by Steve Bryson
Fermions are, by definition, particles that cannot beat the same place at the same time.
There are two observed types of fermions: leptons,lighter fermions (including electrons) which do not feel thestrong nuclear force; and quarks (the particles that makeup the proton and neutron) which do feel the strong nuclearforce. There are six types of leptons and six types of quarks(five of which have definitely been observed). The masses ofthese particles is given compared to the proton mass = 1.672 x 10-24grams.
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 thoseleptons with a non-zero electric charge interact via theelectromagnetic force. By definition, none of the leptonsinteract 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 onlyin groups such as protons and neutrons. In these groups theenergy due to the strong nuclear force contributes far more tothe mass of the group than the quarks themselves (the mass of 2ups and a down quark = at most .0332, or about 1/30, the mass ofa proton), making the actual quark masses difficult to measure(in fact somewhat difficult to define). All quarks interact viathe weak nuclear, strong nuclear, and electromagnetic forces. Dueto the weak nuclear force, any type of quark may, under the rightcircumstances, change into any other type of quark.
In Quantum theory, all matter has both wave and particleaspects. As the forces between the particles has energy, it isconsidered matter. When we look at particle physics, we usuallyconcentrate on the particle aspects of matter, so we say that theforces between particles is carried by other particles. Thesecarrier particles are bosons, which are particles which can be atthe same place at the same time.
The general rule of thumb is that bosons are force carryingparticles that act on fermions and other bosons.
In this course, we will be considering the forces that actsignificantly on single elementary particles. As gravity is soweak as not to be noticed, we will not talk about gravity untilthe end of the class when we consider the unification of allforces.
This leaves us with three forces that act on elementaryparticles in our everyday world:
The Electromagnetic force is a long range force thatacts like a pull or a push between any particles that have anelectric charge. This force is responsible for holding electronsto atoms and for holding molecules together. The carrier particle(photon) is the particle aspect of light. This force is carriedby 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 onall particles and is mainly responsible for turning one kind offermion into another kind of fermion (for example, turning andown quark into an up quark or turning a muon into an electron).This force is responsible for radioactive decay of atoms andparticles. 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 Bosonsall act on all fermions, and other W+, W-,and Z0 Bosons. Only W+, W-, andZ0 Bosons (and photons for the W+ and W-)act on these bosons.
The Strong force is a very very strong long range forcethat acts only between quarks. It is responsible for holdingquarks together to form protons, neutrons, etc. This force isremarkable in that it actually gets stronger the further aparttwo quarks are pulled (which is opposite to the behavior of theelectromagnetic force or gravity which get weaker the further twothings are apart). This is why we should never see a quark all byitself. The analog of electric charge in the strong force maytake on three values and is called color. The three values thatmay be taken are called red, blue and green. Thus the strongforce only acts between colored fermions. This force is carriedby
Eight Gluons which have
mass 0
electric charge 0
Gluons act only on quarks and other gluons. Nothing but gluonsact on gluons.
The Other Boson: The current Standard Model of the forcesbetween elementary particles predict one other particle that hasnot yet been observed: the Higgs Boson. This particle is requiredby our understanding of the weak and electromagnetic forces. Forvarious technical reasons the Higgs Boson gives difficulties asan elementary particle. It is clear, however, that something likea Higgs Boson must exist. It may be that the Higgs is actuallymade out of as yet unknown fermions (this theory is calledtechnicolor) much like the proton is made out of three quarks. Wedo not know, however, and until something like the Higgs isobserved it will be very hard to say.
A Quick Glossary of Terms
In the literature, there are many words that I will not makecommon use of, but let me here introduce some of them and commenton the relationship between these terms and the terms I will beusing.
In this course I will be talking almost entirely on the levelof the particles listed in this handout. Historically, certainconglomeration 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 anantiquark 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. Abaryon 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 inhigh 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 thelaboratory in order to observe them.
• Some of the more remarkable properties of elementaryparticle interactions are more easily observed at high energy.
The easiest method of creating a high energy particleinteraction is to simply have some of the particles moving veryquickly. This is done in a device known as an accelerator, whichis 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 electronhas a negative electric charge, and so will move away fromobjects which also have negative electric charge, and towardsobjects that have positive electric charge (as like charges repeland opposite charges attract).
Now picture an electron at one end of the room and anelectrically charged plate with a hole in it at the other end.
If the plate has a positive charge, the electron willaccelerate towards it:
|
• -->
|
Now, imagining that the electron is exactly moving so that itwill pass through the hole, if we were to switch the charge ofthe plate from positive to negative just as the electron passedthrough 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 righttimes to keep accelerating the electron then we would be able toget the electron moving as fast as we desired:
| | | | | | | | | | | | | | | | | | | |
•---------------->
| | | | | | | | | | | | | | | | | | | |
- - + + + + + + + + +
Then the only limit to the speed that we can accelerate theelectron to is how many electrically charged plates we can put ina row. There is such a row of plates two miles long in Palo Altoat the Stanford Linear Accelerator Center (SLAC) which is capableof accelerating electrons up to about 99.99999% of the speed oflight (we can get as close as we want to the speed of light, butwe can never exceed it). If we wanted the electron to go faster(say 99.9999999999% of the speed of light), we would need to putmore 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 theplates in a circle. You would steer the electrons (or protons)with magnets (which will curve the path of an electricallycharged particle) so that they go around and around as much asyou would like. This type of accelerator is called a cyclotronand there are several in operation at such laboratories asFermilab near Chicago and CERN on the Swiss-French border. Thelimit on the speed of a particle in a cyclotron is mainly thatthe faster a particle goes the stronger the magnets must be tokeep the particles going in a circle. Also, electrically chargedparticles 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 bothlong lived and have an electric charge. This means that the onlyparticles that may be accelerated are electrons (oranti-electrons) and protons (or anti-protons). We do not at thistime know how to accelerate neutrons up to very high energies.
