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.

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标准模型之外的强耦合理论

本文介绍了一些可能有助于辨别希格斯粒子性质的技术工具和结果。在电弱理论中存在额外的强相互作用扇区的情况下，导致复合希格斯和大规模规范玻色子的纵向分量，幺正性、分析性和相关技术对于理解此类扇区的特性至关重要。今天的情况可能让人想起 QCD 之前的日子：一个强相互作用的理论控制着短距离，但我们只能获得涉及南部金石或伪南部金石玻色子的长距离实验。就像在那些日子里，我们只能依靠场论的对称性和一般性质。幸运的是，与 QCD 之前的时代不同，我们现在对我们可能追求的目标有了更清晰的认识。在介绍了各种类型的有效理论的分类之后，我们建立了关于在哪些条件下不同的表示是可能的及其等效的标准。我们详细讨论了分析性、因果性和统一性的含义；描述各种单一化方法并建立动态产生的共振和形状因子的特性。在超越标准模型 (BSM) 物理学和希格斯有效场论 (HEFT) 的背景下解释了与具有显式共振的有效拉格朗日量的关系。我们讨论了如何将各种 BSM 模型简化为 HEFT，以及全息和晶格研究对建立 BSM 现象学的影响。