Renormalization constants of vector (ZV) and axial-vector (ZA) currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schr\"odinger functional method. Non-perturbative values of ZV and ZA turn out to be smaller than the one-loop perturbative values by O(10 at a−1≈1 GeV. A sizable scaling violation of meson decay constants fπ and fρ observed with the one-loop renormalization factors remains even with non-perturbative renormalization.
@article{arxiv.hep-lat/0110128,
title = {Non-perturbative renormalization for a renormalization group improved gauge action},
author = {PACS Collaboration and S. Aoki and R. Burkhalter and M. Fukugita and S. Hashimoto and K. Ide and N. Ishizuka and Y. Iwasaki and K. Kanaya and T. Kaneko and Y. Kuramashi and V. Lesk and M. Okawa and Y. Taniguchi and A. Ukawa and T. Yoshié},
journal= {arXiv preprint arXiv:hep-lat/0110128},
year = {2019}
}