Subsections

• 1.1 The particles
• 1.2 The forces
• 1.3 Unification

1. The Standard Model

Before discussing supersymmetry, we must discuss the Standard Model of Particle Physics (SM), which describes all the elementary particles in nature, and the forces between them.

One of the most important ways of classifying the particles is by their spin (that is, their internal angular momentum quantum number). The spins of particles are quantized in multiples of half of Planck's constant $\hbar$. Particles whose spins are half-integer multiples of Planck's constant have very different behavior from those whose spins are integer multiples of $\hbar$. The former are called fermions, and they make up all the matter that we see around us; the latter are called bosons, and they act as the carriers of the forces by which particles of matter interact with each other¹. The next two sections describe these particles.

Fermilab has a web site where you can learn more about the science of particle physics. The Particle Data Group also has a page (most of it is aimed towards poets, but the ``Beyond the Standard Model'' section is very good). The masses and other properties of all these particles can be found in the Particle Data Book.

1.1 The particles

Table 1 lists the fermions--the particles that make up matter in the world around us. All these particles have spins of $\frac12\hbar$.

Table 1: The fermions; all have half-integer spins.

Generation	Leptons		Quarks
1	$e$	$\nu_e$	d	u
2	$\mu$	$\nu_\mu$	s	c
3	$\tau$	$\nu_\tau$	b	t

We can make the following observations about the fermions:

• The quarks usually interact via the strong force; leptons never do.

• There are three charged massive leptons: the electron, the muon and the tau. Each has a corresponding neutral massless partner called a neutrino.

• There are six quarks; the ``down'', ``strange'' and ``bottom'' quarks have an electric charge of $-1/3$ that of the proton, while the ``up'', ``charmed'' and ``top'' quarks have an electric charge of $+2/3$ that of the proton.

• For each of these particles, there is a corresponding antiparticle with exactly the same mass, but opposite electric charge, lepton and baryon numbers², intrinsic parity, etc. For example, the partner of the electron ($e^-$) is the positron ($e^+$), the partner of the tau neutrino ($\nu_\tau$) is the tau anti-neutrino ( $\overline{\nu}_\tau$), and the partner of the up quark ($u$) is the up anti-quark ($\bar u$). This makes for twelve particles and twelve antiparticles.

• A particle that consists of quarks is called a hadron. A bound state of three quarks is called a baryon (for example, the proton is a $uud$ state, the neutron is a $udd$ state). A meson is a bound state of a quark and and antiquark (for example, a charged pion ($\pi^+$) is a $u\bar{d}$ state). The strong force is so strong that it's impossible to pull a quark free of a hadron.

• The fermions come in three ``generations''; a particle in generations 2 or 3 are identical in almost every respect to the corresponding particle in the first generation, except that it is more massive (and they have different lepton and baryon numbers). All the matter that we know about comes from the first generation--the massive particles of the second and third generation quickly decay into the lighter first generation particles. (It is currently a mystery why there are two extra ``unnecessary'' generations of particles.)

1.2 The forces

Table 2 lists the bosons--the particles that propagate forces. The spins are all integer multiples of $\hbar$.

Table 2: The bosons, and the forces that they are associate with.

Force	Particle	Spin
electromagnetic	$\gamma$ (photon)	1
weak	$W^\pm$, $Z^0$	1
strong	$g$ (gluon)	1
gravity	$G$ (graviton)	2

A number of interesting points about the bosons:

• The electromagnetic force couples only to particles that have an electric charge.
• The weak force couples to every particle, but in general it is only seen in the radioactive decay of particles as in the decay of a neutron to a proton (which might be more properly described as the decay a $d$ quark to a $u$ quark, as described in Appendix A).
• The strong force holds the quarks inside the baryons and mesons.
• Although gravity is mentioned in this table, it is not really part of the Standard Model; it is more properly described by Einstein's general theory of relativity. The rest of the Standard Model is built upon quantum mechanics, and so far no one has come up with a consistent theory that combines both relativity and quantum mechanics. However, see section 1.3 for more about this.

1.3 Unification

To the best of our knowledge, the Standard Model agrees well with experimental data; however, high energy physicists are still unhappy with it since it is so ad hoc. For example, there are several dozen different parameters that describe the model, all of which cannot be predicted a priori, but must be measured. (Think of them as a few dozen different knobs that could be turned--each setting of the knobs gives you a completely different universe.) These parameters include the masses of the particles and the coupling strengths of the forces.

For many years, theorists have been working on trying to unify the forces; that is, to show that all four forces of nature can be derived from a single force (put another way, there could be a single force in nature, and the forces that we see are low-energy approximations to this single unified force). A major step towards unification occurred in the late '60's when Glashow, Weinberg and Salam showed that the electromagnetic force and the weak force are just two facets of the electroweak force.

In the process of unifying these two forces, a new boson called the Higgs boson ($h^0$) had to be introduced. Among other things, this boson gives masses to all the particles. This particle is the only one in the Standard Model that hasn't yet been observed experimentally (the theoretical situation isn't completely clear, either--you will see below that supersymmetry requires more than one Higgs boson).

The successful unification of the electromagnetic and weak forces has given particle physicists hope that all the other forces, including gravity, may be unified. Superstrings are a popular candidate these days, and supersymmetry is a natural consequence of many superstring theories.

There is another reason why supersymmetry is popular these days. We know that the coupling strengths of the forces change with energy; for example, the strength of the electromagnetic force at ordinary energies is $\alpha_{EM}(0) = 1/137$; but at the energies of LEP or SLC (90 GeV) the strength increases to $\alpha_{EM}(90~\mathrm{GeV}) = 1/128$. If the forces really are unified at some high energy scale, then we would expect the electromagnetic, weak and strong forces to have the same strength at this unification scale. However, the top part of Figure 1 shows that the Standard Model coupling strengths extrapolated to very high energies do not converge at a single point. However, the introduction of supersymmetry (bottom plot) causes the coupling strengths to converge at a single point.

Figure 1: The convergence of the electromagnetic, weak and strong coupling constants. (Note that the $y$-axis is the inverse of the coupling strength.) [Langacker]