Strongly coupled theories beyond the Standard Model

Abstract

This article presents a number of technical tools and results that may be instrumental to discern the nature of the Higgs particle. In scenarios where an additional strongly interacting sector is present in the electroweak theory resulting in a composite Higgs and longitudinal components of the massive gauge bosons, unitarity, analyticity and related techniques will be crucial to understand the properties of such a sector. The situation today may be reminiscent of the pre-QCD days: a strongly interacting theory governs the short-distances, but we have only access to long-distance experiment involving Nambu-Goldstone or pseudo Nambu-Goldstone bosons. Like in those days we can only rely on symmetry and general properties of field theory. Luckily, unlike in the pre-QCD days, we have now a much clearer idea of what we may be after. After presenting a classification of the various types of effective theories, we establish the criteria as to under which conditions different representations are possible and their equivalence. We discuss in detail the implications of analyticity, causality and unitarity; describe various unitarization methods and establish the properties of dynamically generated resonances and form factors. The relation to effective Lagrangians with explicit resonances is explained in the context of beyond the Standard Model (BSM) physics and the Higgs effective field theory (HEFT). We discuss how various BSM models may be reduced to the HEFT as well as implications from holography and lattice studies in establishing BSM phenomenology. The methods presented are then applied to various processes relevant to disentangle the existence and nature of an extended electroweak symmetry breaking sector visible in $VV$ fusion: two-Higgs production, vector resonances, $\gamma\gamma$ physics and top-antitop production.