Investigations in Theoretical Particle Physics

大型强子对撞机（LHC）将于今年开始运行，以比以往更大的能量碰撞质子。通过爱因斯坦著名的方程E=mc^2，这种更大的能量可以转化为比以往任何时候都更重的粒子的质量。十年前的实验暗示，至少希格斯粒子，或者类似的东西，应该在大型强子对撞机中产生。剑桥小组正在开发技术，从产生的数十亿其他粒子中提取出少数希格斯粒子的特征衰变。我们将研究如何从数据中提取希格斯粒子的特性，包括它的自旋，理论学家预测它的自旋为零。建立精确的碰撞和随后的衰变的计算机模拟是一项重要的活动。在我们目前的理论中，希格斯粒子是所有其他基本粒子质量的起源，但为什么希格斯粒子没有重得多，这是一个谜。推测性的想法，如超对称，或额外的空间维度，可以解决这个难题，但我们不能相信这些，除非它们的影响是明确测量。一种可能的影响是在大型强子对撞机中产生暗物质粒子，其特征是粒子碰撞中的“缺失能量”。我们需要调查任何暗物质的特征，并检查它们是否与我们关于早期宇宙的理论相一致。分析数据很困难，因为产生的许多粒子是由更基本的粒子（夸克）组成的复杂团块，它们被强大的核力粘在一起。事实上，在大型强子对撞机中，最初的质子碰撞是这样的。没有简单的方法来计算在这个“粘在一起”的过程中会发生什么，必须开发特殊的数学技术。这是我们在剑桥工作的一个重要重点。在我们的一些理论中，方程有很多隐藏的对称性可以被梳理和利用；在其他情况下，我们可以通过一组离散点来近似时空，并在计算机上进行计算。我们想要解决的一个问题是质子和中子本身是如何在原子核中粘在一起的。我们正在发展近似理论，其中原子核的形状可以作为方程的解。即使希格斯粒子和超对称粒子被发现，粒子物理学中仍有许多未解之谜。例如，引力如何适用于粒子物理学？在数学上，引力导致粒子理论在远小于质子大小的距离尺度上不一致，可能是因为时空本身通过量子涨落变得模糊。弦理论，以其微小的卷曲额外维度，为我们提供了一个数学上一致的解决方案的最大希望。该小组的大部分工作将用于进一步调查、检验和发展弦理论的数学结构。弦理论部分地预测了在大型强子对撞机上可能发现的新粒子。当人们试图建立包含我们已经知道的粒子的明确的弦理论时，这些预测就会出现。已知的粒子对卷曲的额外维度的形状施加了限制，这在数学上是非常有趣的。我们将考虑这一切对我们理解整个宇宙的影响。例如，弦理论对宇宙的“弹跳”解产生了有趣的结果，宇宙不断地坍缩和重新膨胀，通过量子力学平滑了大爆炸奇点。这个宇宙模型，以及其他的宇宙模型，将通过对大爆炸余辉的测量——宇宙微波天空——以及对宇宙中“暗能量”和“暗物质”数量的日益精确的测量来进行测试。

The Large Hadron Collider (LHC) will start operating this year, colliding protons at much greater energies than ever achieved before. Through Einstein's famous equation $E=mc^2$, this greater energy can be turned into the masses of heavier particles than ever seen before. Hints from experiments a decade ago suggest that at least the Higgs particle, or something very like it, should be produced at LHC. The Cambridge group are developing techniques to extract the few Higgs particles' signature decays from the billions upon billions of other particles produced. We shall study how to extract properties of the Higgs particle from the data, including its spin, which theorists have predicted to be zero. Building accurate computer simulations of the collisions and subsequent decays is one important activity. In our current theories, the Higgs particle is responsible for the origin of the mass of all other fundamental particles, but it is a puzzle why the Higgs is not far heavier still. Speculative ideas such as supersymmetry, or extra space dimensions, can solve the puzzle, but we cannot believe in these unless their effects are unambiguously measured. One possible effect is the production of particles of dark matter at the LHC, whose signature is 'missing energy' in the particle collision. We shall need to investigate any dark matter signatures and check whether they are compatible with our theories of the early universe. Analysing data is difficult because many of the particles produced are complicated lumps of more fundamental particles, the quarks, stuck together by the strong nuclear force. Indeed, the initial protons colliding at the LHC are like this. There is no easy way to calculate what happens in this 'sticking together' process, and special mathematical techniques have to be developed. This is an important focus of our work at Cambridge. In some of our theories the equations have a lot of hidden symmetry that can be teased-out and exploited; in others we can approximate space-time by a set of discrete points and do calculations on computers. One problem we want to solve is how protons and neutrons themselves stick together in the nuclei of atoms. We are developing approximate theories in which the shapes of nuclei come out as solutions of the equations. Even if the Higgs and supersymmetry were to be discovered, there remain many mysteries in particle physics. For example, how does gravity fit into particle physics? Mathematically, gravity leads to inconsistencies in particle theories at distance scales much smaller than the size of a proton, possibly because space-time itself becomes fuzzy through quantum fluctuations. String theory, with its tiny curled-up extra dimensions, offers our best hope of a mathematically consistent solution. Much of the group's effort will go into further investigating, checking and developing the mathematical structure of string theory. String theories partly predict what new particles might be discovered at the LHC. These predictions emerge when one tries to build explicit stringy theories incorporating the particles we already know about. Known particles place constraints on the shape of the curled-up extra dimensions, and this is very interesting mathematically. We shall be considering the effects of all this on our understanding of the universe as a whole. For instance, string theory has interesting consequences for 'bounce' solutions of the universe where it continually collapses and re-expands, smoothing out the big bang singularity through quantum mechanics. This, and alternative models of the universe, will be tested against measurements of the after-glow of the big bang -- the Cosmic Microwave sky -- and the increasingly accurate measurements of the amount of 'dark energy' and 'dark matter' in the universe.