Concepts in Particle Physics

A Concise Introduction to the Standard Model

V Parameswaran Nair

• Publisher: WSPC
• Year: 2017
• ISBN:
  9789813227576
• Topic: Physical Sciences
• Subtopic: Quantum Theory

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The 2013 discovery of the Higgs boson posed a challenge to both physics undergraduates and their instructors. Since particle physics is seldom taught at the undergraduate level, the question "what is the Higgs and why does its discovery matter?" is a common question among undergraduates. Equally, answering this question is a problem for physics instructors.

This book is an attempt to put the key concepts of particle physics together in an appealing way, and yet give enough extra tidbits for students seriously considering graduate studies in particle physics. It starts with some recapitulation of relativity and quantum mechanics, and then builds on it to give both conceptual ideas regarding the Standard Model of particle physics as well as technical details. It is presented in an informal lecture style, and includes "remarks" sections where extra material, history, or technical details are presented for the interested student. The last lecture presents an assessment of the open questions, and where the future might take us.

--> Contents:

• The Standard Model
• Review of Special Relativity
• Quantum Mechanics and the Propagator
• Scattering Processes and Feynman Diagrams
• Photons and the Electromagnetic Field
• Processes with Photons
• Cross Section and Dimensional Analysis
• More on the Dirac Equation
• Other Forces: Weak Interactions
• The Gauge Principle
• The Gauge Principle II
• Gauge Symmetry: The Matrix Generalization
• Gauge Symmetry: The Matrix Generalization II
• Back to Particles and The Strong Nuclear Force
• More on Quantum Chromodynamics (QCD)
• Mesons and Baryons
• Spontaneous Symmetry Breaking
• Superconductivity and Electroweak Interactions
• Electroweak Interactions and the Story of Mass
• CP-Violation and Matter vs Antimatter
• Many Big Questions Remain

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--> Readership: Advanced undergraduates studying particle physics. -->
Keywords:Particle Physics;Standard ModelReview:0

Chapter 1

The Standard Model

The Standard Model of particle physics is arguably the most important intellectual achievement of the human race. It describes a number of fundamental particles (fundamental to the best of our knowledge, to date) and their interactions. It is a conceptual and logical structure which is expected to have a very wide range of applicability essentially being the kernel for building up most of physics. And while many details of the phenomena which follow from it are still being worked out, there is good reason to believe that most of the observed results within its expected domain of applicability can be obtained from it. Admittedly, there is evidence for phenomena such as dark matter, which may be beyond the purview of the Standard Model. But as for observed results within its expected domain, we do not yet have any evidence for deviations from the Standard Model. This is both good and not so good. The range of observations we have carried out to date stretch from a microscopic distance scale of about 10⁻¹⁸ meters to cosmological scales of the order of 10²⁶ meters. The Standard Model, including classical Einstein gravity (with a cosmological constant), can account for most of these observations, at least in principle. This is a remarkably good situation, when we recall that at the time of Newton, a little over three hundred years ago, all physics was essentially confined to the terrestrial scales. In fact, one of Newton’s great achievements was to realize that the same physics which applies to terrestrial phenomena could also be applied to explain planetary motion and other phenomena at the scale of the solar system. However, the success of the Standard Model is far from complete because there are still many puzzles left, many features of the Standard Model are awkward and it is hard to believe that it is the final theory of the particle interactions, even apart from deeper issues such as quantum gravity and so on. For further progress, we need to push the limits of validity of the Standard Model, until we find deviations from it, so we can improve it and take it to the next level of understanding and explanation. We will talk about the inadequacies of the Standard Model towards the end of this course, but let us begin by accentuating the positive. Here is an immensely successful theory, arguably the most successful theory ever. What does it look like?

