Test of the Kugo-Ojima confinement criterion in the Lattice Landau gauge

We present the first results of numerical test of the Kugo-Ojima confinement criterion in the lattice Landau gauge. The Kugo-Ojima criterion of colour confinement in the BRS formulation of the continuum gauge theory is given by u(b)(a)(O) = -delta(b)(a), where integral dxe(ip(x-y))[0\TD(mu)c(a)(x)g(A(nu) x (c) over bar)(b)(y)\0] = (g(mu nu) = (p mu p nu)/p(2))u(b)(a)(p(2)). (*) We measured the lattice version of u(b)(a)(0) in use of 1/(-partial derivative D(A)) where D-mu(A) is a lattice covariant derivative in the new definition of the gauge field as U = e(A). We obtained that u(b)(a)(O) is consistent with -c delta(b)(a), c = 0.7 in SU(3) quenched simulation data of beta = 5.5, on 8(4) and 12(4). We report the beta dependence and finite-size effect of c.