Two loop lattice expansion of the Schrödinger functional coupling in improved QCD

Abstract

The contributions of the improved fermion action of Sheikholeslami and Wohlert to the two loop coefficient of the expansion of the Schrödinger functional coupling in terms of the lattice coupling are calculated for the gauge group SU(3). These coefficients are required for the second order relation of lattice data to the MS-coupling. By taking into account all improvement coefficients we are able to improve the Schrödinger functional to two loop order. This article is based on the revised version of [9].