QCD with domain wall quarks

Abstract

We present lattice calculations in QCD using a variant of Kaplan fermions which retain the continuum SU(N)xSU(N) chiral symmetry on the lattice in the limit of an infinite extra dimension. In particular, we show that the pion mass and the four quark matrix element related to K_0-K_0-bar mixing have the expected behavior in the chiral limit, even on lattices with modest extent in the extra dimension, e.g. N_s=10.

Figures (2)

• Figure 1: The pion mass squared as function of $m$. $m$ is proportional to the quark mass. The last two points for $N_s=10$ (octagons) extrapolate linearly to zero well within statistical errors. The squares denote results for $N_s=4$.
• Figure 2: The ratio of the four quark matrix element for $K_0-\bar{K}_0$ mixing to the square of the pseudo-scalar density matrix element, calculated with domain wall fermions (octagons($N_s=10$) and squares($N_s=4$)). The $N_s=10$ curve exhibits the correct behavior in the chiral limit. Also shown is the result using the same gauge field configurations for Wilson quarks (crosses) which extrapolates to zero far from $m=0$ (note that for Wilson quarks the quark mass is defined as the difference of the inverse quark hopping parameter with the inverse critical hopping parameter, $m\equiv \frac{1}{2}(\kappa^{-1}-\kappa_c^{-1})$).