Particle physics

Quantum chromodynamics (QCD)

QCD describes the strong interaction among quarks and gluons carrying color charge; confinement and asymptotic freedom are its central features.

Quantum chromodynamics (QCD) is the gauge theory of the strong interaction. Quarks carry color charge and interact by exchanging gluons; unlike photons, gluons also carry color and interact with one another.

\mathcal{L}_{\mathrm{QCD}}=-\frac14G^a_{\mu\nu}G^{a\mu\nu}+\sum_f\bar q_f(i\gamma^\mu D_\mu-m_f)q_f

Definition: Color and color-neutral states

Red, green, and blue are conventional names for three color states; antiquarks carry anticolor. Observed hadrons are overall color singlets: baryons combine three quarks into a singlet, while mesons pair a quark with an antiquark. Color is not optical color.

Illustration of a gamma photon converting in a nuclear field to an electron–positron pair; the opposite charges bend in opposite directions in a magnetic field. This is an electromagnetic process, not a QCD calculation.

Confinement and asymptotic freedom

At large separation the strong interaction does not fall like a Coulomb force; field energy grows with distance, so isolated quarks are not observed (confinement). At very high energy or short distance the effective coupling decreases and quarks behave nearly freely. High-energy collisions produce showers and hadronization.

Example: Identify a singlet

Why can a combination of three quarks, one of each color, form a color-neutral baryon?

Solution

The three color states form an antisymmetric color singlet, so the total color charge is neutral. The full wavefunction must also satisfy symmetry constraints involving spin, space, and flavor.

At high energy scales the strong coupling $α_s(Q)$ decreases, so perturbation theory predicts jet processes well. As a quark emerges and the scale falls, the coupling grows and the color field produces additional quark–antiquark pairs; the resulting shower hadronizes into color-neutral particles. Detectors therefore do not record isolated quarks, but collimated groups of particles called jets.

There are eight independent gluon color states, not nine, because the color-singlet unit matrix is excluded from $SU(3)$ . Gluon self-interactions make the QCD beta function negative for a sufficiently small number of active flavors, so the coupling weakens at short distances. Asymptotic freedom does not remove long-distance confinement, where nonperturbative tools such as lattice simulations are needed.

Why are free quarks not observed at low energy, according to QCD?

At very short distances (very high energies), how does the effective strong coupling behave?

References

David Griffiths (2020). Introduction to Elementary Particles