by Steve Bryson
Fermions are, by definition, particles that cannot be at the same place at the same time.
There are two observed types of fermions: leptons, lighter fermions (including electrons) which do not feel the strong nuclear force; and quarks (the particles that make up the proton and neutron) which do feel the strong nuclear force. There are six types of leptons and six types of quarks (five of which have definitely been observed). The masses of these particles is given compared to the proton mass = 1.672 x 10-24 grams.
The leptons are:
| Name (symbol) | Mass (compared with proton) | Electric Charge | Lifetime (seconds) |
| Electron (e) | 1/1836 | -1 | Stable (forever) |
| Electron Neutrino (ne) | 0 (?) | 0 | Stable (forever) |
| Muon (µ) | 1/8.88 | -1 | 1/455137 |
| Muon Neutrino (nµ) | 0 (?) | 0 | Stable (forever) |
| Tau (t) | 1.9 | -1 | 0.43 trillionths |
| Tau Neutrino (nt) | 0 (?) | 0 | Stable (forever) |
All leptons interact via the weak nuclear force. Only those leptons with a non-zero electric charge interact via the electromagnetic force. By definition, none of the leptons interact via the strong nuclear force.
The quarks are:
| Name (symbol) | Mass (compared with proton) | Electric Charge |
| Up (u) | 1/469 - 1/117 | +2/3 |
| Down (d) | 1/188 - 1/62 | -1/3 |
| Charm (c) | 1.0 - 1.7 | +2/3 |
| Strange (s) | 1/9.3 - 1/3.1 | -1/3 |
| Top (t) | 170 - 180 | +2/3 |
| Bottom (b) | 4.4 - 4.8 | -1/3 |
The quark masses are somewhat uncertain as they are found only in groups such as protons and neutrons. In these groups the energy due to the strong nuclear force contributes far more to the mass of the group than the quarks themselves (the mass of 2 ups and a down quark = at most .0332, or about 1/30, the mass of a proton), making the actual quark masses difficult to measure (in fact somewhat difficult to define). All quarks interact via the weak nuclear, strong nuclear, and electromagnetic forces. Due to the weak nuclear force, any type of quark may, under the right circumstances, change into any other type of quark.
In Quantum theory, all matter has both wave and particle aspects. As the forces between the particles has energy, it is considered matter. When we look at particle physics, we usually concentrate on the particle aspects of matter, so we say that the forces between particles is carried by other particles. These carrier particles are bosons, which are particles which can be at the same place at the same time.
The general rule of thumb is that bosons are force carrying particles that act on fermions and other bosons.
In this course, we will be considering the forces that act significantly on single elementary particles. As gravity is so weak as not to be noticed, we will not talk about gravity until the end of the class when we consider the unification of all forces.
This leaves us with three forces that act on elementary particles in our everyday world:
The Electromagnetic force is a long range force that acts like a pull or a push between any particles that have an electric charge. This force is responsible for holding electrons to atoms and for holding molecules together. The carrier particle (photon) is the particle aspect of light. This force is carried by a
Photon which has
mass 0
electric charge 0
and acts on any fermion or boson with electric charge.
Nothing acts on the photon.
The Weak force is a very short range force that acts on all particles and is mainly responsible for turning one kind of fermion into another kind of fermion (for example, turning an down quark into an up quark or turning a muon into an electron). This force is responsible for radioactive decay of atoms and particles. This force is carried by
W+ Boson which has
mass 85 times proton mass
electric charge +1
W- Boson which has
mass 85 times proton mass
electric charge -1
Z0 Boson which has
mass 97 times proton mass
electric charge 0
The W>+, W-, and Z0 Bosons all act on all fermions, and other W+, W-, and Z0 Bosons. Only W+, W-, and Z0 Bosons (and photons for the W+ and W-) act on these bosons.
The Strong force is a very very strong long range force that acts only between quarks. It is responsible for holding quarks together to form protons, neutrons, etc. This force is remarkable in that it actually gets stronger the further apart two quarks are pulled (which is opposite to the behavior of the electromagnetic force or gravity which get weaker the further two things are apart). This is why we should never see a quark all by itself. The analog of electric charge in the strong force may take on three values and is called color. The three values that may be taken are called red, blue and green. Thus the strong force only acts between colored fermions. This force is carried by
Eight Gluons which have
mass 0
electric charge 0
Gluons act only on quarks and other gluons. Nothing but gluons act on gluons.
