Quarks, Leptons and the Standard Model

$\textbf{Quarks}$ come in six flavours: up, down, strange, charm, top and bottom. Up, charm and top have charge $+\tfrac23 e$; down, strange and bottom have $-\tfrac13 e$. Quarks are never observed alone.

$\textbf{Leptons}$ are the electron, muon and tau, each with charge $-e$, plus a neutral neutrino for each. Leptons are not made of quarks and do not feel the strong nuclear force.

Every particle has an $\textbf{antiparticle}$ with the same mass and the opposite charge, baryon number and lepton number. The antiparticle of the electron is the positron; an anti-up quark has charge $-\tfrac23 e$.

Particles made of quarks are $\textbf{hadrons}$, and they feel the strong force. There are two families.

$\textbf{Baryons}$ contain three quarks and have baryon number $+1$. The proton is $uud$, charge $\tfrac23 + \tfrac23 - \tfrac13 = +1$; the neutron is $udd$, charge $\tfrac23 - \tfrac13 - \tfrac13 = 0$. Antibaryons are three antiquarks with baryon number $-1$.

$\textbf{Mesons}$ contain one quark and one antiquark, so they have baryon number $0$. The positive pion is $u\bar{d}$, charge $\tfrac23 + \tfrac13 = +1$.

Each quark carries baryon number $+\tfrac13$ and each antiquark $-\tfrac13$, which is why three quarks give $+1$ and a quark–antiquark pair gives $0$.

In every particle interaction, these quantities are conserved: $\textbf{charge}$, $\textbf{baryon number}$, $\textbf{lepton number}$, and also energy and momentum.

Leptons have lepton number $+1$ and antileptons $-1$. Hadrons have lepton number $0$.

To test whether an interaction is possible, tabulate each quantity for every particle on both sides. If any total differs, the interaction is forbidden.

In $\beta^{-}$ decay, a neutron becomes a proton: $n \rightarrow p + e^{-} + \bar{\nu}_{e}$. At quark level, a $\textbf{down quark changes to an up quark}$, which only the weak interaction can do.

In $\beta^{+}$ decay, a proton in a nucleus becomes a neutron: $p \rightarrow n + e^{+} + \nu_{e}$, an up quark changing to a down.

The standard model includes three forces relevant here, each carried by exchange particles: the $\textbf{electromagnetic}$ force (photon), the $\textbf{strong}$ force binding quarks (gluons), and the $\textbf{weak}$ force responsible for changing quark flavour (W and Z bosons).

The existence of the neutrino was originally inferred from beta decay: electrons emerged with a range of energies instead of one fixed value, so an unseen particle had to be carrying the rest.