KAHIBARO
Table of Contents
The lepton family
Leptons are a group of fundamental particles in the Standard Model. Fundamental means they are not known to be made of smaller parts. They are matter particles, so they belong to the class called fermions.
The lepton family contains six particles, arranged in three generations. Each charged lepton has a corresponding neutrino. The charged leptons are the electron, the muon, and the tau. The neutrinos are the electron neutrino, the muon neutrino, and the tau neutrino.
| Generation | Charged lepton | Neutrino |
|---|---|---|
| 1 | electron, $e^-$ | electron neutrino, $\nu_e$ |
| 2 | muon, $\mu^-$ | muon neutrino, $\nu_\mu$ |
| 3 | tau, $\tau^-$ | tau neutrino, $\nu_\tau$ |
Each of these particles also has an antiparticle. For example, the electron has the positron, written $e^+$.
Basic properties
Leptons are different from quarks in one very important way. They do not feel the strong interaction. Because of this, leptons do not form hadrons such as protons and neutrons.
Charged leptons carry electric charge $-e$, where $e$ is the elementary charge in magnitude. Neutrinos have electric charge zero. All leptons have spin $\tfrac{1}{2}$, so they are fermions and obey the Pauli exclusion principle.
Important facts about leptons:
Charged leptons have charge $-e$.
Neutrinos have charge $0$.
All leptons have spin $1/2$.
Leptons do not participate in the strong interaction.
A useful summary is shown below.
| Lepton | Symbol | Charge | Strong interaction? |
|---|---|---|---|
| Electron | $e^-$ | $-e$ | No |
| Electron neutrino | $\nu_e$ | $0$ | No |
| Muon | $\mu^-$ | $-e$ | No |
| Muon neutrino | $\nu_\mu$ | $0$ | No |
| Tau | $\tau^-$ | $-e$ | No |
| Tau neutrino | $\nu_\tau$ | $0$ | No |
Generations
The three lepton generations have the same pattern of charges and spins, but different masses. The electron is the lightest charged lepton, the muon is heavier, and the tau is heavier still.
This repeating structure is a major feature of the Standard Model. The first generation is the most common in ordinary matter. Atoms contain electrons, not muons or taus, because the heavier leptons are unstable and decay into lighter particles.
The generations look similar in structure:
$$
\begin{pmatrix}
\nu_e \\
e^-
\end{pmatrix},
\quad
\begin{pmatrix}
\nu_\mu \\
\mu^-
\end{pmatrix},
\quad
\begin{pmatrix}
\nu_\tau \\
\tau^-
\end{pmatrix}
$$
Charged leptons and neutrinos
Charged leptons interact through the electromagnetic force and the weak force. Since they have mass, they also respond to gravity. Neutrinos do not interact electromagnetically because they are neutral, but they do take part in the weak interaction and gravity.
This makes neutrinos much harder to detect than electrons, muons, or taus. They can pass through large amounts of matter with very little interaction.
The electron is stable in ordinary physics. The muon and tau are unstable and decay into lighter particles. Their neutrinos are extremely light and interact very weakly.
A key distinction is this:
Charged leptons, $e^-$, $\mu^-$, $\tau^-$, feel electromagnetic and weak interactions.
Neutrinos, $\nu_e$, $\nu_\mu$, $\nu_\tau$, feel the weak interaction but not the electromagnetic interaction.
Lepton number
Leptons carry a quantum number called lepton number. In basic particle reactions, total lepton number is conserved. A lepton is assigned lepton number $+1$, and an antilepton is assigned lepton number $-1$.
So for example,
$$
L(e^-) = +1, \qquad L(e^+) = -1
$$
and similarly for the other leptons and neutrinos.
Sometimes physicists also track separate family lepton numbers, such as electron lepton number, muon lepton number, and tau lepton number. This is useful in many reactions, although neutrino oscillations show that the separate family numbers are not always strictly preserved in nature.
For many Standard Model processes:
Total lepton number is conserved.
Leptons have $L = +1$.
Antileptons have $L = -1$.
Leptons in ordinary matter
Ordinary matter around us is built mostly from first generation fermions. Among leptons, this means the electron and the electron neutrino are the most familiar. The electron is especially important because it forms the outer structure of atoms and is responsible for chemistry and electricity.
Muons and taus are not part of stable everyday matter. They are produced in high energy processes and then decay. Neutrinos are produced in many nuclear and particle processes, but because they interact so weakly they usually pass through matter almost unnoticed.
Comparison with quarks
Leptons and quarks are both fermions, but they behave very differently. Quarks carry color charge and feel the strong interaction. Leptons do not carry color charge and do not feel the strong interaction.
Quarks combine to form composite particles such as baryons and mesons. Leptons appear as individual particles.
| Property | Leptons | Quarks |
|---|---|---|
| Fundamental particles | Yes | Yes |
| Spin | $1/2$ | $1/2$ |
| Electric charge | Integer, $0$ or $-e$ for known leptons | Fractional |
| Strong interaction | No | Yes |
| Can form hadrons | No | Yes |
A simple picture of the lepton generations
Why leptons matter
Leptons are essential to the structure of the Standard Model. The electron is central to atomic structure. Neutrinos play important roles in nuclear reactions, radioactive decay, stars, and cosmology. Muons and taus help physicists test the theory at higher masses and energies.
Even though leptons are a small set of particles, they appear in many of the most important physical processes in nature.
Summary of the lepton family:
There are six leptons in the Standard Model, in three generations.
Each generation contains one charged lepton and one neutrino.
Leptons are fundamental spin-$1/2$ particles.
They do not experience the strong interaction.