https://doi.org/10.1140/epjc/s10052-025-13825-7
Regular Article - Theoretical Physics
Lattice artifacts of local fermion bilinears up to 
1
Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid, C/ Nicolás Cabrera 13-15, Cantoblanco, 28049, Madrid, Spain
2
Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain
3
Physics and Astronomy, University of Southampton, University Road, SO17 1BJ, Southampton, UK
Received:
12
September
2024
Accepted:
13
January
2025
Published online:
17
April
2025
Recently the asymptotic lattice spacing dependence of spectral quantities in lattice QCD has been computed to 
using Symanzik Effective theory (Husung et al. in Phys Lett B 829:137069, 2022; Husung in Eur Phys J C 83:142, 2023). Here, we extend these results to matrix elements and correlators of local fermion bilinears, namely the scalar, pseudo-scalar, vector, axial-vector, and tensor. This resembles the typical current insertions for the effective Hamiltonian of electro-weak or BSM contributions, but is only a small fraction of the local fields typically considered. We again restrict considerations to lattice QCD actions with Wilson or Ginsparg–Wilson quarks and thus lattice formulations of QCD without flavour-changing interactions realising at least 
flavour symmetries for 
sea-quarks and 
quenched valence-quarks respectively in the massless limit. Overall we find only few cases 
, which worsen the asymptotic lattice spacing dependence ![$$a^n[2b_0{\bar{g}}^2(1/a)]^{{\hat{\Gamma }}}$$](/articles/epjc/abs/2025/04/10052_2025_Article_13825/10052_2025_Article_13825_tex_eq8.png)
compared to the classically expected 
-scaling. Other than for trivial flavour quantum numbers, only the axial-vector and much milder the tensor may cause some problems at 
, strongly suggesting to use at least tree-level Symanzik improvement of those local fields.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjc/s10052-025-13825-7.
© The Author(s) 2025
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