Topological excitations of the gluon field in QCD, which play an important role in generating quark masses and interactions, can be identified by localized quark zero modes. The gluon topological charge (left) and corresponding quark zero mode (right) are shown for a meron pair on a lattice in an ongoing project to explore the role of these configurations in producing quark confinement

Research Objectives
The major focus of the work is on two key issues: Understanding the role of instantons and their associated quark zero modes in nucleon structure, and using the quark zero modes to calculate the sea quark content of the nucleon. This project has several physics objectives. By calculating the spectrum for an ensemble of configurations, we expect to understand the spectrum and the degree of separation of physical modes from unphysical doublers, and to check the relation between the density of fermion modes with low virtuality and the chiral condensate. We will carry out a high statistics study of the degree to which hadron propagators are dominated by zero modes. We will reconstruct the topological charge density from the quark eigenmodes to obtain an unambiguous determination of the instanton content of the QCD vacuum. We will use the zero modes to calculate the disconnected diagrams corresponding to the strange quark content of the nucleon.

Computational Approach
We calculate the low eigenmodes of the Dirac operator using the k-step Arnoldi method. This method has compelling advantages for our work. First, since it works in a fixed dimension space, there is no degradation of orthogonality and corresponding loss or duplication of modes. Second, its insensitivity to the quark mass makes it extremely useful near the chiral limit of low pion mass. We have two complementary implementations. One is an exploratory code in which we can control the region of eigenvalues at will. The other uses the robust and well-optimized PARPACK package from ORNL.

Accomplishments
We began major production late in the fiscal year, but we have verified that our truncated eigenvector approach provides a statistically superior signal to that obtained with conventional stochastic estimators. Results show that using 300 low-lying eigenmodes significantly increases the signal.

Significance
This project will develop a new method that can attain a higher level of statistical accuracy than existing methods and will provide the essential quark zero modes necessary for these calculations. In addition to elucidating the physics for timely parity-violating electron-scattering experiments, this new method should also enable the evaluation of the disconnected diagrams encountered in deep inelastic electron scattering.

We will perform the first quantitative study of the eigenmodes for a full ensemble of configurations. This will enable us to perform the most precise explorations to date of the eigenvalue spectrum of the Dirac operator, the separation of physical modes from lattice artifacts, the instanton content of the QCD vacuum, the quantitative accuracy of the 't Hooft interaction, and the relation between the density of eigenvalues and the chiral condensate, as expected from the Banks-Casher formula.

Publications
James V. Steele and J. W. Negele, "Meron pairs and fermion zero modes," Phys. Rev. Lett. (in press); hep-lat/0007006.

John W. Negele, "Instantons, the QCD vacuum, and hadronic physics," Nucl. Phys. B (Proc. Suppl.) 73, 92 (1999); hep-lat/9810053.

O. Jahn, F. Lenz, J. W. Negele, and M. Thies, "Center vortices, instantons, and confinement," Nucl. Phys. B (Proc. Suppl.) 83, 524 (2000).

http://www-ctp.mit.edu/~negele/