Lattice simulations and analytical computations of five-dimensional gauge theories to study the Higgs boson as an extra-dimensional gauge field

到目前为止，基本粒子的标准模型已经非常成功地预测了粒子在加速器实验中测量到的性质。质量产生的机制依赖于希格斯标量的存在，而希格斯标量迄今尚未被发现。希格斯粒子扇区的参数是标准模型的输入，能否从更深层次的原理来理解它们是一个悬而未决的问题。这个项目的目标是研究标准模型的扩展，其中希格斯标量被确定为规范场的五维分量。标量势是由量子效应产生的，并且被认为是有限的，这使得这些模型具有吸引力。由于五维规范理论是微不足道的，它们需要一个截止点。欧几里得格上的公式提供了规范不变截止。与先前的1环微扰计算结果相反，晶格蒙特卡罗模拟显示了五维轨道空间上非阿贝尔规范理论的自发对称性破缺。我们希望从这些模拟中预测希格斯粒子的质量，并利用一种解释截止效应的有效理论与微扰计算建立联系。

The Standard Model of elementary particles has so far been very successful in predicting the properties of particles as they are measured in accelerator experiments. The mechanism of mass generation relies on the existence of the Higgs scalar, which has not been discovered so far. The parameters of the Higgs sector are inputs in the Standard Model and it is an open question, whether they can be understood from a deeper principle. The goal of this project is to study extensions of the Standard Model, where the Higgs scalar is identified with five-dimensional components of a gauge field. The scalar potential is generated by quantum effects and is believed to be finite, what makes these models attractive. Since five-dimensional gauge theories are trivial, they require a cut-off. The formulation on a Euclidean lattice provides a gauge invariant cut-off. Contrary to previous results from 1-loop perturbative computations, lattice Monte Carlo simulations showed spontaneous symmetry breaking in non-Abelian gauge theories on a five-dimensional orbifold space. We want to predict the Higgs mass from these simulations and make a connection with perturbative computations done using an effective theory which accounts for the cut-off effects.