Once you've got your proton or electron moving at such highspeed, what do you do with it? You aim it at a target of somesubstance (such as liquid hydrogen or iron) in order for theaccelerated particles to collide with the atoms in the target andproduce lots of exotic, short-lived particles. The faster theaccelerated particles are going the more energy is available toproduce more new particles.
There is a way to get much higher energy collisions using youraccelerator than aiming the particles at a fixed target: you canhave another beam of particles (usually antiparticles of theparticle you're accelerating) going around in your ring in theopposite direction. Then once the two oppositely rotating beamsof particles are going as fast as desired, you steer them so thatthey collide head on. This will provide much more energy thansimply aiming the beam at a fixed target. Such an accelerator iscalled a collider. All new large accelerators are colliders.
Particle accelerators are measured in terms of the energywhich they give to their particles. This energy is typicallymeasured in terms of an “electron volt”, which issimply the amount by which the energy of an electron increases asit is accelerated by a one-volt potential difference. An electronvolt is a very small unit of energy = 1.6 x 10-12ergs, so the unit of a billion electron volts, or giga-electronvolts (abbreviated GeV), is now common. While this measure ofenergy is very convenient for particle physicists, it is rathernon-intuitive. As the energy increase is entirely due to theincrease in motion of the particle, there is a simple formulawhich gives the speed of a particle if you know its mass inelectron volts (actually giga-electron volts or GeV), and itsenergy 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 of0.000511 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 specialrelativity.) The speed of light is 186,282.397052 miles/second or299,792.458 kilometers/second. Thus an electron at SLAC, whichhas an energy of 15 GeV has a speed given by
speed of electron at SLAC = speed of light xsquare 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 x10-9)
= 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 tospecial relativity of about .000034, so the 2 mile SLAC tunnelwould appear to the electron to be about 2 inches long. Note thatthe Lorentz contraction factor is always given by (mass ofparticle in GeV/energy in GeV).)
A proton at Fermilab has an energy of 1000 GeV, so its speedis given by
speed of proton at Fermilab = speed of light xsquare 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 10feet long.)
All particles are, in principle, detected in the same way.Charged particles, as they pass through a substance, ionize theatoms of that substance along the path of the charged particle,which is to day that the fast moving particles kick electrons outof nearby atoms.. This ionization is detected in a variety ofways:
Cloud Chambers were the first methods used. If a chargedparticle such as an electron moves through very humid air, littledroplets of water ('clouds') form along the path of the particle.These clouds can be photographed to give a picture of the trackof the particle. This method grew up into--
Bubble Chambers which operate much like cloud chambersexcept that instead of droplets of water forming in air littlebubbles are formed in a liquid that is just at the boiling point.Usually liquid hydrogen is used, primarily because hydrogen is avery simple atom, thus making analysis easier. The bubbles in thebubble chamber is photographed to give a picture of the path ofthe particles. This method was used widely up until the lastdecade, when it was replaced by purely electronic means.
Spark Chambers are stacks of highly charged electricalplates separated by air. As a charged particle passes through theair between the plates, the atoms of the air is ionized and tinybolts of lightning are momentarily created along the paths of theparticle. Photographs of the tiny bolts give a picture of thepath of the particle.
Proportional Counters are a variation on the sparkchamber idea. Instead of electrically charged plates,electrically charged wires are used. These wires can sense theionization of the substance (usually an argon/alcohol gas) aroundthem and send the signal out to detecting instruments. This isvery nice as it allows the information on the path of the chargedparticle to be sent to a computer, thus allowing the immediateautomated 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 passesthrough, one can reconstruct the path of the particle.
Scintillation Counters are basically substances thatglow when a charged particle passes through them, much like atelevision screen. These are not used to observe the path of aparticle, but are rather used to measure the energy of aparticle, as the more energetic the charged particle in thescintillator, the more brightly it glows. The signal from thesecounters is also fed into computers for automated analysis. Alarge collection of scintillators is called a calorimeter.
The last detection method to be mentioned does not use theionization of a medium. It uses the fact that when a chargedparticle passes through a substance faster than the speed oflight in that substance the particle emits a certain kind oflight. By examining that light, the speed of the particle can bededuced. The detector that uses this method of detection iscalled a Cherenkov Counter.
Thus you can see that we have means of detecting only chargedparticles 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 oncharged particles via some non-electromagnetic interaction(usually the weak interaction). Particular methods will beexamined as we examine the forces individually.