Table 1.1 gives a list of all the types of fundamental particles in the Standard Model. There are six species of leptons: the electron (e), the electron-neutrino (ν_e), the muon (μ), the mu-neutrino (ν_μ), the tau (τ) and the tau-neutrino (ν_τ). Of these, the electron is familiar as one of the particles constituting the atoms of all elements. There are also six species of quarks; the names are the up (or up-quark u), the down (or the down-quark d), charm (c), strange (s), top (t) and bottom (b). Protons and neutrons which are the basic constituents of atomic nuclei are bound states of three quarks each, the combination uud for the proton and udd for the neutron. Other combinations of quarks form other particles such as the baryons Σ, Λ, Δ, etc., and mesons. There are a large number of these, but being unstable, most of them do not make it into the matter we know from everyday experience. The quarks and leptons form the set of “matter” particles, so to speak, in the sense that all matter is primarily made of these particles. They are organized into three “generations”, with (e, v_e, u, d) forming the first generation, (μ, ν_μ, c, s) and (τ, ν_τ, t, b) being the second and third generations.

But the quarks and leptons by themselves are not sufficient to make up matter. There should be forces between these particles which help them to bind together and form protons, neutrons, nuclei and atoms. We know from the theory of relativity that nothing can travel faster than the speed of light in vacuum. This means that if we consider two particles with a certain force between them, and we move one of the particles, the other, even though it is bound to the first, cannot respond at least until the time it takes a light signal to go from the first to the second. This ultimately leads to the idea that even the forces between particles must be thought of as caused by the exchange of some particle. In other words, there must be force-carrying particles as well. Of the various force carriers listed in the table, the photon is the quantum of light or the basic quantum of the electromagnetic field. It is responsible for electromagnetic forces, including the binding of electrons to atomic nuclei to form atoms. The graviton is the force carrier for gravity, although we must keep in mind that we do not yet have a quantum theory of gravity. There are 8 types of gluons which are the force carriers for the strong nuclear force. They help to bind the quarks to form nucleons such as the protons and neutrons; they are also ultimately responsible for binding protons and neutrons into atomic nuclei. So they are a very important ingredient of matter. The graviton, the photon and the gluons are massless particles. The gluon is not seen as an isolated particle but many gluons can be bound together to form “glue balls” which are massive particles. Among the remaining force carriers, W^±, Z⁰ are responsible for the weak nuclear force, whose most familiar manifestation is the β-decay of some of the atomic nuclei. They are massive particles as well.

Finally, we have the Higgs particle. This is somewhat special. It is responsible for giving masses to many of the other particles, including the quarks, leptons and the W^±, Z⁰ and itself, via an effect similar to the Bose-Einstein condensation. Such a particle is necessary to construct a theory of electroweak forces consistent with the requirement of the conservation of probability to arbitrarily high energies. The detection of this particle in 2012 has brought to completion the essential ingredients of the Standard Model. We have arrived at a new watershed in the long journey of trying to understand fundamental interactions, a journey that has taken well over a hundred years. A brief glance at this history is certainly worthwhile.

Table 1.1: List of fundamental particles (antiparticles are not separately listed.)

A century of particle physics

The idea that matter is made of particles, in the modern scientific context, goes back to John Dalton’s atomic hypothesis in 1805. (One could argue that the idea of a unit of matter goes back to Democritus in ancient Greece, Kanada in ancient India or to many others in many other ancient civilizations.) But modern particle physics essentially started with the discovery of the electron in 1897 by J.J. Thomson. It was clear (because it was produced from matter under high temperature and electric fields) that the electron is a constituent of the atom, and since it carries a negative electrical charge and atoms are neutral, one could immediately argue that there should be some entity of positive electrical charge in the atom. Experiments on scattering of α-particles by thin gold foils, carried out in Rutherford’s laboratory in 1911, in conjunction with the theoretical analysis done by Rutherford himself, made it clear that the positive charge was carried by a central nucleus localized to a size much smaller than the size of the atom. The nucleus also carried most of the mass of the atom, the electron being much lighter. (The electron has a mass of approximately 0.5 MeV, while the nucleus of the lightest element Hydrogen has a mass of approximately 938 MeV.) The atom thus looked more like a miniature solar system, although the compatibility of such a picture with classical electrodynamics was a major issue. (The resolution of this difficulty was one of the key steps in the development of quantum mechanics.) The lightest of all nuclei, that of the Hydrogen atom, could be taken as the new particle of positive charge; this was the proton. The Helium nucleus had a mass approximately 4 times that of the Hydrogen nucleus, but had charge only equal to twice the charge of the proton. This suggested the existence of an additional neutral particle of approximately the same mass as the proton. Such a particle would also give a natural explanation of isotopes. The discovery of the neutron, as this particle came to be called, by J. Chadwick in 1932 confirmed this simple hypothesis.

