14.3 Leptons

Introduction

In the Standard Model of particle physics, leptons are a class of fundamental, elementary particles. They are not composed of any smaller constituents. Along with quarks, leptons are the basic building blocks of matter. The family of leptons includes the familiar electron, as well as two heavier, unstable cousins: the muon and the tau. Each of these has an associated neutral partner called a neutrino.

Properties of Leptons

Leptons are defined by a set of common characteristics:

• Spin: They all have a spin of $\frac{1}{2}$, which classifies them as fermions.
• Interaction: Leptons do not experience the strong nuclear force. They do, however, interact via the weak nuclear force, the electromagnetic force (if charged), and gravity.
• Lepton Number: Each lepton is assigned a Lepton Number ($L$) of $+1$. Their antimatter counterparts, anti-leptons, have a Lepton Number of $-1$. This quantity is conserved in all known particle interactions.
• Antiparticles: Every lepton has a corresponding anti-lepton with the same mass but opposite charge and lepton number. For example, the antiparticle of the electron ($e^{-}$) is the positron ($e^{+}$).

The Three Generations of Leptons

Leptons are organized into three generations or families, each consisting of a charged lepton and its corresponding neutrino.

• The electron is stable and is a component of all atoms.
• The muon and tau are much more massive and are unstable. They are created in high-energy collisions (e.g., in particle accelerators or from cosmic rays) and decay very quickly into lighter particles via the weak nuclear force.
• Neutrinos are electrically neutral and have an extremely small mass. They interact only via the weak nuclear force and gravity, making them extremely difficult to detect.

Neutrinos and Beta Decay

Neutrinos and antineutrinos are produced during beta decay. This was first proposed by Pauli to explain why the electron in beta decay appeared to carry a continuous range of energies — the missing energy is carried away by the (anti)neutrino.

• In beta-minus (${\beta }^{-}$) decay, an electron antineutrino (${\bar{\nu }}_e$) is emitted: $n\to p^{+}+e^{-}+{\bar{\nu }}_e$
• In beta-plus (${\beta }^{+}$) decay, an electron neutrino (${\nu }_e$) is emitted: $p^{+}\to n+e^{+}+{\nu }_e$

Both the electron and the neutrino/antineutrino are leptons.

Antiparticles of Leptons

Every lepton has a corresponding anti-lepton:

Antiparticles have the same mass as their particle counterparts but opposite charge (and opposite lepton number). Antimatter is the counterpart of matter — when a lepton meets its anti-lepton, they annihilate.

Conservation of Lepton and Baryon Numbers

In particle physics, all interactions must obey strict conservation laws. In addition to conserving energy, momentum, and charge, reactions must also conserve the Lepton Number and the Baryon Number.

• Lepton Number Conservation: The total lepton number must be the same before and after a reaction.
• Baryon Number Conservation: The total baryon number must also be the same before and after a reaction.

Example: Beta Decay

Beta-Negative Decay: $n\to p^{+}+e^{-}+{\bar{\nu }}_e$

Beta-Positive Decay: $p^{+}\to n+e^{+}+{\nu }_e$