Particle Physics Tutorial 7 - Classification of Particle (Leptons)

 Contents

We can show the way the particles are classified as a tree:

From this diagram we can see that there are three classes of leptons.

Each lepton has a neutrino, an antiparticle, and an anti-neutrino.

Leptons

Leptons are fundamental particles such as the electron. They are called leptons as they are considered to be light-weights, although the muon is as massive as a meson and the tau has a greater mass than a gold atom.

Leptons do not feel the strong force.  They only feel the weak force (e.g. beta minus decay) and the electromagnetic force.  Neutrinos are neutral, so only feel the weak force.  Since they have a mass, they feel gravity, although gravity is too weak to play any role in interactions.

The only stable lepton is the electron.  The muon and the tau are highly unstable with very short life times.  Each has an escorting neutrino.

Neutrinos are not well understood.  While the universe is under a constant hail of neutrinos, they rarely interact with matter, so they are very difficult to measure.  During the day you get a hail from the Sun.  At night, you are peppered with the little brutes while asleep in your bed.  But they won't interact with you (unlike the fleas on the cat...).

There are six particle-antiparticle pairs known.  Leptons (Greek – “light thing” or “small coins”) are the smallest of the fundamental particles.  They have the following properties:

• fundamental particles without structure

• they interact by the weak interaction.  If they are charged, they interact by the electromagnetic interaction, but NOT the strong interaction.

The names of the leptons are:

Lepton

# Rest Energy

electron

e-

-1e

1/1800 mass of a proton

0.511 MeV

electron neutrino

ne

0

Very small

2.2 eV

muon

m-

-1e

2/3 mass of a proton

105 MeV

muon neutrino

nm

0

very small

0.17 MeV

tau

t-

-1e

Mass of gold atom

1800 MeV

tau neutrino

nt

0

Very small

15.5 MeV

Each particle has an antiparticle; for the electron, it is the positron, the muon the anti-muon, and the tau, the anti-tau

Anti Lepton

# Rest Energy

positron

e+

+1e

1/1800 mass of a proton

0.511 MeV

Electron antineutrino

0

Very small

2.2 eV

anti-muon

m+

+1e

2/3 mass of a proton

105 MeV

Muon antineutrino

0

very small

0.17 MeV

Anti-tau

t+

+1e

Mass of gold atom

1800 MeV

Tau antineutrino

0

Very small

15.5 MeV

We show the anti-particle either by an opposite charge (e+) or by putting a bar across the symbol (, pronounced “noo-bar e”).  In text and tables I will represent the antiparticle with white text on a black background, e.g. ne.

Quantum Numbers

There are some quantum numbers that you need to be aware of (Quantum is Latin for "how much?".):

• Lepton numbers (L).  In all interactions the lepton number has to be conserved.

• Charge (Q).  The charge has to be conserved.

• Baryon number (B).  In all interactions the baryon number has to be conserved.  All leptons have a baryon number of 0 (because they aren't baryons!).

• Strangeness (S).  This only applies to hadrons.  It is not relevant to lepton interactions.

You need to know about lepton numbers:

• if it’s a lepton, the lepton number is +1;

• if it’s an anti-lepton, the lepton number is -1.

The lepton number tells us whether a particle is a lepton or not.  If L = 0, it is not a lepton.

There are three smaller categories of lepton number, Le, Lm, and Lt.   Each one of these has to be conserved if a lepton interaction is to go ahead.  For a muon, Lm = +1.

Consider this interaction between an electron and a positron:

We know that it's an annihilation.

 Particle e- + e+ ® g Yes/No Q -1 + +1 ® 0 Y Le +1 + -1 ® 0 Y Lm 0 + 0 ® 0 Y Lt 0 + 0 ® 0 Y

The gamma photon produced is not a lepton, nor has it any charge.  Since neither the electron nor the positron are muons or tau, the muon and tau lepton numbers are 0.  If the lepton number and charge are not conserved, the interaction will not proceed.

Why do we have to bother with splitting the lepton number into three separate numbers?  Consider this:

Let's just use charge (Q)  and lepton number (L):

 Particle e+ + m- ® m+ + e- Yes/No Q +1 + -1 ® +1 + -1 Y L -1 + +1 ® -1 + +1 Y

This suggests the interaction should work.

Now let's look at how it works if we split it:

 Particle e+ + m- ® m+ + e- Yes/No Q +1 + -1 ® +1 + -1 Y Le -1 + 0 ® 0 + +1 N Lm 0 + +1 ® -1 + 0 N Lt 0 + 0 ® 0 + 0 Y

We can see from this that the Le numbers and the Lm numbers are NOT conserved (-1 ® +1), even though the charge is (0 ® 0).  So this interaction does NOT work.

Now consider this:

 Particle m- ® e- + nm + ne Yes/No Q -1 ® -1 + 0 + 0 Y Le 0 ® +1 + 0 + -1 Y Lm +1 ® 0 + +1 + 0 Y Lt 0 ® 0 + 0 + 0 Y

Notice how the lepton number and charge are conserved for electron, muon, and tau.  This tells us that the decay can proceed.

If leptons interact with hadrons, the hadrons are considered to have a lepton number of 0.

 What are the symbol, the charge, and the lepton numbers of the particle anti-tau? Use quantum numbers to show that  this interaction can happen: Question 3 Show that the electron neutrino has a mass of approximately 4.0 × 10-36 kg