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Joined 2026-09-21 Message
Incoming links: Lattice QCD
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 is the gauge covariant derivative and the field strength contains the nonlinear term .
The running coupling is weak at high momentum scales. At one loop, for active flavours,The positive coefficient produces asymptotic freedom: short-distance, large- 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 and is not, by itself, a mathematical proof of confinement.
- Deep inelastic scattering resolves approximately pointlike spin-half constituents. Approximate Bjorken scaling supplies the starting parton picture, while the measured logarithmic departures from scaling agree with QCD evolution of parton distribution functions.
- The hadronic R ratio in electron-positron annihilation counts squared quark charges multiplied by three colors, with calculable strong corrections. It tests color multiplicity as well as the quark charge assignments.
- Two-jet events identify a quark-antiquark hard topology. Three-jet events test hard gluon radiation, ; their angular correlations support a spin-one gluon. Four-jet correlations and radiation patterns further probe the non-Abelian color factors and gluon self-interactions.
- Determinations of from processes at widely separated scales follow the same running coupling, rather than independent interaction strengths. Jet rates, event shapes, hadronic weak-boson decays and high-energy hadron collisions provide complementary tests.
- Lattice QCD calculations reproduce many hadronic masses and other low-energy quantities from the same underlying theory, connecting its strongly coupled regime to the observed spectrum.