Towards precision results in lattice Quantum Chromo Dynamics

Quantum Chromo Dynamics (QCD) is the underlying theory of the strong
nuclear interactions and thus constitutes a central pillar of the
Standard Model of particle physics.  One of the characteristic
features of QCD is the confinement of quarks inside hadronic bound
states such as the proton or the pion. Lattice QCD has been designed
to calculate properties of hadrons by means of numerical
simulations. On the other hand, at distances much smaller than the
size of the hadrons, the quarks behave almost like free particles, a
property known as asymptotic freedom. Interactions between quarks at
such short distance scales can be calculated by perturbing around a
hypothetical situation of free quarks.  Since QCD is a single theory
describing both regimes, the challenge is to provide a controlled
connection between properties of quarks and those of hadrons.  For
lattice QCD as a numerical approach, the main difficulty consists in
accommodating very different length scales while keeping the lattice
sizes affordable. I will explain how this problem can be overcome by
using the finite space-time volume to probe the theory, and I will
present a few results that have been obtained by the Alpha
collaboration over the last few years.