Here is a challenge no experiment has ever won: take a proton, reach inside, and pull out a single quark to hold up to the light. It cannot be done. Not because our tools are too clumsy, and not because quarks are somehow fictional — we have mapped their charges, spins and momenta in exquisite detail by firing electrons into protons. It is that the force binding quarks together, the strong interaction, behaves like nothing in everyday life. Try to separate two quarks and the force between them does not fade with distance the way gravity or electricity does; it stays stubbornly strong, so that the energy you pour in eventually conjures a brand-new quark–antiquark pair out of the vacuum rather than let a lone quark go free. You always end up with more particles, never a bare quark.

This page is about the single idea that ties that strangeness together: colour is the charge of the strong force, and the two most famous peculiarities of the strong force — confinement (quarks are permanently locked inside colour-neutral bundles) and asymptotic freedom (deep inside those bundles the quarks rattle around almost free) — both flow from one structural fact: the carriers of colour, the gluons, carry colour themselves, so they pull on each other. The photon never does that. That one difference remakes the entire character of the force. The theory built on it is Quantum Chromodynamics, QCD — literally the "dynamics of colour", and it rests on the group whose Feynman diagrams we already know how to read.

Colour: a new kind of charge

Electric charge comes in one type, with two signs, + and -. Colour charge is richer: it comes in three types, labelled — purely by convention — red, green and blue (r,\ g,\ b). Each quark carries one unit of colour; each antiquark carries one unit of anti-colour (\bar r,\ \bar g,\ \bar b, "anti-red" and so on). The name is a physicist's joke that turned out to be a good mnemonic: just as red, green and blue light add up to colourless white, the strong force only permits combinations that are "white" — colour-neutral.

The mathematics underneath is the symmetry group SU(3): the special unitary group of 3\times 3 matrices, rotating the three colours into one another. Where electromagnetism is built on the single-parameter group U(1) (one charge, one photon), the strong force is built on SU(3) — and that jump from one dimension to three is the source of everything that follows. It is why there are several force-carriers instead of one, and why those carriers are themselves charged.

Gluons carry colour — and that changes everything

In electromagnetism the force-carrier is the photon, and the photon is electrically neutral: it couples to charge but carries none itself, so two photons sail straight through each other without interacting. Gluons are different. A gluon changes the colour of the quark that emits it — say a red quark turns blue — so to conserve colour the gluon must carry away the difference: it is colour–anticolour, here a r\bar b gluon. Gluons are charged under the very force they mediate.

Counting the colour–anticolour combinations gives 3 \times 3 = 9 possibilities, but one of them is the perfectly symmetric colourless combination (r\bar r + g\bar g + b\bar b)/\sqrt 3, which would behave like a second, strongly-interacting "photon" and is not realised. That leaves 9 - 1 = 8 physical gluons — exactly the 3^2-1 = 8 generators of SU(3).

Because gluons carry colour, gluons pull on gluons: the theory contains vertices where three or four gluon lines meet directly, with no quark in sight. A photon has no analogous self-coupling. This gluon self-interaction is the single seed from which both great surprises of QCD grow. Keep it in mind as the one fact that explains the rest.

Hadrons are colour singlets

Since only colourless states go free, quarks must huddle into combinations whose colours cancel. Nature uses two clean recipes, and together they are the hadrons:

• Baryons — three quarks, qqq, one of each colour: r + g + b \to white. The proton (uud) and neutron (udd) are the everyday examples.
• Mesons — a quark and an antiquark, q\bar q, carrying a colour and its exact anticolour: r + \bar r \to white. Pions and kaons are mesons.

In both cases the total colour is zero — a colour singlet, invariant under SU(3) rotations. A lone quark carries net colour and so is forbidden as a free particle; a pair of same-colour quarks (rr) is not neutral either. The rule "hadrons are colourless" is not an add-on — it is the definition of what can exist on its own. (Exotic colourless states such as tetraquarks q q \bar q \bar q and pentaquarks are allowed too, and a few have now been seen; they are still colour singlets.)

