# Lattice QCD - Interactions of Quarks and Gluons

The research of Dr. Walter Wilcox centers around the study of the interactions of particles known as quarks and gluons. He does extensive numerical simulations of the theory describing these particles, known as Quantum Chromodynamics (QCD). "Lattice QCD" represents a numerical attempt to solve, and compare to experiment, physically observable quantities. State of the art numerical methods, including matrix deflation, are used to solve the theory on high performance computers.

### "Lattice" QCD

Dr. Wilcox talks about his "lattice" QCD research:

"My field is called “lattice" QCD because it simulate the interactions of the theory on a discrete space-time lattice using numerical methods on supercomputers. The variables in the lattice represent the QCD vacuum, the basis of all other particle states. These variables are determined via a Monte Carlo procedure in each “configuration” and all physical quantities are then defined by an average over these configurations. Lattice QCD benefits from a synergy of field theory, experimental particle physics and computer technology.

My collaborative research work with Dr. Ron Morgan of the Baylor Mathematics Department is centered on developing new mathematical techniques to speed up the solution of ill-conditioned linear equations, especially for lattice QCD (where it is termed "fermion matrix inversion"). Our work is helping to defeat the so-called "critical slowing down" which affects lattice QCD simulations at small quark masses. In addition, it turns out that at small quark masses the numerical methods used to isolate physical signals in lattice QCD become swamped with statistical noise. Ron Morgan, Victor Guerrero and I have recently begun investigating an exciting new technique we call "eigenvalue noise subtraction" which should dramatically improve the situation.

### A New Analytic Model of Hadron Structure

"I have also begun investigating a new analytic model of hadron structure based upon the Thomas-Fermi (TF) statistical model," says Dr. Wilcox. "The TF approach is normally used to model atomic interactions, but I have applied it instead to assemblies of quarks. It turns out to be a natural application of the method. I am developing it to guide more expensive lattice simulations to likely areas in the search for high multi-quark hadronic states. I think the model has the potential to shed light on the stability characteristics of such states, and to be applied to other types of exotic matter. A type of universal spatial wave function, labeled as "f(x)", is produced by the model, independent of the quark mass, which is reproduced below in Fig. 1."

Dr Wilcox further explains how the "distance "x" is a scaled radial distance. The model also can be extended to situations with an external pressure that is modeling quark confinement, as in bag models. This pressure produces a discontinuity on the TF function, as is also shown in the figure."