The Other Boson: The current Standard Model of the forces between elementary particles predict one other particle that has not yet been observed: the Higgs Boson. This particle is required by our understanding of the weak and electromagnetic forces. For various technical reasons the Higgs Boson gives difficulties as an elementary particle. It is clear, however, that something like a Higgs Boson must exist. It may be that the Higgs is actually made out of as yet unknown fermions (this theory is called technicolor) much like the proton is made out of three quarks. We do not know, however, and until something like the Higgs is observed it will be very hard to say.
A Quick Glossary of Terms
In the literature, there are many words that I will not make common use of, but let me here introduce some of them and comment on the relationship between these terms and the terms I will be using.
In this course I will be talking almost entirely on the level of the particles listed in this handout. Historically, certain conglomeration of these particles have been given certain names:
Hadron: Any particle made of any number of quarks.
Meson: Any particle that is made of a quark and an antiquark bound together. A meson is therefore a hadron.
Examples:
Positive Pion = up + anti-down
Neutral Pion = up + anti-up
Negative Kaon = strange + anti-up
J/Psi = charm + anti-charm
Baryon: Any particle that is made of three quarks. A baryon is therefore a hadron.
Examples:
Proton (p) = up + up + down
Neutron (n) = up + down + down
Omega minus = strange + strange + strange
There are many more examples of both mesons and baryons.
Elementary particles and their interactions are observed in high energy collisions for two reasons:
• Lots of energy is available to create many particles. As many particles are short lived, we need to create them in the laboratory in order to observe them.
• Some of the more remarkable properties of elementary particle interactions are more easily observed at high energy.
The easiest method of creating a high energy particle interaction is to simply have some of the particles moving very quickly. This is done in a device known as an accelerator, which is capable of accelerating only particles with electric charge. Here is a sketch of how it works:
Let's say that we wish to accelerate an electron. The electron has a negative electric charge, and so will move away from objects which also have negative electric charge, and towards objects that have positive electric charge (as like charges repel and opposite charges attract).
Now picture an electron at one end of the room and an electrically charged plate with a hole in it at the other end.
If the plate has a positive charge, the electron will accelerate towards it:
|
• -->
|
Now, imagining that the electron is exactly moving so that it will pass through the hole, if we were to switch the charge of the plate from positive to negative just as the electron passed through the electron would be accelerated away from the plate:
|
•------->
|
In this way the electron is set into motion.
Now if we had the electron pass through a series of plates, all of which switched their electric charge at just the right times to keep accelerating the electron then we would be able to get the electron moving as fast as we desired:
| | | | | | | | | | | | | | | | | | | |
•---------------->
| | | | | | | | | | | | | | | | | | | |
- - + + + + + + + + +
Then the only limit to the speed that we can accelerate the electron to is how many electrically charged plates we can put in a row. There is such a row of plates two miles long in Palo Alto at the Stanford Linear Accelerator Center (SLAC) which is capable of accelerating electrons up to about 99.99999% of the speed of light (we can get as close as we want to the speed of light, but we can never exceed it). If we wanted the electron to go faster (say 99.9999999999% of the speed of light), we would need to put more plates in a row (or increase the charge on each plate). This, of course, leads to technical difficulties.
SLAC is the only large accelerator that is in a straight line, and it accelerates electrons. There is another way--put the plates in a circle. You would steer the electrons (or protons) with magnets (which will curve the path of an electrically charged particle) so that they go around and around as much as you would like. This type of accelerator is called a cyclotron and there are several in operation at such laboratories as Fermilab near Chicago and CERN on the Swiss-French border. The limit on the speed of a particle in a cyclotron is mainly that the faster a particle goes the stronger the magnets must be to keep the particles going in a circle. Also, electrically charged particles loose energy as they go around a curved path. Cyclotrons accelerate both electrons and protons.
Note that to accelerate the particle the particle must be both long lived and have an electric charge. This means that the only particles that may be accelerated are electrons (or anti-electrons) and protons (or anti-protons). We do not at this time know how to accelerate neutrons up to very high energies.
Once you've got your proton or electron moving at such high speed, what do you do with it? You aim it at a target of some substance (such as liquid hydrogen or iron) in order for the accelerated particles to collide with the atoms in the target and produce lots of exotic, short-lived particles. The faster the accelerated particles are going the more energy is available to produce more new particles.
There is a way to get much higher energy collisions using your accelerator than aiming the particles at a fixed target: you can have another beam of particles (usually antiparticles of the particle you're accelerating) going around in your ring in the opposite direction. Then once the two oppositely rotating beams of particles are going as fast as desired, you steer them so that they collide head on. This will provide much more energy than simply aiming the beam at a fixed target. Such an accelerator is called a collider. All new large accelerators are colliders.
