We present the formalism necessary to reduce the errors due to the finiteness of the lattice spacing from terms of O(a) to terms of O(g02a) in lattice computations of hadronic matrix elements. We tabulate the results of the perturbative calculations necessary to determine these matrix elements. By performing a numerical simulation in a theory with an improved fermion action, we demonstrate explicitly that for matrix elements of the vector current these errors are reduced from about 20–30% to about 5%. We therefore propose that future simulations in lattice QCD be performed using an improved fermion action.
