They are structured into 3 duplets (generations of 2)
$$ \xrightarrow{\qquad \text{Increasing mass} \qquad } \\\begin{pmatrix} \nu_e \\ e^- \end{pmatrix} \quad \begin{pmatrix} \nu_\mu \\ \mu^- \end{pmatrix} \quad \begin{pmatrix} \nu_\tau \\ \tau^- \end{pmatrix} $$
⚙️ Properties:
- Spin-$\frac 12$ particles
- $e^-,\mu^-,\tau^-$ have electric charge $(-1e)$ and weak isospin $( -\frac 12)$
- $\nu_e,\nu_\mu,\nu_\tau$ have no electric charge and weak isospin $(\frac 12)$
They are again structured in 3 duplets
$$ \xrightarrow{\quad \text{Increasing mass} \quad } \\\begin{pmatrix} u \\ d \end{pmatrix} \quad \begin{pmatrix} c \\ s \end{pmatrix} \quad \begin{pmatrix} t\\ b \end{pmatrix} $$
⚙️ Properties:
- Spin-$\frac 12$ particles
- $u,c,t$ have electric charge $(+\frac 23 e)$, weak isospin $(\frac 12)$, colour charge $(r,g,b)$
- $d,s,b$ have electric charge $(-\frac 13 e)$, weak isospin $(-\frac 12)$, colour charge $(r,g,b)$
⚙️ Properties:
Same mass
Opposite charge
Same interactions
| Interaction | Mediators | Spin | Long distance behaviour | Relative strength against gravity | Range ($\rm m$) |
|---|---|---|---|---|---|
| 🪨 Strong | gluons | 1 | $\sim 1$ | $10^{38}$ | $10^{-15}$ |
| ⚡ EM | photons | 1 | $1/r^2$ | $10^{36}$ | $\infin$ |
| 💤 Weak | W and Z boson | 1 | $(1/r)e^{-m_{W,Z}r}$ | $10^{25}$ | $10^{-18}$ |
⚙️ Properties:
- Spin-$0$ particle, ie it is a scalar not a vector, in fact the only scalar in the standard model
- It is a consequence of the Higgs mechanism
$$ \mathcal L_{\rm SM} =\underbrace{-\frac 14 F^a_{\mu\nu} F^{a\mu\nu}+i\overline \psi D\hspace{-0.7em}/ \psi}\text{3 fundamental forces} +\underbrace{|D\mu H|^2 - V(H)+\psi_i \lambda_{ij} \psi_j H+\text{h.c.}}_\text{Higgs mechanism} $$