Theoretical Particle Physics at the University of Liverpool

粒子物理学，也被称为高能物理学，研究在最短距离或最高能量下揭示的自然基本定律。近几十年来，通过大规模高精度实验和理论物理的研究，这一领域取得了很大的进展。我们目前建立的知识被编纂在所谓的标准模型中，这是一种高度非平凡的量子场论（QFT），基于规范不变性和希格斯机制的数学概念（希格斯机制的一个关键结果，希格斯粒子，尚未在实验中被发现）。有充分的理由，包括来自宇宙学的暗示——一个成熟的研究领域，现在与粒子物理学密切相关——假设标准模型并不是对自然的最终描述，即使在不久的将来可以获得能量。此外，似乎需要一个新的数学框架来一致地描述引力和粒子物理学中直接研究的其他基本力，而弦理论是主要的候选者。随着欧洲核子研究中心（CERN）的大型强子对撞机（LHC）实验的开始，高能物理学现在已经进入了几十年来最令人兴奋的阶段。利物浦大学的理论物理小组——目前由9名全职学术人员、3名全职研究人员（包括一名从行政和教学部门退休的教授）和13名博士生组成——致力于与上述挑战相关的粒子物理的各个方面。我们的工作可以用三个研究小组来描述，主要解决1。弦与超越标准模型（BSM）现象学与宇宙学，2。QFT中的高阶和全阶计算，以及对撞机中的QCD， 3。低能强子物理，晶格QFT及其应用。弦理论在数学上的一致性要求微观空间的存在多于宏观空间的三个维度。因此，第一组成员面临的主要挑战是理解这些额外维度的所谓紧化，目的是获得LHC能量的预测并推导出它们的宇宙学含义。弦理论的另一个重要主题，也是我们小组讨论的，是黑洞的描述。现实弦理论需要一种叫做超对称（SUSY）的新型高能对称，因此我们工作的另一个重点是研究标准模型的超对称扩展。像标准模型这样的qft及其可能的扩展（如SUSY）是如此复杂，以至于无法精确解决。对于像大型强子对撞机这样的对撞机的散射过程，唯一已知的方法是通过称为微扰理论的连续近似，该理论的预测是根据一个小参数展开的。这种方法类似于简单数学函数的泰勒展开，但要困难得多。第二组的成员在这类计算中发挥着国际领先的作用，这不仅对正确解释实验结果必不可少，而且对获得指导进一步研究的结构见解也是必不可少的。微扰理论不适用于强相互作用（QCD）理论中的许多（例如静态）量，在强相互作用（QCD）理论中，基本粒子，夸克和胶子被“限制”在强子（如质子的束缚态）中。晶格理论在超级计算机上使用不连续的时空晶格，是解决这些量的唯一“从头开始”方法。第3组的成员进行这样的计算和其他与约束和非摄动对观测值的贡献有关的研究，特别是μ子的异常磁矩，这在这一点上为BSM物理学提供了最有趣的提示之一。

Particle physics, also called high-energy physics, addresses the fundamental laws of nature which are revealed at the shortest distances or highest energies. Great progress has been made in this field during recent decades, both by large-scale and high-precision experiments and by research in theoretical physics. Our presently established knowledge is codified in the so-called Standard Model, a highly non-trivial quantum field theory (QFT) based on the mathematical concepts of gauge invariance and the Higgs mechanism (of which a crucial consequence, the Higgs particle, has not yet been found in experiment). There are strong reasons, including hints from cosmology - a matured field of research now intimately connected to particle physics - to assume that the Standard Model is not the ultimate description of nature even at energies accessible in the near future. Furthermore a new mathematical framework, for which string theory is the leading candidate, appears to be required for a consistent description of gravity and the other fundamental forces directly studied in particle physics. With the start of experimentation at the LHC at CERN, a proton-proton collider with a multi-TeV centre-of mass energy, high-energy physics has now entered what promises to become its most exciting phase in decades. The Theoretical Physics Group at the University of Liverpool - at this point comprising 9 full-time academic staff members, 3 full-time researchers (including one professor retired from admin and teaching) and 13 PhD students - is engaged in all aspects of particle physics relevant to the challenges indicated above. Our work can be described in terms of three research groups, mainly addressing 1. String and Beyond the Standard-Model (BSM) phenomenology and cosmology, 2. Higher- and all-order calculations in QFT, and QCD at colliders, 3. Low-energy hadron physics, lattice QFT and applications. String theory requires, for its mathematical consistency, the microscopic existence of more than the three macroscopic dimensions of space. Therefore a main challenge, taken up by members of group 1, is to understand the so-called compactification of these extra dimensions, with the aims of obtaining predictions at LHC energies and deriving their cosmological implications. Another important topic in string theory, also addressed by our group, is the description of black holes. Realistic string theories require a new high-energy symmetry called supersymmetry (SUSY), so another focus of our work is the study of supersymmetric extensions of the Standard Model. QFTs such as the Standard Model and its possible extensions (e.g. SUSY) are so complicated that they cannot be solved exactly. For scattering processes at colliders such as the LHC, the only known method is by successive approximations called perturbation theory, where the predictions of the theory are expanded in terms of a small parameter. This method is analogous to, but much more difficult than, the Taylor expansion of simple mathematical functions. Members of group 2 play an internationally leading role in such calculations, which are not only indispensable for the correct interpretation of the experimental results, but also for gaining structural insights which will guide further research. Perturbation theory is not applicable to many (e.g. static) quantities in the theory of the strong interaction (QCD) where the fundamental particles, quarks and gluons, are `confined' in hadrons (bound states such as the proton). Lattice theory, which uses a discontinuous space-time lattice on supercomputers, is the only `ab initio' method to address such quantities. The members of group 3 perform such computations and other studies relevant to confinement and non-perturbative contributions to observables, in particular the anomalous magnetic moment of the muon which at this point offers one of the most intriguing hints for BSM physics.