(Material comes from Introduction to Elementary Particles by Griffiths, Introduction.

Introduction (cont'd)

Recall from last lecture:

The goal of elementary particle physics is to find the basic constituents of our universe and understand the interactions between them.

We learn about particles from scattering, decays, and bound states.

What is Elementary Particle Physics? (cont'd)

What are the ingredients needed for a theory of elementary particles? The microscopic size of the particles might lead you to guess (correctly) that quantum mechanics is needed. For elementary particles, it is often the case that their kinetic energy is comparable to their (rest) mass. In other words, they usually move at speeds close to the speed of light, where special relativity is required. The marriage of quantum mechanics and special relativity was originally accomplished by Paul A.M. Dirac. The results of his work lead to quantum field theory.

Note the difference between a type of mechanics and a particular force law. Quantum field theory describes the mechanics of particle interactions, and the goal is to understand the "force law" that correctly describes the behavior.

We will often deal with situations where the details of the interaction are unimportant. For instance, given a decay such as D⁰ → K^-π⁺, we can determine the energy and momentum of the outgoing particles using conservation of energy and momentum in the context of relativistic kinematics.

The D⁰ decays to many other final states as well. When we have a quantum mechanical state that can decay to a number of final states, then each of the possible transitions has a certain probability. We can't say with certainty which final state a particular particle will decay to, but we can determine the probability.

The union of special relativity with quantum mechanics brings additional results:

anti-particles
Pauli exclusion
CPT theorem

The theory that we now have that describes the known particles and their interactions is called the Standard Model of particle physics.

How Do We Produce Elementary Particles?

There are two main sources of elementary particles:

cosmic rays: Elementary particles in outer space are constantly bombarding the Earth from all directions. The Sun, stars, supernovae explosions, and gamma ray bursters are some of the sources of these particles. From cosmic rays we can learn about both elementary particles and their sources.
accelerators: Accelerators are devices capable of confining and accelerating a beam of charged particles. Accelerators are now used for many purposes other than research on elementary particles: to make radioactive isotopes, for medical diagnostics or treatment, for the creation of intense ultraviolet or x-ray radiation, and for the modification of materials. The accelerators for particle research are usually part of a large complex capable of producing beams of particles (electrons and protons) and anti-particles (positrons and anti-protons), and accelerating them to very high energies.

Chapter 1: Quarks and Leptons

(Taken from Perkins)

Some Basics

Why High Energies?

A particle is elementary if it has no internal structure, that is, it is point-like. Whether or not an object can be treated as point-like depends on the resolution of your probe -- to the unaided eye, atoms, molecules, and even cells are point-like. With a microscope we can improve on our unaided eyes, and resolve smaller objects. From optics we learn that the resolution is given by

Δr = λ / sin θ

where θ is the angular aperture of the light of wavelength λ used to view the object.

In particle physics we "view" objects with particles not light. But light is just photons, particles with a known de Broglie wavelength. Interpreting the wavelength as the de Broglie wavelength, we get a similar expression valid when other particles are used as probes:

Δr = h / p sin θ = h / q

where q is the momentum transferred from the probe to the object. (Note the similarity to the uncertainty relation.) So the first reason to go to high energies is to resolve smaller structures.

The second reason is to have sufficient energy to create massive particles. The relation between energy and mass is given by Einstein's famous expression:

E = mc².

The most massive particle presently known is the top quark, about 180 times as massive as the proton. To create top quarks requires energies at least that large.

Units in Particle Physics

It is convenient to work in units appropriate to the problem at hand. In particle physics it is convenient to work in units in which ℏ = c = 1. Additionally, setting ε₀ = μ = 1, we have Heaviside-Lorentz units. In these units, the fine structure constant (from quantum mechanics applied to the hydrogen atom) is given by

α = e² / ℏ c ≈ 1/137.

We still have one more unit to choose, the unit of mass. Masses in particle physics are normally expressed in MeV (millions of electron volts) or GeV (billions of electron volts). The proton mass is 938MeV, and the electron mass is 0.511MeV.

Relativistic Transformations

We will normally deal with processes where at least some particles are moving at speeds close to the speed of light. In such situations, the rules of special relativity must be followed in order to apply energy and momentum conservation.