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Chapter 39: Problem 21

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 decay equation for a positive pion to a muon and a neutrino is \( \pi^+ \rightarrow \mu^+ + \nu_{\mu} \)

Step by step solution

01

Identify particles and antiparticles

The exercise mentions the decay of a positive pion into a muon and a neutrino. A positive pion (\( \pi^+ \)) is a type of meson. It decays to a positive muon (\( \mu^+ \)), which is an antiparticle.
02

Apply conservation laws

In particle physics, there's a rule of lepton number conservation. Leptons and antileptons have lepton numbers of +1 and -1, respectively. Therefore, if a positive pion decays to a positive muon (\( \mu^+ \), an antiparticle with a lepton number -1), it must also produce some particle with a lepton number of +1 to ensure balance.
03

Identify the neutrino

In this case, the neutrino produced must be a muon neutrino (\( \nu_{\mu} \)). The muon neutrino is the associated neutrino of the muon and has a lepton number of +1, ensuring conservation.
04

Write the decay equation

Finally, write the equation for the decay of the positive pion to a muon and a neutrino using the particle symbols. \( \pi^+ \rightarrow \mu^+ + \nu_{\mu} \)

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