Muon Decay Examine the process of muon decay μ^- → e^- + νe + νμ from the standpoint of conservation laws.

Question

Muon Decay

Examine the process of muon decay [latex]\mu^{-} ightarrow e^{-}+\bar{ u}_{e}+ u_{\mu}[/latex] from the standpoint of conservation laws.

Accepted Answer

The particles here are all leptons. With the muon and electron and their corresponding neutrinos involved, we need to consider both electron lepton number [latex]L_{e}[/latex] and muon lepton number [latex]L_{\mu}[/latex] .The appropriate numbers are

[latex] ext { Muon and muon neutrino: } L_{\mu}=1[/latex].

[latex] ext { Electron: } L_{e}=1[/latex].

[latex] ext { Electron antineutrino: } L_{e}=-1[/latex].

Therefore, the muon lepton number is [latex]L_{\mu}=1[/latex] both before and after the reaction. The electron lepton number is zero before the reaction, and after the reaction the two [latex]L_{e}[/latex]numbers add to zero.
Therefore, both lepton numbers are conserved. Electric charge is also conserved; neutrinos are uncharged, so the charge before and after the reaction is the same: -e.

REFLECT It wasn't necessary to consider baryon number in this reaction, which only involved leptons. And there's no problem with energy conservation, because the electron is lighter than the muon and the neutrinos have nearly zero rest energy.

Question 26.5: Muon Decay Examine the process of muon decay μ^- → e^- + νe ...

Related Answered Questions

Λ Decay In Conceptual Example 26.4, you saw one possible decay of the lambda particle (a baryon): Λ → p^+ + π^-. Describe the quark transformation in this decay and in the one that follows it. ...

Verified Answer:

Speed of a High-Energy Electron What s the speed of the electrons in the 50-GeV linac at SLAC? Express the answer as a fraction of the speed of light. ORGANIZE AND PLAN This kinetic energy is much higher than the electron s rest energy (0.511 MeV), so relativity is essential here. Useful ...

Verified Answer:

Positron Decay and Electron Capture Discuss the quark transformation that occurs during positron decay and electron capture. ...

Verified Answer:

Stationary Targets versus Colliding Beams Compare the energies available from a 1.0-TeV proton accelerator when (a) two 1.0-TeV protons collide head-on and (b) a 1.0-TeV proton strikes another proton in a stationary target. ORGANIZE AND PLAN For colliding particles each with kinetic energy K, ...

Verified Answer:

Range of the Weak Force Use the masses of the weak-force mediators to estimate the range of the weak force. ORGANIZE AND PLAN Equation 26.2 relates particle mass m and interaction range R: m = h/2πRc ...

Verified Answer:

Antiproton Creation Two protons moving in opposite directions collide, causing the reaction p + p → p + p + p + p. What’s the minimum kinetic energy for each proton? ORGANIZE AND PLAN Figure 26.2 shows the situation before and after the collision, where we’ve defined the x-axis to be along ...

Verified Answer:

Photon Mass Use the fact that the electromagnetic force acts over an infinite distance to predict the photon’s mass. ...

Verified Answer:

Age of the Universe Use the current value of the Hubble constant, H0 = 72 km/s/Mpc, to estimate the age of the universe in years. Assume that the galaxies have always been moving apart with their current speeds. ...

Verified Answer: