Flowed quark field renormalization in lattice QCD: A Ward-identity approach and its validation using quark bilinears
Abstract
We present a non-perturbative Ward-identity prescription for determining the flowed quark field renormalization factor Zχ, avoiding the computational difficulties of the conventional ringed prescription. The method is based on vector-current normalization and ratios of flowed and unflowed meson two-point functions. We determine the resulting mathringZχV(tf,a) on five 2+1-flavor clover ensembles and validate it in the pseudoscalar, scalar, axial-vector, and tensor channels. Renormalized matrix elements obtained through sequential continuum and zero-flow-time extrapolations agree with independent RI/MOM and RI/SMOM determinations. The finite-lattice-spacing bilinear renormalization factors show differences that decrease toward finer lattices, reflecting the different discretization effects of the renormalization methods. The cross-channel agreement demonstrates the viability of the proposed prescription; together, the method and its systematic validation establish a robust foundation for the non-perturbative renormalization of flowed fermionic operators in future lattice calculations.
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BibTeX
@misc{gao2026flowed,
title = {{Flowed quark field renormalization in lattice QCD: A Ward-identity approach and its validation using quark bilinears}},
author = {Mei-Qi Gao and Long-cheng Gui and Jun Hua and Jian Liang and Jun Shi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23379},
eprint = {2609.23379},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23379},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Flowed quark field renormalization in lattice QCD: A Ward-identity approach and its validation using quark bilinears
AU - Mei-Qi Gao
AU - Long-cheng Gui
AU - Jun Hua
AU - Jian Liang
AU - Jun Shi
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23379
UR - https://arxiv.org/abs/2609.23379
AB - We present a non-perturbative Ward-identity prescription for determining the flowed quark field renormalization factor Z_χ, avoiding the computational difficulties of the conventional ringed prescription. The method is based on vector-current normalization and ratios of flowed and unflowed meson two-point functions. We determine the resulting mathringZ_χ^V(t_f,a) on five 2+1-flavor clover ensembles and validate it in the pseudoscalar, scalar, axial-vector, and tensor channels. Renormalized matrix elements obtained through sequential continuum and zero-flow-time extrapolations agree with independent RI/MOM and RI/SMOM determinations. The finite-lattice-spacing bilinear renormalization factors show differences that decrease toward finer lattices, reflecting the different discretization effects of the renormalization methods. The cross-channel agreement demonstrates the viability of the proposed prescription; together, the method and its systematic validation establish a robust foundation for the non-perturbative renormalization of flowed fermionic operators in future lattice calculations.
ER -