The renormalised quark mass in the Schrodinger functional of lattice QCD - a one-loop calculation with a non-vanishing background field

The critical quark mass, at which the renormalised mass vanishes, is computed in the Schrodinger functional scheme with a non vanishing background field at one-loop order of perturbation theory. Further one-loop calculations are done for the renormalisation constant of the pseudo scalar density and for several discretisation errors and compared to results obtained with a vanishing background field.