High School Teachers at CERN
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Particle Physics
 
Introduction

This set of lessons on particle physics is designed to give you a logical introduction to the subject. It starts by introducing the fundamental particles, some of their properties and the rules that determine how they all combine together. Once the names, properties and rules have been established, you are shown how the fundamental particles can be combined to make all the familiar particles seen in bubble chambers, cloud chambers and other detectors.

The way the particles interact with each other are then described. The work leads up to a series of examples of reactions that can be interpreted in terms of the rules developed through the lessons.

The major headings of the sections are:
 

1) The building blocks: quarks and leptons, and their antiparticles 

2) The fundamental interactions

3) Building matter

4) Energy, mass: particle creation and annihilation

5) More about the interactions between fundamental particles

6) Examples of particle reactions ñ interpreted in terms of the rules of the game
 

1) The building blocks: quarks and leptons, and their antiparticles
  

Quarks	combine with each other to make matter particles like protons and neutrons
Leptons	are particles like electrons. Unlike the quarks, they do not combine with each other to make other particles

The current model of fundamental particles, called the standard model, says that there are six quarks and six leptons. 
 

Classifying the quarks and leptons

Quarks and leptons are classified according to their electric charge and rest mass. 

Note: the rest mass of a particle is the mass it has when it is at rest with respect to you. Generally, when we talk about a particleís mass we are referring to its rest mass.
 

The quarks:
 

Charge in units of the electron charge	1st generation quarks	2nd generation quarks	3rd generation quarks
+2/3	up  (u)	charm (c)	top (t)
-1/3	down  (d)	strange (s)	bottom (b)

 

The masses of the quarks increase in the following way:

up  down  strange  charm   bottom  top 

i.e. up is the lightest, top is the heaviest.

It is important to get to know the mass sequence. Particles decay by losing energy and changing into particles with a lower rest mass. This means that a strange quark can turn into an up quark by losing energy, but energy is needed if an up based particle is to turn into anything else. The most stable particles contain up quarks. They are stable because there are no lighter particles they can decay to.
 
 

The leptons:
 

Charge in units of the electron charge	1st generation leptons	2nd generation leptons	3rd generation leptons
-1	electron  (e)	muon (m )	tau (t )
0	electron neutrino (ne)	muon neutrino (nm)	tau neutrino (nt)

 

The leptons are much less massive than the quarks. The electron is the lightest of the three charged leptons, the muon comes next and the tau is the heaviest. 

The rest masses of the uncharged leptons, the neutrinos, are much smaller than those of the charged leptons. Some theories say that the neutrinos have zero mass but current physics indicates that they might have some rest mass. If they do have rest mass then the electron neutrino will be the lightest, the muon neutrino will come next and the tau neutrino will be the heaviest; but they will still be lighter than the other leptons. Even if the neutrinos have no rest mass, they do have energy and it is this energy that gives them reality.

The most up-to-date theories suggest that the neutrinos change from being one type to another as they travel through space. Space is filled with neutrinos, about 10¹² neutrinos pass through your body each second.
 
 

Antiparticles

For each of the building block particles there is a corresponding particle having the same mass but opposite electric charge.

These are called antiparticles.
 

Antiquarks:
 
 
 

Charge in units of the electron charge
-2/3	antiup  ()	anticharm ()	antitop ()
+1/3	antidown  ()	antistrange ()	antibottom ()

 

Antileptons:
 

Charge in units of the electron charge
+1	positron  (e+)	muplus (m+)	tauplus (t+)
0	electron antineutrino  ()	muon  antineutrino ()	tau  anti neutrino ()

 

Note: uncharged particles can also have antiparticles.

The antiparticle character is expressed through other properties that will be described next; there is more to antiparticleness than opposite charge.
 
 

Other properties

This description of other properties might come across as being a bit too much to take in at this stage. It is not expected that you fully understand the terms and ideas that are introduced here, but it is useful to have been introduced to them. Their use and meaning will become clearer once we start looking at building particles and constructing possible reactions. It is a bit like being introduced to lots of people at a social event: you do not remember their names or their jobs, but it is useful to have made some kind of contact.
 

Spin.

This is a property of particles that isnít really a rotation. It is called spin because it behaves like a rotation, but its real nature is not fully understood yet. Rotations combine together in a complicated way; spins combine in a similar way.

 
Spin is measured in units of h/2p , where h is Planck's constant 

(h = 6.67 x 10^-34 J.s). This is a cumbersome thing to keep referring to so we use a shorthand and say that a particle having that amount of spin is a spin 1 particle. A particle having half that amount of spin is called a spin 1/2 particle.

The quarks and leptons all have spin 1/2. The messenger particles, that we will meet later, are spin 1 particles with the exception of the graviton which has spin 2.

Particles and antiparticles generally have the same spin. The most notable exception is the neutrino. The neutrino and the antineutrino have opposite spin. If we use the rotation picture of spin then we say that the neutrino moves through space like a left handed screw; the antineutrino moves like a right handed one.
 

Lifetime. 

Most newly created particles change into others after a short time interval (we say that they have decayed). The mean lifetime of a particle is a measure of the probability of decay in a given time interval. The lifetime of a particle is a good indicator of the type of interaction involved in its decay.

