The Standard Model of Particle Physics: A Lunchbox's Guide

Dave Fehling
2nd Year Seminar
The Johns Hopkins University

Background

Early in human history, people thought that all matter was composed of 4 main elements: Earth, Wind, Water, and Fire. This was a very simplistic viepoint, but it had the advantage of employing a simple classification scheme. As science evolved, though, people realized that this was not the case, but rather that all matter was composed of many elements, not just four. However, a system to categorize the elements was created: Mendeleev's periodic table. A great advantage of this classification scheme was its ability to predict the existence and properties of several previously unknown elements.

Eventually, the substructure of elements was discovered, somewhat simplifying the model of matter. In 1897, Thompson discovered the electron while Rutherford discovered the nucleus in 1911 in his famous gold foil experiment.

Antiparticles

Antiparticles are essestially identical to their ``normal'' partners with the exception that they have opposite charge. The antiparticle of an electron is a positron which is identical to the electron except that it has charge +e. A particle may be its own antiparticle (the photon).

In quantum mechanics, the equation which describes particles and their states is the Schrödinger Equation

This equation describes a 1-Dimensional free particle but is not relativistically correct. To get a relativistically correct equation, we replace the momentum term with the relativistically correct analogue

and we get the relativistically correct Klein-Gordon equation

This equation now has E^2 which means that solutions with both positive and negative energies are allowed. Another consequence of this equation is that probability is no longer conserved in time. However, there is a new quantity which is conserved: the charge density. The charge density can be either positive or negative; the negative corresponds to an antiparticle with a negative energy.

Fermions

Fermions are matter constituents and have half-integer spins (1/2, 3/2,etc.). As such, fermions obey the Pauli Exclusion Principle, which states that no two particles can have the same set of quantum numbers. Two classes of fermions are leptons and quarks. These classes are further divided into generations. Both the 2nd and 3rd generations of a particle behave like the first generation except they have increased mass. One interesting thing about fermions is that, with the discovery of neutrino oscillations, all fermions have mass.

Leptons

There are 6 leptons (and their corresponding anti-leptons). One 1st generation lepton is the electron previously discussed. The electron has a mass of 0.000511 GeV/c^2. The 2nd generation equivalent, the muon was discovered in cosmic rays in 1937 and has a mass of 0.106 GeV/c^2. The tau is in the 3rd generation, was found in 1975 at SLAC from electron-position annihilation and has a mass of 1.7771 GeV/c^2. There are 3 neutrinos, one for each generation. They were originally thought up as bookkeeping devices to account for the lost energy and momentum in &beta -decay. Their existence has since been verified. Lepton Number is a conserved quantity, meaning that in reactions the number of leptons initially balances those finally. In this scheme, leptons are given a lepton number of 1 while their antiparticles have lepton number -1.

Quarks

Quarks were discovered by a method very similar to Rutherford's Scattering Experiment called Deep Inelastic Scattering. In this experiment, high energy electrons are scattered off protons. From the results of this experiment, the proton was found to have substructure. The proton is made up of the combination uud. These are the two first generation quarks. The up (u) quark has charge +2/3 and mass 0.003 GeV/c^2 while the down (d) quark has charge -1/3 and mass 0.006 GeV/c^2. The strange (s) quark was created along with the quark model, has mass 0.1 GeV/c^2 and charge identical to the down quark. Rounding out the 2nd generation quarks is the charm (c) quark. It was predicated in 1970 and found shortly thereafter. The c quark has mass 1.3 GeV/c^2. The 3rd generation analogue to the u is the bottom (b) quark. The b quark was discovered in 1977 at Fermi lab and has a mass of 4.3 GeV/c^2. The top quark was found recently and has a mass of 175 GeV/c^2. The top quark is so massive, in fact, that no bound states involving it have been observed.

Baryons

Baryons are bound states of 3 quarks. Like fermion number, baryon number is a conserved quantity. Baryons are fermions of spin 1/2 or 3/2. However, this leads to a contradiction of sorts. Consider for example the Ω - particle. This is a fermion of spin 3/2 consisting of sss. This appears to violate the Pauli Exclusion Principle. However, the violation is removed if a new quantum number called color charge is introduced. The study of this new quantum number is called QCD - Quantum ChromoDynamics.

QCD

The quantum number of QCD may take 3 values: red, blue, or green. Other than these names, QCD has nothing to do with colors. This solves the inconsistency created by the Ω -. Each s quark in this bound state is given a different color, removing the previous degeneracy. This underscores a theorem of QCD: all naturally occuring particles must be colorless. This means that baryons must have equal parts red, blue, and green; and mesons, bound states of two quarks, must have color anticolor. A problem with QCD is that color charge has not been observed in nature. This is answered by quark confinement.

Bosons

Bosons are force mediators and have integer spin (0,1, etc.). Because of this integer spin, they do not obey the Pauli Exclusion Principle. Bosons may be either massive like the W and Z bosons or massless like the photon or gluon.

The Higgs boson is the last particle predicted by the Standard Model that has yet to have been found. The Higgs is predicted to be the reason everything in the universe has mass. It is also supposed to break the ElectroWeak symmetry: the fact that the EM boson is massless while the Weak bosons have mass.

Forces

Forces are the exchange of virtual particles. Because of the uncertainty relation

Energy doesn't have to be conserved if the time interval over which it isn't conserved is small enough. This allows two particles to exchange particles and thus transfer energy if the interaction is short enough. In the Standard Model, there are 3 forces: Electromagnetic (EM), Weak, and Strong. At high energies, The EM and Weak forces combine into the Electroweak force.

The Electromagnetic force is mediated by the massless photon. All charged particles participate in the EM force. Partly because of its massless mediator, the EM force acts over a long range.

The Weak force is mediated by the massive W (80.4 GeV/c^2) and Z (91.187 GeV/c^2) bosons. The Weak force affects quarks and leptons and is capable of changing flavor. Flavor refers to the type of quark or lepton. For example, in the decay of a neutron into a protron and an electron, there is also an antineutrino produced.

The flavor of one of the d quarks in the neutron (udd) has been converted into a u quark in the proton (uud). The Weak force is the only interaction in which neutrinos participate. Because the Weak force mediators are massive, the range of the force is very short.

The Strong force is mediated by the massless gluon and affects all particles with color charge. The gluon carries c cbar. This makes it unique amongst the force mediators. Because the gluon carries color charge, it itself can participate in the strong interaction. Another unique thing about the Strong force is that its strength increases with distance. This is the solution to the problem of Quark Confinement mentioned earlier. As two quarks are separated, the energy to keep seperating them increases to a point where a new quark-antiquark pair are produced. Therefore, a single quark is never isolated so no color charge can be detected.

Problems

The Standard Model (SM) predicts that neutrinos should be massless. However, recent developments have found neutrino oscillations, indicating that neutrinos have mass. The SM can be adjusted to include the masses, but it should include them with no changes needed.

In fact, the SM doesn't predict any of the masses of any particle. A good model should predict the masses of all the particles and not simply their existence.

Another problem with the SM is dark matter. Dark matter is supposed to be a particle. Regardless of the properties of this exotic particle, it should be included in the Standard Model of Particle Physics, but it isn't.