Step-scaling with off-shell renormalization

We make use of twisted boundary conditions for off-shell, Rome-Southampton renormalization. This allows us to define vertex functions at a fixed physical momentum that need not be a Fourier mode. This definition includes choosing a fixed orientation with respect to the lattice axes; only then do lattice artifacts, which include $O(4)$ breaking effects, have a valid expansion in powers of the lattice spacing, a. The use of nonexceptional momenta has been found to greatly reduce the dependence of the vertex functions on both mass and momentum, p. Excellent statistical precision is afforded by plane-wave sources. Together this enables both a theoretically well-founded and statistically clean continuum limit. Thereafter all p² dependence can be identified with the anomalous running of the operator. We present initial results and develop a practical scheme for step-scaling with off-shell renormalization. The size of the steps is continuous rather than discrete, allowing arbitrarily small steps and the scheme is easy to implement for general operators.