Exercises 9.8 Problems
1.
Baryons and leptons are both fermions. In what ways are they different?
2.
Mesons and baryons are each sensitive to the strong force. In what way are they different?
3.
Test the conservation laws for energy, charge, baryon number, lepton number, and strangeness for each of the following proposed reactions. Which ones are violated?
\(\displaystyle \mu^- \to \pi^- + \nu_\mu\)
\(\displaystyle \pi^- + p \to \Lambda + \overline\nu_e\)
4.
Classify each of the following particles as bosons, fermions, hadrons, leptons, baryons, mesons and/or messengers. Use as many of these terms as apply.
(a) photon (b) \(\Lambda\) (c) \(\pi^+\) (d) \(\nu_e\)
5.
A \(\rho^0\) particle initially at rest is observed to decay by \(\rho^0 \to \pi^+ + \pi^-\text{.}\) The pions have a mass of \(140\Xunits{MeV/ c^2 }\text{.}\) The magnitude of the momentum of each of the oppositely directed pions is measured to be \(361.5\Xunits{MeV/ c }\text{.}\) Conserve energy and momentum to determine the rest energy of the \(\rho^0\text{.}\) Compare to the value given in Table 9.1.
6.
Use the appropriate conservation laws in each of the strong reactions below to determine the additive properties of the unknown particle \(x\text{.}\) Then identify the \(x\) particle using Tables 9.1 through Table 9.3.
\(\displaystyle p + p \to p + \Lambda + x\)
\(\displaystyle e^- + p \to n + \pi^0 + x\)
\(\displaystyle K^- + p \to \Xi^- + \pi^0 + x\)
7.
Check strangeness conservation to determine which of the following reactions may proceed by the strong interaction.
\(\displaystyle K^- + p \to \Lambda + \pi^0\)
\(\displaystyle \Xi^- \to \Lambda + \pi^-\)
\(\displaystyle K^+ \to \pi^+ + \pi^0\)
\(\displaystyle \Delta^{++} \to p + \pi^+\)
8.
Use the data in Tables 9.1 through Table 9.3 to check that (9.5) and (9.6) do not violate the laws of conservation of energy, charge, lepton number, and baryon number.
9.
Can an electron decay by disintegrating into two neutrinos? Why, or why not?
10.
A neutron is massive enough to decay by the emission of a proton and two neutrinos. Why does it not do so?
11.
Consider the reaction \(\pi^- + p \to \Xi^0 + K^0 + K^0\text{.}\) Assuming this reaction occurs via the strong interaction, determine the strangeness of the \(\Xi^0\text{.}\) Compare to the value in Table 9.3.
12.
What are the quark constituents for each of the following particles?
(a) \(\Lambda\) (b) \(\Xi^-\) (c) \(\pi^+\)
13.
Use the quark model to explain why there is no baryon with \(S = -2\text{,}\) \(Q = +1\text{.}\)
14.
Determine the additive quantum numbers (\(B\text{,}\) \(Q\text{,}\) and \(S\)), and thus the identities, of the particles formed from the following combinations of quarks. Then use the tables in Chapter 9 to identify each particle. Note that a quark ingredient list does not always identify a particle uniquely. Sometimes several particles contain the same set of quarks.
(a) \(ddu\) (b) \(uus\) (c) \(d\overline s\) (d) \(\overline u\overline u\overline d\) (e) \(ssd\) (f) \(u\overline d\)
15.
Consider the ten baryons with spin 3/2 listed in Table 9.3. Make a strangeness vs. charge plot for these baryons, similar to Figure 9.4. Compare your plot with that in Figure 9.4.
16.
Consider the reaction \(\Lambda + \pi^- \to \mbox{baryon} + \mbox{meson}\text{.}\) What possible baryon-meson pairs can be produced? Consider only the simplest cases, in which no quarks are created or destroyed, but merely rearrange themselves.