Step Scaling with off-shell renormalisation

Abstract

We make use of twisted boundary conditions for off-shell Rome-Southampton renormalisation. This allows to define the vertex function precisely, at a fixed physical momentum that need not be one of the Fourier modes of a simulation. This definition includes choosing the orientation with respect to lattice axes, and so lattice artefacts including $\mathcal{O}(4)$ breaking then have a valid Symanzik expansion. Excellent statistical precision is afforded by volume plane-wave sources, enabling both a theoretically and statistically clean continuum limit to be taken. Thereafter all $p^2$ dependence can be unambiguously identified as continuum anomolous running. The use of non-exceptional momenta has been found to greatly reduce the dependence of non-perturbative vertex functions on both mass and $p^2$. We illustrate how this can be developed into a practical scheme for step-scaling the RI/SMOM approach with initial results. The size of the possible steps is continuous, rather than discrete allowing one to take arbitrarily small steps, and the scheme inherits from RI/MOM the property that it is easy to implement for general operators.

35 pages

References in corpus (10)

• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
• Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
• Kl3 semileptonic form factor from 2+1 flavour lattice QCD
• Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the RI/SMOM schemes
• Localization and chiral symmetry in 2+1 flavor domain wall QCD
• K->pi form factors with reduced model dependence
• Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme
• First results from 2+1-Flavor Domain Wall QCD: Mass Spectrum, Topology Change and Chiral Symmetry with $L_s=8$
• Perturbative Wilson loops with massive sea quarks on the lattice

Cited by in corpus (1)

• Two loop renormalization of the n = 2 Wilson operator in the RI'/SMOM scheme