格點場論與大強子對撞機物理

Abstract

本計劃的主要課題為用格點場論的方法來解決大強子對撞機物理中的問題。格點場論 是在量子場論中唯一的第一原理非微擾計算方法，很試合應用在大強子對撞機物理上 許多重要的計算。格點場論可用來研究標准模型中希格士-湯川部門的非微擾定義，以 解決此模型中尺度中的“自然問題”。格點場論也可用來尋找取代希格士-湯川理論的 電弱對稱性破壞之動力學機制。此外，格點場論亦可用在量子色動力學的計算上，以 期對大強子對撞機的b 物理計劃做出貢獻。以上研究方向包含許多量子場論中有趣而 未知的面向，因此充滿了挑戰。例如希格士-湯川理論中是否可能有紫外定點，而不是 藍道奇點？是否存在有大的紅外“奇維度”之非超對稱規範場論？ 格點場論在這些 問題上的應用是一個挑戰性高而蓬勃發展的領域。以本研究群的經驗，我們將針對這 個主題進行更進一步的研究。

I propose research projects on Lattice Field Theory in physics of the Large Hadron Collider (LHC). Lattice calculation is the only first-principle non-perturbative method in Quantum Field Theory, and can be applied to solve many important problems in LHC physics. These include the search for a non-perturbative definition of the Higgs-Yukawa sector in the Standard Model for evading the naturalness problem, the investigation of possible scenario for dynamical electroweak symmetry breaking, and the computation for the relevant QCD matrix elements in a b-physics programme at the LHC. There are many challenges in such research avenues. In particular, we are venturing into the unexploited territory of Quantum Field Theory, such as the possibility of having an ultraviolet fixed point (instead of a Landau pole) in the Higgs-Yukawa model, the search for non-supersymmetric gauge theories containing large anomalous dimensions in the infrared, etc. It is not straightforward to implement lattice calculations for such problems, and the research field is growing very fast. Based on the experience in my group, we plan to further our study on such topics in the next three years.