Field-theoretical aspects of Brout-Englert-Higgs physics

在大型强子对撞机上发现的希格斯玻色子证实了我们目前对宇宙基本组成部分之间相互作用的看法。希格斯机制和粒子物理学标准模型的理论预测和实验证实，是两者之间富有成果的相互作用的范例。尽管标准模型在解释目前已知的基本粒子之间的相互作用方面取得了前所未有的成就，但它也存在一些缺陷。例如，它既没有对暗物质的起源提供合理的解释，也没有对各种粒子的耦合强度和质量的等级提供合理的解释。此外，由于所谓的平凡性问题，标准模型在高能尺度下从数学观点变得不一致。因此，标准模型只是被认为是一种有效的理论，必须被一个更基本的模型所取代。许多标准模型的扩展也依赖于广义希格斯机制。因此，在制定这些理论时必须全面了解这一关键因素。该项目的目的是Brout-Englert-Higgs物理学的场论方面是获得一个一致的数学公式的更深入和彻底的理解，以及揭示由此产生的场论理论的粒子谱的影响。为了计算质谱，有各种工具可用，如微扰理论，晶格模拟或泛函方法。特别地，对于标准模型中出现的粒子，从不同的方法获得相同的质谱。此外，Fröhlich，Morchio和Strocchi开发了一种形式主义，以一种令人惊讶的和非平凡的方式连接不同方法的结果，并为粒子谱提供了一个适当的规范不变定义。然而，事实证明，这种情况更多地涉及标准模型之外的理论。最近的晶格数据表明，微扰理论预测的粒子谱和从晶格模拟在一个特定的模型中获得的一个之间的不匹配。为了更全面地理解这种可能的不匹配，Fröhlich，Morchio和Strocchi开发的方法将被推广并首次应用于各种标准模型扩展。这将对现有模型提供进一步的限制，但也将为模型构建提供新的路线。此外，创新和强大的重整化群技术将被用作进一步检查结果的补充工具。这些允许从微观量子涨落到宏观可观察的理论自由度的连续过渡，因此将增加质谱的另一个观点。

The discovery of the Higgs boson at the Large Hadron Collider confirmed our current picture of the interactions between the elementary building blocks of our Universe. The theoretical prediction as well as the experimental confirmation of the Higgs mechanism and the standard model of particle physics counts as a paradigm for the fruitful interplay between both. Despite the unprecedented achievement of the standard model in explaining the interactions between the currently known elementary particles, it has some shortcomings. For instance, it does not provide a reasonable explanation for neither the origin of dark matter nor the hierarchy of the coupling strengths and masses of the various particles. Furthermore, the standard model becomes inconsistent from a mathematical viewpoint at high energy scales due to the so-called triviality problem. Therefore, the standard model is only considered as an effective theory which has to be replaced by a more fundamental model. Also many of the proposed standard-model extensions rely on a generalized Higgs mechanism. Thus, a comprehensive understanding of this key ingredient in the formulation of these theories is mandatory. The objective of the project Field-theoretical aspects of Brout-Englert-Higgs physics is to obtain a deeper and thorough understanding of a consistent mathematical formulation as well as to uncover the resulting field-theoretical implications for the particle spectrum of the theory. In order to calculate the mass spectrum, various tools are available like perturbation theory, lattice simulations, or functional methods. In particular, same mass spectrum for the particles occurring in the standard model is obtained from the different methods. Moreover, Fröhlich, Morchio, and Strocchi developed a formalism which connects the results of the different methods in a surprising and nontrivial way and provide a proper gauge-invariant definition for the particle spectrum. However, it turns out that the situation is more involved for theories beyond the standard model. Recent lattice data show a mismatch between the particle spectrum predicted by perturbation theory and the one obtained from lattice simulations in a specific model. In order to get a more comprehensive understanding of such a possible mismatch, the method developed by Fröhlich, Morchio, and Strocchi shall be generalized and applied to various standard-model extensions for the first time. This will provide further constraints on existing models but will also offer new routes for model building. In addition, innovative and powerful renormalization group techniques will be used as a complementary tool to further examine the results. These allow for a continuous transition from microscopic quantum fluctuations to macroscopic observable degrees of freedom of a theory and thus will add another viewpoint on the mass spectrum.