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The HiggsTools Handbook: Concepts and observables for deciphering the Nature of the Higgs Sector was finally completed and submitted to the arXiv this week. This Report summarizes some of the activities of the HiggsTools Initial Training Network working group in the period 2015-2017. The main goal of this working group was to produce a document discussing various aspects of state-of-the-art Higgs physics at the Large Hadron Collider (LHC) in a pedagogic manner. Fifteen of the ESRs helped writing the Report.

The first part of the Report is devoted to a description of phenomenological searches for New Physics at the LHC. As the experimental measurements become more and more precise, there is a pressing need for a consistent framework in which deviations from the SM predictions can be computed precisely. We critically review the use of the \k{appa}-framework, fiducial and simplified template cross sections, effective field theories, pseudo-observables and phenomenological Lagrangians.

In the second part of the Report, we propose a new observable for studying Higgs boson production at large transverse momentum in the case where the Higgs boson decays to two photons. We make a detailed study of the phenomenology of the new variable, contrasting the behaviour with the Higgs transverse momentum distribution using a variety of theoretical tools including event generators and fixed order perturbative computations.

Work on the Handbook started at the HiggsTools Third Young Researchers Meeting in Zeuthen, continued in working groups over the winter of 2016/7, leading up to presentations of the work at the Third Annual Meeting and Young Editors School 2017 in Torino. The report was finalised over summer 2017.