We show that the running of operators which mix under renormalization can be computed fully non-perturbatively as a product of continuum step scaling matrices. These step scaling matrices are obtained by taking the "ratio" of Z matrices computed at different energies in an RI-MOM type scheme for which twisted boundary conditions are an essential ingredient. Our method allows us to relax the bounds of the Rome-Southampton window. We also explain why such a method is important in view of the light quark physics program of the RBC-UKQCD collaborations. To illustrate our method, using n_f=2+1 domain-wall fermions, we compute the non-perturbative running matrix of four-quark operators needed in K->pipi decay and neutral kaon mixing. Our results are then compared to perturbation theory.
@article{arxiv.1109.1223,
title = {Opening the Rome-Southampton window for operator mixing matrices},
author = {R. Arthur and P. A. Boyle and N. Garron and C. Kelly and A. T. Lytle},
journal= {arXiv preprint arXiv:1109.1223},
year = {2012}
}
Comments
8 pages, 7 figures. v2: PRD version, minor changes and few references added