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We perform a benchmark study of the step scaling procedure for the ratios ofrenormalization constants extracted from position space correlation functions.We work in the quenched approximation and consider the pseudoscalar, scalar,vector and axial vector bilinears. The pseudoscalar/scalar cases allow us toobtain the non-perturbative running of the quark mass over a wide range ofenergy scales - from around 17 GeV to below 1.5 GeV - which agrees well withthe 4-loop prediction of continuum perturbation theory. We find that stepscaling is feasible in X-space and we discuss its advantages and potentialproblems.

Step scaling in coordinate space: running of the quark mass