🗒️ Notes: on the course

• Use natural units $\hbar =c=1$ which means lengths and time have the same units
  • Energy, momentum, mass $[\rm E]^{1}$
  • Length, time $[\rm E]^{-1}$
  • Cross section $\rm [ E]^{-2}$
• Her notes are not complete however I will try to include her notes + video + lectures and maybe textbooks if i get the time

Recap of decays

• $\alpha$ -decay: $^4_2\rm He$ this is well approximated by the tunnelling model we previously saw (strong force)

• $\beta$-decay: is an interaction of the weak force which leads to changing quark flavor

  🗒️ Note: the weak force is the only force which flavor changes

• $\gamma$ -decay: excited nucleus will de-excite by emitting a high energy photon (electromagnetic)

Quarks and leptons

⚙️ General properties: of leptons, quarks, force carriers and Higgs boson

• Leptons and quarks: spin-$\frac 12$ fermions

• Force carriers: spin-$1$ bosons which mediate the fundamental forces:

  • Electromagnetism (photon)
  • Weak force ($W^+,W^-$ and $Z$ bosons)
  • Strong force (gluon)

  🗒️ Note: gravity is excluded because it is not understood yet

• Higgs boson: spin-$0$ boson associated to the Higgs field giving other particles mass

🗒️ Note: the fermions (leptons and quarks) are classed into generations (or families)

Quarks

There are 3 generations, “up-down”, “charm-strange” and “top-bottom” quarks represented by

$$ \begin{pmatrix} u \\ d \end{pmatrix} ; \begin{pmatrix} c \\ s \end{pmatrix} ; \begin{pmatrix} t \\ b \end{pmatrix} $$

• First generation makes up the nuclei(protons and neutrons)
  • Up-type quarks have electric charge of $+ \frac 23e$ (electron charge)
  • Down-type quarks have electric charge $-\frac 13e$
• Second and third generation are heavier siblings (unstable)

⚡ All 3 quarks feel all three fundamental forces

Leptons

There are 3 families with familiar names represented by

$$ \begin{pmatrix} e \\ \nu_e \end{pmatrix} ; \begin{pmatrix} \mu \\ \nu_\mu \end{pmatrix} ; \begin{pmatrix} \tau \\ \nu_\tau \end{pmatrix} $$

• Charged leptons ($e,\mu,\tau)$:
  • Only the first generation $e$ is stable and found in everyday matter
  • $\mu,\tau$ are the heavier siblings
  • ⚡ Experience the electromagnetic and weak force
• Neutrinos ($\nu_e,\nu_\mu,\nu_\tau$):
  • Electrically neutral and almost massless
  • ⚡ Experience only the weak force

Force carriers