Particle accelerators are measured in terms of the energy which they give to their particles. This energy is typically measured in terms of an “electron volt”, which is simply the amount by which the energy of an electron increases as it is accelerated by a one-volt potential difference. An electron volt is a very small unit of energy = 1.6 x 10-12 ergs, so the unit of a billion electron volts, or giga-electron volts (abbreviated GeV), is now common. While this measure of energy is very convenient for particle physicists, it is rather non-intuitive. As the energy increase is entirely due to the increase in motion of the particle, there is a simple formula which gives the speed of a particle if you know its mass in electron volts (actually giga-electron volts or GeV), and its energy in the accelerator, also in electron volts (again in GeV). A proton has a mass of 0.938 GeV, and an electron has a mass of 0.000511 GeV. This formula is given by
speed = speed of light times square root of (1 - (mass of particle in GeV/energy in GeV)2)
(This formula follows from the formula for energy in special relativity.) The speed of light is 186,282.397052 miles/second or 299,792.458 kilometers/second. Thus an electron at SLAC, which has an energy of 15 GeV has a speed given by
speed of electron at SLAC = speed of light x square root of (1 - (0.000511/15)2)
= speed of light x square root of (1 - (0.000034)2)
= speed of light x square root of (1 - 1.16 x 10-9)
= speed of light x square root of (.99999999884)
= .99999999942 times the speed of light
= 186282.396944 miles/second
(This electron would have a Lorentz contraction factor due to special relativity of about .000034, so the 2 mile SLAC tunnel would appear to the electron to be about 2 inches long. Note that the Lorentz contraction factor is always given by (mass of particle in GeV/energy in GeV).)
A proton at Fermilab has an energy of 1000 GeV, so its speed is given by
speed of proton at Fermilab = speed of light x square root of (1 - (0.938/1000)2)
= speed of light x square root of (1 - (0.000938)2)
= speed of light x square root of (1 - .000000879844)
= speed of light x square root of (.99999912)
= .99999956 times the speed of light
= 186282.315102 miles/second
(This proton would have a Lorentz contraction factor of .000938, so 2 miles would appear to the proton to be almost 10 feet long.)
All particles are, in principle, detected in the same way. Charged particles, as they pass through a substance, ionize the atoms of that substance along the path of the charged particle, which is to day that the fast moving particles kick electrons out of nearby atoms.. This ionization is detected in a variety of ways:
Cloud Chambers were the first methods used. If a charged particle such as an electron moves through very humid air, little droplets of water ('clouds') form along the path of the particle. These clouds can be photographed to give a picture of the track of the particle. This method grew up into--
Bubble Chambers which operate much like cloud chambers except that instead of droplets of water forming in air little bubbles are formed in a liquid that is just at the boiling point. Usually liquid hydrogen is used, primarily because hydrogen is a very simple atom, thus making analysis easier. The bubbles in the bubble chamber is photographed to give a picture of the path of the particles. This method was used widely up until the last decade, when it was replaced by purely electronic means.
Spark Chambers are stacks of highly charged electrical plates separated by air. As a charged particle passes through the air between the plates, the atoms of the air is ionized and tiny bolts of lightning are momentarily created along the paths of the particle. Photographs of the tiny bolts give a picture of the path of the particle.
Proportional Counters are a variation on the spark chamber idea. Instead of electrically charged plates, electrically charged wires are used. These wires can sense the ionization of the substance (usually an argon/alcohol gas) around them and send the signal out to detecting instruments. This is very nice as it allows the information on the path of the charged particle to be sent to a computer, thus allowing the immediate automated analysis of the event.
Drift Chambers are exactly like proportional counters, except that there are many tubes each filled with a single wire. By recording the firing of each tube as the particle passes through, one can reconstruct the path of the particle.
Scintillation Counters are basically substances that glow when a charged particle passes through them, much like a television screen. These are not used to observe the path of a particle, but are rather used to measure the energy of a particle, as the more energetic the charged particle in the scintillator, the more brightly it glows. The signal from these counters is also fed into computers for automated analysis. A large collection of scintillators is called a calorimeter.
The last detection method to be mentioned does not use the ionization of a medium. It uses the fact that when a charged particle passes through a substance faster than the speed of light in that substance the particle emits a certain kind of light. By examining that light, the speed of the particle can be deduced. The detector that uses this method of detection is called a Cherenkov Counter.
Thus you can see that we have means of detecting only charged particles that live long enough to produce the effects above. Detection of neutral and very short lived particles is indirect. In the case of neutral particles, one looks for the effects on charged particles via some non-electromagnetic interaction (usually the weak interaction). Particular methods will be examined as we examine the forces individually.