Lattice QCD

Lattice QCD is a numerical formulation of quantum chromodynamics that discretizes spacetime and evaluates the resulting theory, usually with Monte Carlo methods. It enables nonperturbative calculations of quarks and gluons.

Lattice gauge theory: A framework for studying gauge fields by defining them on discrete spacetime lattices. Lattice QCD is the specific application of this framework to the strong interaction.
Hadron spectroscopy: The study of hadron properties and energy levels through their observed or calculated spectra. Lattice QCD predicts hadron masses and excited states from the underlying quark and gluon dynamics.
Quantum chromodynamics: The quantum field theory of quarks and gluons and their strong interaction. Lattice QCD numerically realizes this underlying theory rather than replacing it.
Perturbative QCD: Calculations in quantum chromodynamics organized as expansions in the strong coupling constant. Perturbation theory works at high energies, while lattice methods access strongly coupled low-energy physics.
Continuum limit: The limit in which a discretized theory's lattice spacing approaches zero while physical quantities remain fixed. Reliable predictions require extrapolating finite-spacing results toward this limit.
Euclidean quantum field theory: A quantum field theory formulated with imaginary time, often used to make numerical calculations tractable. Wick rotation converts many lattice QCD calculations into a Euclidean statistical problem.
Hadron structure: The distribution of quarks, antiquarks, and gluons inside hadrons, described by measurable matrix elements and distributions. Lattice calculations estimate structure observables that connect QCD to scattering experiments.
Gauge field: A field whose local symmetry transformations encode interactions between charged particles. The gluon field is represented by gauge links connecting neighboring lattice sites.
Chiral perturbation theory: An effective field theory describing low-energy interactions among hadrons using approximate chiral symmetry. It provides analytic low-energy descriptions that complement lattice results and help extrapolate them.
Chiral limit: The limit in which the masses of light quarks approach zero. Simulations at physical light-quark masses remain costly, so controlled extrapolation matters.

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