latticeQCD

Lattice QCD is a non-perturbative formulation of quantum chromodynamics in which spacetime is discretized on a four-dimensional lattice. The theory is defined in Euclidean space to make the path integral amenable to numerical evaluation through probabilistic methods, enabling large-scale simulations of strong-interaction dynamics.

In the lattice formulation, gauge fields are represented by SU(3) matrices on the links between lattice sites, and quark fields reside on the sites. The gauge part of the action is built from closed loops, with the standard Wilson gauge action based on plaquettes. Fermions can be discretized with various lattice actions, such as Wilson, staggered (Kogut-Susskind), domain-wall, or overlap fermions. The choice of action affects chiral symmetry properties and lattice artifacts.

A central challenge is fermion doubling, where naive discretization yields extra fermion species. Wilson and improved Wilson-type actions remove doublers but break chiral symmetry explicitly; domain-wall and overlap fermions preserve chiral symmetry more faithfully at higher computational cost. Improvements like Clover (Sheikholeslami-Wohlert) and highly improved staggered quarks (HISQ) reduce discretization errors and taste breaking.

Observables are computed via Monte Carlo sampling of the path integral, using algorithms such as Hybrid Monte Carlo (HMC) or Rational Hybrid Monte Carlo (RHMC). From Euclidean correlation functions, one extracts hadron spectra, decay constants, and quark masses; the strong coupling constant and various matrix elements can also be determined. Scale setting employs quantities like Sommer parameters r0, r1, or physical hadron masses.

Simulations are performed at multiple lattice spacings and volumes to approach the continuum limit a → 0 and to control finite-volume effects. Lattice QCD demands substantial computational resources and often involves international collaborations utilizing supercomputers and GPUs.