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Chapter 39: Problem 23

Write the equation for the decay of a positive pion to a muon and a neutrino, being sure to label the type of neutrino. (Hint: The positive muon is an antiparticle.)

Short Answer

Expert verified
The equation for the decay of a positive pion into a muon and a neutrino, where the neutrino type is labelled, is: \(\pi^+ \rightarrow \mu^+ + \bar{\nu}_\mu\).

Step by step solution

01

Identify Decay Particles

Given that a positive pion (\(\pi^+\)) decays into a muon and a neutrino. The muon, based on the hint given, is a positive muon which is an antiparticle.
02

Apply Conservation Laws

According to the conservation laws, since we have a positive pi-meson decaying, we expect a positive muon and the corresponding neutrino which is a muon neutrino (\(\nu_\mu\)). But due to the conservation of lepton number, the positive pion, being a matter particle, has to decay into other matter particles. The positive muon, being an anti-particle, doesn't suffice. Hence, it decays into an anti-neutrino.
03

Formulate Decay Equation

By putting all these findings together, the decay equation can be written as: \(\pi^+ \rightarrow \mu^+ + \bar{\nu}_\mu\). In this equation, \(\pi^+\) stands for the initial particle, the positive pion. \(\mu^+\) is the positive muon (an antiparticle), and \(\bar{\nu}_\mu\) is the muon antineutrino, conserving lepton numbers.

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