Grand Unification without a Hierarchy Problem

关于大统一场论的大量研究一直是在超对称的背景下进行的，主要是将其作为层次问题的解决方案。随着大型强子对撞机现在已经彻底探索了TeV的能量状态，超对称正被越来越多地推向更高的能量，这就产生了它自己的“小层次问题”，使它成为一个没有吸引力的解决方案。最近，这激发了研究探索没有低能超对称的大统一的丰富主题，但大多数研究没有正面面对层次问题，而是简单地忽略了它。在这个项目中，我们的目标是构建和研究大统一的模型，这些模型使用层次问题的替代解决方案。这些模型需要满足四个属性：它们必须不需要微调；它们必须对标准模型的三种力有统一的描述，包括规范耦合和汤川统一；它们必须重现低能量下的标准模型物理和实验观测；他们还必须提供新的预测，以便在当前或未来的对撞机上进行测试。学生将被要求在动作水平上帮助模型的构建，包括对微调的检查，推导和实现耦合演化的重整化群方程，确定模型的低能量行为以面对实验数据，并最终执行关键观测值的模拟以测试模型。这项研究将发表在高影响力的期刊上，并由学生在国际会议上介绍。

The vast body research on Grand Unified Field Theories has been within the context of Supersymmetry, presenting it primarily as a solution to the Hierarchy Problem. With the LHC now having thoroughly explored the TeV energy regime, Supersymmetry is being pushed more and more to higher energies and this creates its own "little hierarchy problem", making it an unattractive solution. Recently this has inspired research to explore the rich topic of Grand Unification without low energy Supersymmetry, but instead of confronting the Hierarchy Problem head on, most research simply ignores it. In this project we aim to construct and study models of Grand Unification that use alternative solutions for the Hierarchy problem. These models need to fulfil four properties: they must be free from fine-tuning; they must have a unified description of the three forces of the Standard Model, including gauge coupling and Yukawa unification; they must reproduce Standard Model Physics and Experimental observations at low energies; and they must provide new predictions that can be tested at current or future colliders. The student will be required to aid in the construction of the models at the level of the Action including an examination of the fine-tuning, derive and implement the Renormalisation Group Equations for the evolution of couplings, determine the low energy behaviour of the model to confront with the experimental data, and finally perform simulations of crucial observables to test the models. This research will be published in high impact journals and presented by the student at international conferences.