unclustered energy patterns or glueballs are also discussed. After a review of the theory, existing benchmarks and constraints, this work addresses how to build consistent benchmarks from the underlying physical parameters and present new developments for the pythia Hidden Valley module, along with jet substructure studies. Finally, a series of improved search strategies is presented in order to pave the way for a better exploration of the dark showers at the LHC. 
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  3. Typical LHC analyses search for local features in kinematicdistributions. Assumptions about anomalous patterns limit them to arelatively narrow subset of possible signals. Wavelets extractinformation from an entire distribution and decompose it at all scales,simultaneously searching for features over a wide range of scales. Wepropose a systematic wavelet analysis and show how bumps, bump-dipcombinations, and oscillatory patterns are extracted. Our kinematicwavelet analysis kit KWAK provides a publicly available framework toanalyze and visualize general distributions. 
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  4. We estimate the reach of global Higgs analyses at a 27 TeV hadroncollider in terms of Higgs couplings and in terms of a gauge-invarianteffective Lagrangian, including invisible Higgs decays and the Higgsself-coupling. The new collider will indirectly probe new physics in theTeV range and allow for a meaningful test of the Higgs self-couplingalso embedded in a global analysis. 
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