Fellow 1998-99

Aida X El-Khadra


Phenomenology with Improved Lattice QCD

The standard model of particle physics describes the strong, electro-magnetic and weak interactions of elementary particles. In many cases, perturbation theory is an adequate calculational tool to derive predictions of the standard model that can be tested in experiments. These tests are the foundation of the standard model as the correct theory of elementary particle interactions. In the standard model, the strong interactions are described by the theory of Quantum Chromodynamics (QCD). However, in QCD, perturbation theory is reliable only at high energies. Consequently, our understanding of the theory is not complete. A quantitative understanding of the interactions of quarks inside hadrons (e.g., the proton or neutron) requires nonperturbative methods. Lattice field theory offers a systematic approach to solving QCD nonperturbatively. Calculations in lattice QCD can be performed using Monte Carol methods. However, the computational cost of such calculations has, to date, prevented us from obtaining definitive results. In lattice field theory, the space-time continuum is replaced by a discrete lattice. Therefore, the continuum field theory is approximated by a discretization in the lattice field theory, replacing, for example, derivatives with discrete differences. In general, this introduces lattice spacing artifacts into physical quantities. They can be controlled by reducing the lattice spacing, however, at a great computational cost. An alternative, called improvement, is the use of better discretizations in the theory. This idea is behind most of the important progress made in lattice QCD calculations in recent years. In continuation of her work on improvement, Professor El-Khadra proposes to develop and test highly improved lattice actions. This may lead to a sufficient reduction of the computational cost otherwise associated with such calculations and may make it possible to perform accurate calculations of strong interaction phenomena.