Quark number.

This is associated with keeping track of the number of quarks before and after an interaction. We say that each quark has a quark number of 1/3 and each antiquark has a quark number of -1/3.

The reason why the number 1/3 appears is associated with the fact that quarks combine in threes to form composite particles called baryons. Baryons were given a baryon number 1, antibaryons were given a baryonnumber -1. These quantities allowed particle physicists to keep track of the numbers of baryons and antibaryons in particle reactions.

 

Lepton number.

This is associated with counting types of leptons before and after an interaction. The electron has an electron lepton number of 1, the positron has an electron lepton number of -1. The muon has a muon lepton number of 1, the anti muon has a muon number of -1 etc.

We use the symbol L to refer to lepton number:

e.g. for e^- L_e = 1 for e⁺ L_e = -1

for n_e L_e = 1 for  L_e = -1

for m^- Lm = 1 for m⁺ Lm = -1 etc.

Quarks have lepton number of 0 because quarks are not leptons. (Similarly, leptons have quark number 0 because they are not quarks.)

e.g. In the reaction where a gamma ray decays into an electron 

and a positron 

® e⁺ + e^-

the lepton numbers are 0 -1 +1

The total lepton number before the reaction is the same as after the reaction. 
Lepton numbers and quark numbers are used in this way, they form part of the set of rules that govern how particle reactions work.

Strangeness.

This is a property that was assigned to particles in the days before quarks and leptons were fully understood. If a composite particle contains a strange quark then it has a strangeness of -1 (i.e. S = -1). If a composite particle contains an anti-strange particle then it has a strangeness value of +1 (i.e. S = +1). 

The use of the strangeness number becomes a bit redundant when particle reactions are seen in terms of quarks and leptons.

2) The fundamental interactions
 

On a macroscopic level we talk about forces as 'every cause of acceleration or distortion'. All the forces in our every day world can be explained from the four existing interactions on the most fundamental level. (Sometimes physicists also use the word force when they talk about these fundamental interactions.)

Messenger particles are exchanged between the building block particles or between particles made of them.
 
 

The four interactions are:

- the gravitational interaction;

- the electro magnetic interaction;

- the weak ineraction;

- the strong interaction between quarks.

These interactions give rise to the forces we know in our every day live.
 
 

The strength of all these interactions is different.
 

	relative strength	range (m)
gravitation	10-39	infinity
electromagnetic	10-2	infinity
weak	10-13	~ 10-17
strong	1	~ 10-15

It is worth noting that the range of the strong interaction is roughly the same as the diameter of the proton whereas the range of the weak interaction is about 1/100^th of the proton diameter.

Particles come within the range of the strong interaction before they manage to get close enough for the weak interaction to have an effect. This means that strong interactions are more likely to occur than weak ones. This is why the lifetimes of strongly interacting particles are short.
 
 

3) Building matter

Starting from the quarks as basic building blocks we can build particles that are all detected.

Historically a lot of particles were found in cosmic rays and created using accelerators. All these particles seem to be leptons or to be built up of quarks. 
 

 

Particles constructed from quarks are called hadrons.

There are two types of hadron, they are:

1) mesons consisting of a quark and antiquark pair.
This combination is often written as q.
Examples of common mesons are pions and kaons.

e.g. p⁺ p^-p⁰ , K⁺ K^- K⁰

The pions are built from particle + antiparticle combinations of u, , d,  quarks.

e.g. p⁺ is u so the charges add as  to give charge = 1
p ^- is d so the charges add as to give charge = -1

p⁰ is a mix of u and d which gives a charge of 0 in each case.

 

The kaons are constructed from one of these lighter quarks together with an s (or ) quark to make the required quark antiquark pair.

The kaons were originally called strange particles because when they were discovered in cloud chamber events, in the 1940s, their behaviour could not be explained using particles with charges and masses that were known at the time. It was noted that when they were created they were always created in pairs. This behaviour can now be understood in terms of their structure involving a quark that is more massive than the familiar u and d quarks - we will illustrate this later. This quark became called the strange quark. 

e.g  is the combination u this gives a charge of  = 1

is the combination s this gives a charge of  = -1

is the combination d giving a charge of  = 0

is the combination s giving a charge of  = 0

(It is worth noting that in the original allocation of strangeness values to the particles, the  was defined as having a strangeness of +1. This means that the antistrange quark, , is allocated a strangeness value of +1.)
 
 
 

2) baryons consisting of three quarks
This combination is often written as qqq (or  for antibaryons)
Examples of common baryons are protons and neutrons i.e. p, n. 

 
These two particles involve the use of the u and d quarks only.

e.g. the proton is uud i.e. the charges add as  to give charge = 1

the neutron is udd i.e. the charges add as  to give charge = 0
 
 

Further examples of hadrons:

Other heavier and less stable particles can be shown also to have simple quark structures:
 

e.g. the lambda particle, L , has the quark structure uds 

the omega minus particle, W^-, has the quark structure sss

the D meson has the quark structure d

the psi, y , meson has the quark structure c

At this stage, you should be able to use the basic quark properties to work out the charges carried by these particles.