33.4 Particles, Patterns, and Conservation Laws

When a π^- decays, the products may include:

1. A positron.
2. A muon.
3. A proton.
4. All of the above.

The $\pi^{0}$ is its own antiparticle and decays in the following manner: $\pi^{0} \rightarrow \gamma + \gamma$. What is the energy of each $\gamma$ ray if the $\pi^{0}$ is at rest when it decays?

The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is $\text{10}^{\text{14}} \text{GeV}/ c^{2}$.

(a) How many proton masses is this?

(b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity $\gamma$ would have to be.)

The decay mode of the positive tau is $\tau^{+ } \rightarrow \mu^{+ } + \nu_{\mu} + \left(\overset{-}{\nu}\right)_{\tau}$.

(a) What energy is released?

(b) Verify that charge and lepton family numbers are conserved.

(c) The $\tau^{+ }$ is the antiparticle of the $\tau^{- }$.Verify that all the decay products of the $\tau^{+ }$ are the antiparticles of those in the decay of the $\tau^{- }$ given in the text.

(a) What is the uncertainty in the energy released in the decay of a $\pi^{0}$ due to its short lifetime?

(b) What fraction of the decay energy is this, noting that the decay mode is $\pi^{0} \rightarrow \gamma + \gamma$ (so that all the $\pi^{0}$ mass is destroyed)?