Amarjit Soni, Thomas Blum, Christopher Dawson,
and Matthew Wingate, Brookhaven National Laboratory

Research Objectives

We are in the process of setting up a comprehensive framework for using lattice gauge methods with domain wall quarks (DWQ) for the calculation of weak matrix elements.

Figure 1: The kaon B parameter. The Kogut-Susskind result is from JLQCD and OSU. DWF indicate improved scaling in this case. The DWF values are not renormalized.

Figure 2: The I = 3/2 electroweak B parameters (not renormalized).

Computational Approach

The basic ingredient in the method is a calculation of the quark propagator. The novel element in our method is that it requires introduction of a fictitious fifth dimension. The T3E-900 machine at NERSC is being used for these computations.

Accomplishments

We have demonstrated that DWQ start to exhibit the crucial symmetries of the continuum theory (chiral symmetries) with a modest extent in the fifth dimension, i.e., even when the number of lattice sites in the extra dimension is as few as about 16 at > 6.0. In the work finished so far, we have obtained a number of key results, including a calculation of the important matrix elements, B_K (see Fig. 1), B₇^3/2 and B₈^3/2 (Fig. 2), and the value of the

strange quark mass. Furthermore, our results show that DWQ have significantly improved scaling behavior: the discretization errors are O(a²) and not O(a). Our data indicate that the good scaling and chiral behavior of DWQ more than compensate for the added cost of the extra dimension.

Significance

This work opens up an entirely new method for attacking some of the basic challenges in particle physics computations. For the past many decades, we have not been able to understand the strength of some simple reactions such as K decays to . Consequently, we have been unable to test the Standard Model of elementary particles through existing data and with improved experiments that are now under way. Using DWQ, we are now in the process of calculating the crucial CP violation parameter . Successful completion of this calculation should enable us to test for clues for the new physics that lies beyond the Standard Model.

Publications

T. Blum, A. Soni, and M. Wingate, "Calculation of the strange quark mass using domain wall fermions," Phys. Rev. D 60, 114507 (1999).

T. Blum and A. Soni, "QCD with domain wall quarks," Phys. Rev. D 56, 174 (1997).

T. Blum and A. Soni, "Domain wall quarks and kaon weak matrix elements," Phys. Rev. Lett. 79, 3595 (1997).