Exercises 10.8 Problems
1.
Think about what you are doing (or not doing) right at this minute. (a) Identify (and write down) as many forces as you can that are acting on you right now and/or are affecting your environment. (b) Describe what your life would be like if there were no forces or interactions at all.
2.
(a) What is the minimum energy fluctuation \(\Delta E\) required to create a virtual electron-positron pair? (b) Roughly how long could such a virtual pair survive?
3.
The \(Z\)-boson (one of the mediators of the weak force) has a mass of \(91.2\Xunits{GeV/ c^2 }\text{.}\)
What is the minimum energy fluctuation required to create a virtual \(Z\)-boson?
Roughly how long could such a virtual \(Z\) survive?
What is the farthest that this particle could travel during this lifetime?
How does this result compare with the known range of the weak force (\(\sim 10^{-3}\Xunits{fm}\))?
4.
Several years ago, a group of physicists claimed to have discovered a fifth force with a range of approximately \(100\Xunits{m}\text{.}\) If this force had turned out to be valid (few people believe this to be the case), what would have been the approximate (order of magnitude) mass of its messenger particle? Express your answer in eV/\(c^2\text{.}\)
5.
Draw a Feynman diagram corresponding to the annihilation of an electron-positron pair. An electron moves to the right and hits a positron moving to the left. They annihilate each other, resulting in the formation of two photons, one moving left and the other moving right. Hint: You will need two vertices.
6.
A Feynman diagram can be played with like a Gumby doll. You can bend all the branches up and down, as long as you follow one simple rule: every time you bend an upward-going branch downward (or a downward-going branch upward), you replace the particle with its antiparticle. For example, in Figure 10.3, if the \(\nu_\mu\) branch is bent downward, you can get the interaction \(\overline\nu_\mu + \mu^- \to \overline\nu_e + e^-\text{.}\)
Verify that this new reaction satisfies all the appropriate conservation laws.
Use the Gumby approach to come up with several other possibilities for interactions, starting with Figure 10.3.
7.
Show with some examples that the colorless rule yields particles with integer charge.
8.
An antiblue antiquark emits a green-antiblue gluon. What color is the antiquark after emission?
9.
Explain in your own words how camouflage leads to confinement of quarks inside hadrons.
10.
Draw a diagram like Figure 10.8 for each of the reactions in Table 10.9.
11.
Draw a diagram like Figure 10.10 for each of the reactions in Table 10.11.
12.
For each vertex diagram below, identify the missing particles, colors, or flavors denoted by a question mark. In other words, wherever you see a ‘?’, replace it with a type of particle, a color, or a type of quark.
