Cambridge University Press 978-1-108-49698-8 — Elementary Particle Physics Andrew J. Larkoski Excerpt More Information 1 Introduction Particle physics is the study of the fundamental principles of Nature. Within the purview of particle physics are some of the deepest questions we can ask, like “What is responsible for mass?” or “Why are there three spatial and one time dimensions?” These are such big questions that no individual or even individual country can hope to answer them alone. Contemporary particle physics is truly an international endeavor, with scientists from nearly every country on Earth involved in the major experiments. Today’s particle physicist may regularly travel to conferences in Argentina, visit collaborators in Japan, watch a live news conference about a major discovery from Switzerland, or even collect data at the South Pole. It is also a dynamic field, with numerous new results in particle physics published every week testing those theories that we have or suggesting new ones. The liveliness and brisk rate at which ideas are transferred in this field is largely due to particle physics having one of the largest and most widely used preprint article servers in all of science. These reasons also make taking a course on particle physics attractive to many physics students. All of the machinery, formalism, insight, and tools that you have gained as a physics student is essential for studying particle physics. This involves the whole range of advanced physics courses: • Classical Mechanics. Lagrangians and Hamiltonians are the principle way in which we express a system in particle physics. • Special Relativity. The particles we explore are traveling at or near the speed of light, c. • Quantum Mechanics. The particles and physical systems we investigate are extremely small, so the fundamental quanta of action, , is necessary in our analysis. • Statistical Mechanics. Particles are classified by their intrinsic spin, which defines them as fermions or bosons. • Electromagnetism. Likely electromagnetism, through Maxwell’s equations, is the first field theory that you encounter in physics courses. The language of particle physics is mathematics. From complex analysis to Fourier transforms, group theory and representation theory, linear algebra, distribution theory, and statistics myriad fields of mathematics are vital to articulate the principles, theories, and data of particle physics. As we will see in this book, the physics is extremely helpful in guiding the mathematical expressions. The goal of this book is to use the intuition gained through other physics courses and apply it to particle physics, which gets us a long way toward understanding, without just blindly following the mathematics. The particle physics introduced in this book is also the gateway to quantum field theory, the result of the harmonious marriage of quantum mechanics and special relativity. 1 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-108-49698-8 — Elementary Particle Physics Andrew J. Larkoski Excerpt More Information 2 Introduction A complete treatment of quantum field theory is beyond the scope of this book, but we will see glimpses of a richer underlying structure as the book progresses. In particular, quantum field theory is the framework in which three of the four fundamental forces of Nature are formulated. The three forces are electromagnetism, the strong force, and the weak force. The strong and weak forces are the focus of most of this book, with aspects of electromagnetism studied throughout. Quantum field theory enables a formalism which produces predictions that can be compared to data, and it is often (and rightfully!) stated that quantum field theory is the most wide-reaching and precise theory of Nature that exists. This chapter serves as the overview that invites you to study this rich field. Our goal is to frame the rest of the book, which necessitates a review of the forces of Nature, a preview of the Standard Model of Particle Physics, and a glimpse of the Large Hadron Collider, the currently running and most superlative particle physics experiment ever. We also need to introduce natural units to describe particle physics phenomena, and we find that familiar SI units are woefully inadequate. 1.1 A Brief History of Forces Interactions between particles can be expressed through the four fundamental forces. Gravity is the force that was first understood at some analytical level. Gravity is a universally attractive force that couples to energy and momentum. By “universally attractive” we mean that two particles are always attracted to one another through gravity. By “couples” we mean that the strength of the gravitational force is proportional to the energy of the particle. For particles with slow velocities with respect to the speed of light, the energy to which gravity couples is just the mass of the particle. The strength of the force of gravity, defined by either Newton’s universal law of gravitation or general relativity, is quantified by Newton’s constant, GN. For example, in Newton’s theory, the force of gravity between two masses m1 and m2 separated by distance r is G m m F = − N 1 2 ˆr , (1.1) g |r|2 where ˆr is a unit vector in the direction of r. We say that GN is the “strength of coupling” of gravity, or “coupling constant” for short. If GN is larger, the force is larger; if GN is smaller, the force is smaller. In SI units, the value of GN is −11 3 −1 −2 GN = 6.67 × 10 m kg s . (1.2) It turns out that, in appropriate units that we will discuss further later in this chapter, GN is incredibly tiny. Gravitational forces are completely ignorable for any microscopic experiment involving individual particles, like electrons or protons. The next force that was understood is electromagnetism. Unlike gravity, which is universally attractive because mass is always positive, electromagnetism can be either attractive or repulsive (or neutral). Particles or other objects can have positive, negative, © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-108-49698-8 — Elementary Particle Physics Andrew J. Larkoski Excerpt More Information 3 1.2 The Standard Model of Particle Physics or no charge and the relative sign of charges determines whether the force is attractive or repulsive. The electric force between two charges q1 and q2 separated by distance r is 1 q1q2 Fe = 2 ˆr . (1.3) 4πǫ0 |r| −1 Here, the factor of (4πǫ0) is the coupling constant of electromagnetism. The value of ǫ0 in SI units is −12 −1 ǫ0 = 8.85 × 10 F · m , (1.4) where F is the SI unit of the farad. In appropriate units to enable comparison, this is billions and billions of times larger than the coupling of gravity, GN. Electricity and magnetism are intimately related as an electric field in one reference frame produces a magnetic field in another reference frame. This is also the starting point for special relativity, which we’ll review in Chapter 2. This was the story at the end of the nineteenth century. Knowing the mass and charge of an object is sufficient to determine how it will interact with any other object, assuming that the only forces are gravity and electromagnetism. This is also the point where this book begins, at the beginning of the twentieth century. At this time, physics was undergoing huge revolutions: in addition to the formulation of the modern pillars of relativity and quantum mechanics, the electron was recently discovered, as was the nuclear structure of the atom, and even odder things like superconductivity. A nineteenth century physicist was completely powerless to address these phenomena and understand them. They are not described strictly within the paradigm of Newtonian gravity and Maxwellian electromagnetism. Throughout the twentieth century, more and more particles and interactions were discovered: the positron, the anti-particle of the electron; neutrinos, very light cousins to the electron that are electrically neutral and seem to pass through nearly everything; the muon, similar to the electron but more massive; and so on. Near the end of the 1960s, hundreds of new particles had been discovered and their properties (like mass, charge, and intrinsic spin) measured. It was looking like quite a mess, with no clear organizing principle. However, in the late 1960s through the late 1970s, heroic efforts from theoretical and experimental physicists around the world yielded a simple underlying framework that could explain all experimental results. It became known as the Standard Model of Particle Physics. 1.2 The Standard Model of Particle Physics The Standard Model consists of all but one of the fundamental particles and forces that are important in our experiments. It provides an organizing principle for how to construct more complicated objects from these basic building blocks. A fundamental particle is one which we believe is truly elementary: it has no spatial extent (it is a point) and is not made up of any more fundamental parts. For example, hydrogen is not fundamental because it © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-108-49698-8 — Elementary Particle Physics Andrew J. Larkoski Excerpt More Information 4 Introduction Fig. 1.1 Artistic representation of the 17 Standard Model particles. The top outer ring are the six quarks, the bottom outer ring are the six leptons, the middle ring are the four force-carrying bosons, and the center is the Higgs boson. Courtesy of Particle Fever, LLC. consists of a proton and an electron, while it is believed that the electron is fundamental. In this book, we will study the theoretical predictions and experimental justification of the Standard Model. The particles of the Standard Model can be artistically arranged and represented as a series of concentric rings displayed in Fig.