$O(4)$-symmetric position-space renormalization of lattice operators

Abstract

We extend the position-space renormalization procedure, where renormalization factors are calculated from Green's functions in position space, by introducing a technique to take the average of Green's functions over spheres. In addition to reducing discretization errors, this technique enables the resulting position-space correlators to be evaluated at any physical distance, making them continuous functions similar to the $O(4)$-symmetric position-space Green's functions in the continuum theory but with a residual dependence on a regularization parameter, the lattice spacing $a$. We can then take the continuum limit of these renormalized quantities calculated at the same physical renormalization scale $|x|$ and investigate the resulting $|x|$-dependence to identify the appropriate renormalization window. As a numerical test of the spherical averaging technique, we determine the renormalized light and strange quark masses by renormalizing the scalar current. We see a substantial reduction of discretization effects on the scalar current correlator and an enhancement of the renormalization window. The numerical simulation is carried out with $2+1$-flavor domain-wall fermions at three lattice cutoffs in the range 1.79--3.15~GeV.

34 pages, 12 figures

References in corpus (8)

• Five-Loop Running of the QCD coupling constant
• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
• Step Scaling with off-shell renormalisation
• Massless correlators of vector, scalar and tensor currents in position space at orders alpha_s^3 and alpha_s^4: explicit analytical results
• Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action
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• Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor
• Gauge-invariant Renormalization of the Gluino-Glue operator
• Quark flavor physics and lattice QCD
• Nonperturbative renormalization of the supercurrent in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory
• Towards non-perturbative matching of three/four-flavor Wilson coefficients with a position-space procedure