Quarkbinders

Quarkbinders come in threes, and never alone. Here is why three.

In 1964 a puzzle sat in the particle tables. The Δ⁺⁺ baryon is made of three up quarks, all with their spins pointing the same way, in the same state of motion. Quarks are fermions, and the Pauli exclusion principle forbids identical fermions from sharing a state. Oscar Greenberg, and then Moo-Young Han and Yoichiro Nambu, proposed a way out: quarks carry a new three-valued property, later called colour. Three quarks can be identical in every other way and still differ in colour.

The first formula on this page is how a baryon wears its colour. The Levi-Civita symbol combines one quark of each colour in a fully antisymmetric mix, the only combination that is colourless overall. Experiments agree on three: the rate at which electron–positron collisions make hadrons comes out three times what colourless quarks would give.

The second formula is the running of the strong coupling. In 1973 David Gross and Frank Wilczek, and independently David Politzer, found that the strength of the strong force falls at short distances, or high momentum transfer Q. This is asymptotic freedom: inside a proton struck hard, quarks act almost free. The 33 in the formula comes from the gluons, which carry colour themselves; the 2 times the number of quark flavours fights it, and as long as there are fewer than seventeen flavours, the gluons win. The 2004 Nobel Prize recognised it.

The flip side is confinement. Pull quarks apart and the force does not fade. The energy in the gluon field grows until it is cheaper to create a new quark–antiquark pair, and you get more hadrons, never a free quark.

Quarkbinders do not split. Pull hard and the pull turns into new quarks, never a free one.