Chapter 44: Problem 23
In which of the following decays are the three lepton numbers conserved? In each case, explain your reasoning. (a) \(\mu^-\rightarrow e^- + \nu_e + \overline{\nu}_\mu\); (b) \(\tau^-\rightarrow e^- + \overline{\nu}_e + \overline {\nu} _\tau\); (c) \(\pi^+ \rightarrow e^+ + \gamma\); (d) \(n \rightarrow p + e^- + \overline{\nu}_e\).
Short Answer
Step by step solution
Understand Lepton Number Conservation
Evaluate Decay (a) \(\mu^-\rightarrow e^- + \nu_e + \overline{\nu}_\mu\)
Evaluate Decay (b) \(\tau^-\rightarrow e^- + \overline{\nu}_e + \overline{\nu}_\tau\)
Evaluate Decay (c) \(\pi^+ \rightarrow e^+ + \gamma\)
Evaluate Decay (d) \(n \rightarrow p + e^- + \overline{\nu}_e\)
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Muon Decay
In the decay \(\mu^-\rightarrow e^- + u_e + \overline{u}_\mu\), the muon decays into:
- an electron \((e^-)\),
- an electron neutrino \((u_e)\), and
- a muon antineutrino \((\overline{u}_\mu)\).
- Electron lepton number \( (L_e) \) starts at 0 and ends at 1 (electron) + 1 (electron neutrino) = 2.
- Muon lepton number \( (L_\mu) \) starts at 1 (muon) and ends at 0 - 1 (muon antineutrino) = 0.
- Tau lepton number \( (L_\tau) \) remains unchanged at 0 throughout the process.
Tau Decay
In the decay \(\tau^-\rightarrow e^- + \overline{u}_e + \overline{u}_\tau\), the tau transforms into:
- an electron \((e^-)\),
- an electron antineutrino \((\overline{u}_e)\), and
- a tau antineutrino \((\overline{u}_\tau)\).
- Electron lepton number \( (L_e) \) begins at 0 and changes to 1 (electron) - 1 (electron antineutrino) = 0.
- Muon lepton number \( (L_\mu) \) starts and remains at 0 both before and after decay.
- Tau lepton number \( (L_\tau) \) begins at 1 (tau) and results in 0 - 1 (tau antineutrino) = 0.
Leptons in Particle Physics
There are three types of lepton numbers in particle physics:
- Electron lepton number \((L_e)\)
- Muon lepton number \((L_\mu)\)
- Tau lepton number \((L_\tau)\)
Conservation of lepton number ensures that for each type of lepton participating in a reaction:
- The number of these leptons minus the number of their corresponding antineutrinos remains constant.
- This conservation maintains the balance and predictability in particle interactions.
- It plays a crucial role in understanding processes such as particle decay and interactions.