Now we enter the saga of the mesons. Protons carry positive electrical charge, so they repel each other. How can we then bind them together to form nuclei of higher charge, from Helium with charge equal to 2 in the units of the charge of the proton, to Uranium with charge equal to 92? There had to be an attractive force strong enough to overcome the repulsive electrostatic force between protons. Yet, two faraway protons did not seem to show any evidence of this force. So the putative new force should have a very short range. This led Hideki Yukawa in 1935 to suggest that there should be a massive particle whose exchange created this force and the mass of the particle would explain why the range was short. Based on the size of the atomic nuclei, he estimated that the new particle should have a mass around 250 times that of the electron, something over 100 MeV. Thus it would be a “meson”, something of mass between those of the proton and the electron. Cosmic ray experiments by C.D. Anderson and S. Neddermeyer did detect a meson in 1936. However, it turned out that this particular particle had only a very weak interaction with the proton and neutron, ruling it out as the carrier of a nuclear force which could overcome the electrostatic repulsion of the protons. This particle is what we now call the muon (μ). Yukawa’s meson was eventually detected by C.F. Powell’s group in 1947; it is now called the pi-meson or the pion (π). There are three types of these, with charges +1, −1 and 0, in units of e, the charge of the electron.

Another whole new category of particles, it became clear from the early 1930s, would be needed on theoretical grounds. These are the antiparticles for the known fermions of the day. Dirac’s theory of the electron in 1928 led to the idea of the positron as an antiparticle to the usual electron. Although there was some early confusion about whether this could be the proton, it was clear by the year 1930 or so that this would be an as-yet-unseen new particle. Anderson (1932) was able to observe the pair creation of an electron-positron pair by gamma rays in cosmic ray emulsions, confirming Dirac’s prediction. The antiproton was discovered in 1955 by E. Segre and O. Chamberlain. Shortly afterwards (in 1956), the antineutron was also discovered by B. Cork.

Today we know that many particles have corresponding antiparticles. This applies to the quarks and leptons, for sure. If we are willing to extend the terminology to include that the particle and the antiparticle may be the same in some cases, then we can say that all particles have antiparticles. Thus the neutral pion is its own antiparticle, while the π⁻ is the antiparticle to the π⁺. The Higgs is its own antiparticle as well.

The 1930s also led to the prediction of neutrinos. The β-type of radioactivity had been known since the turn of the twentieth century. With the discovery of the neutron, it seemed like one could interpret this as arising from the decay of a neutron in the atomic nucleus, with the products being a proton and an electron, i.e., n → p + e⁻. The electron would escape from the nucleus and would be detected as β-radiation. However, this interpretation ran into trouble because energy conservation did not seem to work out: the energy carried away by the electron was less than the energy difference between the parent and daughter nuclei. This prompted Wolfgang Pauli to suggest that there was perhaps another particle among the decay products which escaped detection because it was neutral and hence did not interact significantly with the detector. Enrico Fermi very quickly included this idea in constructing a phenomenological theory for β-decay; he also named this little neutral particle as the “little neutral one” or the neutrino in Italian. Fermi’s theory also showed that the neutrino would be a fermion. The decay of the neutron would thus be

where we use the benefit of hindsight to identify the extra particle as the anti-electron-neutrino. The neutrino was eventually detected by the group led by F. Reines and C. Cowan in 1956. The work by L. Lederman, M. Schwartz and J. Steinberger (1962) showed that there are at least two species of the neutrino, ν_e and ν_μ. (The third one, ν_τ came much later.)

Most of the particles we talked about so far were somehow expected, except perhaps for the electron. Once the electron was discovered, the proton was needed for the neutrality of atoms, the neutron was needed to explain isotopes, and the pion was needed for binding the neutrons and protons into nuclei. The discovery of the muon was somewhat accidental and it was certainly not clear, at least at that time, why the muon was needed from theoretical considerations. The zoo of unexpected particles, however, grew rapidly in the 1950s. The K-meson was originally detected in...