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The strong interaction is the color interaction described by quantum chromodynamics. Quarks carry color charge, gluons mediate the interaction and also carry color themselves, and physical low-energy states organize into color-singlet hadrons.

At short distances, asymptotic freedom makes a perturbative treatment useful. At hadronic distances, confinement and strong collective dynamics require other methods. The binding of quarks into a proton and the residual interaction between nucleons in an atomic nucleus are related effects at different descriptive levels. The latter can be modeled using hadrons rather than pretending that a free gluon simply travels between two structureless nucleons. Scattering resolves the short-distance constituents, while hadron and nuclear spectra constrain their low-energy collective behavior.

An ideal Bjorken scaling model has $F_2(x,Q^2)=f(x)$: varying $Q^2$ at fixed Bjorken x leaves this dimensionless deep-inelastic structure function unchanged. The comparison requires extracting a deep-inelastic structure function, rather than plotting raw event counts. Quantum chromodynamics predicts departures from exact Bjorken scaling; finite hadron masses also limit the idealization.

For an original shape comparison, choose $f(x)=x(1-x{)}^3$ and define $S(Q^2)=F_2(0.3,Q^2)/F_2(0.3,Q_0^2)$ with $Q_0^2=2{\mathrm{GeV}}^2$. The ideal model has $S=1$. To display a contrasting size-dependent suppression, define an illustrative elastic-form-factor shape $G(Q^2)=(1+Q^2/{\Lambda }^2{)}^{-2}$ with the freely chosen ${\Lambda }^2=1{\mathrm{GeV}}^2$. Its normalized squared magnitude isThus $A(5{\mathrm{GeV}}^2)=1/16$, whereas $S(5{\mathrm{GeV}}^2)=1$. The elastic-form-factor shape is a comparison of suppression mechanisms, not an elastic differential scattering cross-section assigned to $x=0.3$: actual elastic scattering from a proton has $W=M$ and $x=1$. Neither curve is measured data or a fit to the SLAC-MIT experiment.

The experimental interpretation required more than a flat curve. The angular dependence and small longitudinal response supported spin one-half partons, expressed at leading order by the Callan-Gross relation $F_2=2x{F}_1$. Identification with fractionally charged quarks also drew on later electron, muon and neutrino comparisons. A scaling plot alone does not determine the individual electric charges of constituents.^[ref]

The leading parton model formula already shows the ambiguity: $F_2=x{\sum }_f{Q}_f^2(q_f+{\bar{q}}_f)$ combines squared electric charges with unknown parton distribution functions. One measured function cannot independently fix all these quantities. Confinement also explains why an inclusive final hadron state need not contain an isolated outgoing quark.

Three light quarks have a six-dimensional single-quark spin-flavour space ${\mathbb{C}}^3\otimes {\mathbb{C}}^2$. A symmetric spatial ground state and the antisymmetric three-quark colour singlet require the symmetric cube of that space. Its dimension is $\left(\genfrac{}{}{0ex}{}{8}{3}\right)=56$, and restriction to flavour $SU(3)$ and spin $SU(2)$ gives a baryon decuplet of spin $3/2$ and a baryon octet of spin $1/2$. The two mixed-permutation multiplicity spaces pair once in the symmetric sector, explaining why the two flavour-octet copies in the unconstrained tensor cube do not represent two distinct ground-state octets.

The invariant colour state of three fundamental quarks is the normalized completely antisymmetric tensor ${ϵ}_{abc}/\sqrt{6}$. With this colour factor, the Pauli exclusion principle requires the remaining spatial-spin-flavour wavefunction to be symmetric. Colour and approximate flavour symmetry are distinct SU(3) actions.

Toshihide Maskawa and Makoto Kobayashi investigated how CP violation could fit within a renormalizable theory of the weak interaction. A complex quark mixing matrix is not enough by itself: phases removable by redefining quark fields have no physical effect. With three fermion generations, a physical complex phase can remain in the Cabibbo-Kobayashi-Maskawa matrix. Their 1973 analysis connected an observed symmetry failure with the possible number and organization of quarks.^[ref]

A physicist working on quark mixing.^[ref]

With three massless lepton families, two accessible up-type quarks, three colors, and no quantum chromodynamics radiative correction, a W boson has total decay width $9{\Gamma }_{\ell }$. With an identity CKM matrix, each leptonic channel has branching fraction $1/9$ and each of the two allowed quark-flavour channels has $1/3$. With mixing, each accessible quark channel is weighted by $|V_{ij}{|}^2$, while row unitarity preserves the total at this order if all down-type channels are accessible.

A three-dimensional representation. The isospin-one irreducible representation of SU(2) is a triplet with third components $-1,0,+1$; the fundamental SU(3) quark representation is also a triplet but belongs to a different group.

A theoretical nuclear physicist who studies nuclear forces using effective field theory. His joint review with Evgeny Epelbaum and Hans-Werner Hammer explains how the symmetries of quantum chromodynamics constrain low-energy interactions between nucleons. The approach organizes increasingly accurate calculations without treating a nucleus directly as a collection of interacting quarks.^[ref]

The up quark $u$ is the first-generation up-type quark, with electric charge $+2e/3$, spin $1/2$ and baryon number $1/3$. It is a light quark, and the up quark and down quark together account for the net valence flavor content of ordinary nuclei.^[ref]

The minimal proton content $uud$ has total charge $2(2e/3)-e/3=e$ and baryon number one. The proton's mass is not simply the sum of three free-quark masses: its interacting quark and gluon fields carry most of its energy. The quark model organizes the flavor content, while quantum chromodynamics describes the dynamics needed to compute hadron properties.

The $SU(2)$ flavor symmetry rotating down and strange quarks, with the up quark a singlet. Since down and strange quarks have equal electric charge, the charge operator commutes with all U-spin generators, and every irreducible U-spin multiplet has a common charge. Unequal down- and strange-quark masses break this symmetry.

A constituent used to specify the net quark flavor content of a hadron. The quark model uses three valence quarks for an ordinary baryon and a quark-antiquark pair for an ordinary meson; this does not exclude additional sea pairs and gluons in the full state.

A meson with total angular momentum one and negative parity. In the ordinary quark model, a quark-antiquark pair with orbital angular momentum zero and total spin one has these quantum numbers; its neutral self-conjugate states have charge conjugation $C=-1$. The light-flavour tensor product gives an octet and a singlet, forming a vector nonet, just as spin-zero negative-parity pairs form a pseudoscalar meson nonet. Nonzero orbital excitations can also produce vector states.

In a massless Fermi interaction approximation, a charged-current decay channel contributes a common mass-to-the-fifth width multiplied by its mixing and final-state multiplicity factors. A final quark-antiquark pair has three color choices, while a lepton pair has one. An initial quark does not acquire a factor of three in its lifetime merely from its possible initial colors.

A hyperon decay that changes quark flavour while emitting a photon. An example is ${\Xi }^0\to \Lambda \gamma$, which changes strangeness and cannot be purely electromagnetic. Its amplitude can contain short-distance loops and long-distance hadronic contributions. photon attachments to a weak quark-exchange graph must be completed consistently with electromagnetic gauge invariance. A quark topology identifies allowed flavour flow but does not by itself calculate a reliable hadronic rate.

The baryon octet contains the isospin doublet ${\Xi }^0,{\Xi }^{-}$. Each has strangeness $-2$, with valence quark content $uss$, $dss$.