Non-perturbative running of renormalization constants from correlators in coordinate space using step scaling

Abstract

Working in a quenched setup with Wilson twisted mass valence fermions, we explore the possibility to compute non-perturbatively the step scaling function using the coordinate (X-space) renormalization scheme. This scheme has the advantage of being on-shell and gauge invariant. The step scaling method allows us to calculate the running of the renormalization constants of quark bilinear operators. We describe here the details of this calculation. The aim of this exploratory study is to identify the feasibility of the X-space scheme when used in small volume simulations required by the step scaling technique. Eventually, we translate our final results to the continuum MSbar scheme and compare against four-loop analytic formulae finding satisfactory agreement.

arXiv comment35 pages, 10 figures; version accepted in Nucl. Phys. B

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Cited by in corpus (5)

• Non-perturbative determination of improvement coefficients using coordinate space correlators in $N_f=2+1$ lattice QCD
• Non-perturbative determination of improvement coefficients using coordinate space correlators in $N_f=2+1$ lattice QCD
• Running coupling constant from position-space current-current correlation functions in three-flavor lattice QCD
• Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor
• $O(4)$-symmetric position-space renormalization of lattice operators