Inside the nucleus are protons and neutrons, and for decades they looked fundamental. Then accelerators produced hundreds of new short-lived particles, and in 1964 Murray Gell-Mann and George Zweig proposed that most of them, protons and neutrons included, are built from a few smaller pieces: quarks. Experiments at SLAC in 1968, firing electrons into protons, found hard, point-like bits inside, just as Rutherford had found the nucleus inside the atom.
Key idea
Matter is built from two families of fundamental particles, each with an antiparticle:
- Leptons (not made of anything smaller): the electron, muon and tau, each with its neutrino.
- Quarks: up $(+\frac{2}{3}e)$, down $(-\frac{1}{3}e)$, strange $(-\frac{1}{3}e)$, charm $(+\frac{2}{3}e)$, bottom $(-\frac{1}{3}e)$, top $(+\frac{2}{3}e)$.
Why it works
Quark charges are fractions, yet every particle ever observed has a whole-number charge. The rule that explains it is color: each quark carries one of three “color” charges of the strong force, and only color-neutral combinations can exist on their own: three quarks with one of each color, or a quark with an antiquark carrying its anticolor. Check the charges: $uud$ gives $\frac{2}{3} + \frac{2}{3} - \frac{1}{3} = +1$, and $udd$ gives $0$. Pulling a quark out of a hadron takes so much energy that new quark–antiquark pairs form first (confinement), so no lone quark has ever been seen. Each quark has baryon number $\frac{1}{3}$, which is why every baryon has $B = 1$ and every meson $B = 0$.
| Particle | Quarks | Charge | Kind |
|---|---|---|---|
| proton $p$ | $uud$ | $+1$ | baryon |
| neutron $n$ | $udd$ | $0$ | baryon |
| lambda $\Lambda^0$ | $uds$ | $0$ | baryon |
| omega $\Omega^-$ | $sss$ | $-1$ | baryon |
| pion $\pi^+$ | $u\bar{d}$ | $+1$ | meson |
| kaon $K^+$ | $u\bar{s}$ | $+1$ | meson |
Worked examples
Worked example: Charge from quarks
The $\Sigma^+$ is made of $uus$. What is its charge?
- $\frac{2}{3} + \frac{2}{3} + \left(-\frac{1}{3}\right) = +1$.
Answer: $+1e$, a baryon
Worked example: A meson's charge
What is the charge of the meson $s\bar{u}$ (the $K^-$)?
- An antiquark has the opposite charge of its quark: $\bar{u}$ has $-\frac{2}{3}$.
- $-\frac{1}{3} + \left(-\frac{2}{3}\right) = -1$.
Answer: $-1e$
Worked example: Antimatter's building blocks
The antiproton is made of antiquarks. Which ones, and what is its charge and baryon number?
- Replace each quark of the proton ($uud$) with its antiquark: $\bar{u}\bar{u}\bar{d}$.
- Charge: $-\frac{2}{3} - \frac{2}{3} + \frac{1}{3} = -1$. Baryon number: $3 \times (-\frac{1}{3}) = -1$.
Answer: $\bar{u}\bar{u}\bar{d}$, with charge $-1$ and $B = -1$
Common mistake
Thinking protons and neutrons are fundamental particles. Each is three quarks held together by the strong force, and its mass comes mostly from the energy of that binding, not from the quarks' own small masses. The electron, by contrast, really does seem fundamental: no experiment has found any size or structure in it. A quick check: if the proton were fundamental, the neutron (with no charge) and the proton (charge $+1$) would have no reason to be so similar in mass.