Questions after Lecture 1

Particles, Fields, and Interactions

Control Questions

  1. In natural units, why do energy, mass, inverse length, and inverse time have the same dimension?
  2. How does the uncertainty relation limit a simultaneous coordinate and momentum description of a GeV particle?
  3. What distinguishes fermions, gauge bosons, and the Higgs boson in the Standard Model?
  4. In what sense is a particle a quantum of a field mode rather than a small classical object?
  5. What information does a Feynman diagram encode, and what should not be read from it literally?
  6. What does a cross-section measure, and why is it more useful than a classical geometric size?
  7. Why does the Rutherford cross-section develop an apparent divergence at small angles?
  8. Why is the assumption of exactly zero emitted photons unphysical for scattering of charged particles?

Additional Questions

  1. Why are free quarks absent from the list of directly observable particles?
  2. What changes at a weak charged-current vertex, and what remains unchanged at a weak neutral-current vertex?
  3. How does the wave-packet picture soften, but not completely remove, the small-angle problem?
  4. Why must unresolved soft photons be included in the observable cross-section?
  5. What cancels between real and virtual soft-photon corrections in the inclusive result?

Short Written Check

Choose one process and explain what the diagram tells you:

\[ e^-e^-\to e^-e^-, \qquad \nu_\mu\mu^-\to\nu_\mu\mu^-, \qquad \nu_\mu e^-\to\nu_e\mu^-, \qquad qq\to qq. \]

In your answer, name the exchanged boson, the relevant charge or current, and whether particle type or flavor changes at the vertex.

Short Calculation

\[ d\sigma_{\mathrm{obs}} = d\sigma(p\to p') + \sum_{E_\gamma<\Delta E} d\sigma(p\to p'+n\gamma). \]

Explain in words why the detector resolution (E) enters this formula and why the observable result is finite.