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Lattice QCD is a lattice gauge theory formulation of quantum chromodynamics. A Euclidean path integral on a discrete spacetime lattice provides a route to computing hadron observables numerically, particularly when weak-coupling expansions are inadequate. Physical predictions require control of lattice spacing, finite spatial volume and quark-mass effects.

Theory. Quantum chromodynamics is a local, non-Abelian gauge theory with gauge group SU(3) acting on color charge. Its matter fields are spin-half quarks of six flavours, each in three colors; its eight massless spin-one gluons are the gauge fields. Unlike the neutral photon, gluons themselves carry gauge charge. Consequently there are three-gluon and four-gluon vertices as well as the quark-gluon vertex. A compact Lagrangian density iswhere $D_{\mu }$ is the gauge covariant derivative and the field strength contains the nonlinear term $g_s{f}^{abc}{G}_{\mu }^b{G}_{\nu }^c$.

The running coupling is weak at high momentum scales. At one loop, for $n_f$ active flavours,The positive coefficient $11-2n_f/3$ produces asymptotic freedom: short-distance, large-$Q$ processes admit perturbation theory. The gluon self-interaction is crucial to its sign. At low scales the coupling grows and isolated colored particles are not observed; the physical spectrum consists of color-singlet hadrons, the phenomenon of confinement. A hard-produced quark or gluon radiates and undergoes hadronization, giving a collimated jet. The one-loop formula is not valid at $Q\sim {\Lambda }_{\mathrm{QCD}}$ and is not, by itself, a mathematical proof of confinement.

Experimental tests. Different measurements test different ingredients of this account:

The convincing evidence is the quantitative consistency across these probes, with a common color group and coupling evolution. A jet by itself is evidence for a hard parton; its rates and correlations supply the more specific tests of quantum chromodynamics.^[ref]

Adding the three characteristic quark energies from b givesThe estimate recovers a sub-GeV scale but underestimates the stated neutron mass by a factor of a few. This is consistent with its deliberately crude uncertainty and geometry assumptions; it is not a precision mass prediction.

A better model needs the actual spatial and momentum correlations, a confining interaction, and the energy in the quark and gluon fields. In quantum chromodynamics, hadron masses are not simply the sum of three freely moving particles with tiny masses. The supplied $5$ MeV rest-energy scale resembles a light current-quark scale; a phenomenological constituent-quark mass includes substantial dressing and is a different parameter. Color, spin correlations, relativistic dynamics and sea components all matter when defining a more realistic bound-state Hamiltonian operator or performing a lattice QCD calculation. The prescribed uniform-sphere model supplies none of those extra dynamical inputs, so its discrepancy should not be repaired by an unannounced change of the given radius or mass.