Confinement: the potential that never lets go

Why can you never isolate a quark? Look at how the energy stored between two quarks grows as you drag them apart. At short range the exchange of gluons gives an ordinary attractive -1/r Coulomb-like piece, just as in electromagnetism. But the gluon self-interaction squeezes the colour field between the quarks into a narrow flux tube, a "string" of roughly constant cross-section. Stretch a string and its energy grows in proportion to its length. So at large separation the potential rises linearly:

the Cornell potential. The constant k is the string tension, the energy stored per unit length of tube; experimentally k \approx 0.9\ \text{GeV/fm} — about a tonne of pulling force, packed into the size of a proton. The crucial term is the linear one: unlike -a/r, which flattens out and lets a charge escape to infinity at finite cost, k\,r keeps climbing without bound. The energy needed to separate two quarks completely is infinite. That is confinement, written as a formula.

Below, plot the Cornell potential and drag the sliders. Notice how the faint Coulomb-only curve -a/r levels off, while the full potential is dragged relentlessly upward by the linear k\,r term. That upward march is the reason no quark ever gets out.

Worked examples

Example 1 — building a colour singlet. Which of these can exist as a free particle: (a) rg, (b) r\bar r, (c) rgb? A free particle must be a colour singlet — net colourless. Combination (a) carries leftover r and g colour, so it is not allowed. Combination (b), a colour and its exact anticolour, cancels to white — that is a meson. Combination (c), one quark of each colour, also cancels (r+g+b \to white) — that is a baryon. Only (b) and (c) are physical.

Example 2 — energy in the string. Ignore the small Coulomb term and use V \approx k\,r with k = 0.9\ \text{GeV/fm}. Pull a quark and antiquark to a separation of r = 1.5\ \text{fm}. How much energy is stored in the flux tube?

That is more than the rest energy of a whole proton, invested in a string barely wider than an atomic nucleus. Push a little further and you reach the next example.

Example 3 — the string snaps into a new pair. A pion (the lightest meson) has a rest energy of about m_\pi c^2 \approx 0.14\ \text{GeV}, so making a fresh q\bar q pair costs only a couple of hundred MeV. Once the stored string energy k\,r exceeds that threshold, it becomes energetically cheaper for the vacuum to break the string — snap it in the middle and cap each new end with a freshly-made antiquark or quark — than to keep stretching. Estimate the separation at which k\,r reaches, say, 0.28\ \text{GeV} (enough for a light pair):

Barely a third of a femtometre — a fraction of a proton's width — and the string is already ready to break. You set out to separate one quark from another and you finish holding two mesons. Try again and you make two more. This is why the harder you pull, the more particles you get, and never a naked quark. It is exactly what happens in a particle collider: a struck quark flies off, the string behind it snaps again and again, and the quark shows up not as itself but as a jet of hadrons streaming in its direction.

Asymptotic freedom: nearly free inside

Now the flip side, and the genuine shock. We have just seen that the strong force is ferocious at large separation. So common sense says it should be even more ferocious close up. It is the opposite. At short distance — equivalently, at high energy or high momentum transfer Q — the strong coupling \alpha_s gets weaker, and deep inside a proton the quarks behave almost as if they were free. This is asymptotic freedom, and it is precisely what the deep-inelastic scattering experiments saw: electrons fired hard into a proton bounced off quarks that acted nearly independent, not glued rigidly together.

The coupling is not a constant; it runs with the energy scale. To one-loop order,

where n_f is the number of quark flavours and \Lambda \approx 0.2\ \text{GeV} is the scale where the coupling blows up. The sign of b_0 decides everything. The 33 = 11\times 3 comes from the gluon self-interaction (it depends on the 3 colours); the -2n_f comes from quark loops and works the other way. Because the gluon term wins (33 > 2n_f for the real world's six flavours), b_0 > 0, and \alpha_s falls as Q rises. In QED, with no self-coupling of the photon, the sign is reversed and the coupling grows with energy. The self-interacting gluon is once again the culprit — this time producing the surprise that quarks are asymptotically free.

Establishing this — proving that a non-Abelian gauge theory like QCD is asymptotically free — earned David Gross, Frank Wilczek and David Politzer the 2004 Nobel Prize in Physics. It rescued the whole idea of quarks: they could be real, permanently confined constituents and yet look point-like and free in violent collisions, with no contradiction.