TY - JOUR
T1 - Step Scaling with off-shell renormalisation
AU - Arthur, R.
AU - boyle, P.
N1 - 35 pages
PY - 2010/6/2
Y1 - 2010/6/2
N2 - 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 ${\cal O}(4)$ 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.
AB - 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 ${\cal O}(4)$ 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.
U2 - 10.1103/PhysRevD.83.114511
DO - 10.1103/PhysRevD.83.114511
M3 - Article
JO - Physical Review D, particles, fields, gravitation, and cosmology
JF - Physical Review D, particles, fields, gravitation, and cosmology
ER -