Exercises 11.6 Problems
1.
Construct a reaction diagram for each of the following.
\(\displaystyle \Delta^{++} \to p + \pi^+\)
\(\displaystyle p + e^- \to n + \nu_e\)
2.
Construct a reaction diagram for each of the following:
\(\displaystyle \pi^- + \Lambda \to K^- + n\)
\(\displaystyle K^- \to \mu^- + \overline\nu_\mu\)
3.
Suppose the proton's mean lifetime is \(10^{31}\) years. Now consider a pool of water \(10\Xunits{m} \times 10\Xunits{m} \times 3\Xunits{m}\text{.}\) Estimate the number of protons in the pool and then the number that you would expect to decay in one year. For this calculation, consider only the protons not bound in a complex nucleus; that is, only the protons in hydrogen atoms.
4.
\(\Sigma^-(1197)\) decays into hadrons only. List all the possible decay schemes that conserve baryon number, energy, and charge, using the tables given in Chapter 9 as a resource.
5.
For each of the following reactions, tell which interaction is involved (strong, weak or electromagnetic).
a green up quark emits a gluon
\(\displaystyle \gamma \to e^+ + e^-\)
\(\displaystyle \nu_e + n \to e^- + p\)
6.
Which lives longer, \(\Sigma^0(1192)\) or \(\Lambda(1116)\text{?}\) Why?
7.
An \(\Omega^-\) particle is constructed from three \(s\)-quarks and is the lightest \(S = -3\) baryon. Refer to Table 11.5 to answer the following:
Why must strangeness (\(S\)) change when \(\Omega^-\) decays?
By what interaction does \(\Omega^-\) decay?
Why does \(\Omega^-\) live relatively long?
8.
The particles \(\Xi^-(1322)\) and \(\Xi^{*-}(1535)\) both carry strangeness \(S = -2\text{.}\) Which decays faster? Why? When the faster one decays, what are the likely decay products?
9.
Pions are the lightest hadrons. What can they decay to? Why do \(\pi^+\) and \(\pi^-\) live so much longer than \(\pi^0\text{?}\)
10.
In Section 11.4 we discussed the possibility of proton decay. Figure 11.8 shows a hypothetical process in which proton decay is mediated by a proposed \(X^{4/3}\) boson, which carries a \(+\textstyle{\frac{4}{3}}\) charge. (The \(X^{4/3}\) boson has not been observed, and is not one of the particles included in the tables in this supplement.) Note that the general rule for interactions involving an \(X\)-boson would be:
Another possible proton decay scheme, using a \(X^{1/3}\) boson (with \(+\textstyle{\frac{1}{3}}\) charge), would be \(p \to \pi^+ + \overline\nu_e\text{.}\) Construct a reaction diagram like Figure 11.8 showing this hypothesized decay process. Be sure to conserve charges at each vertex!
11.
In Figure 11.1, label the colors of any particle in the diagram that has a color. Be sure to satisfy the colorless rule for any hadron, and don't label colors on any particle that does not carry color. (Note: there are several right answers to this question.)
12.
For each of the following reaction diagrams, identify the messenger particle and state the type of interaction involved (strong, weak, electromagnetic, or gravitational). Denote the colors and/or charges for each messenger, where appropriate.
