| 要約: | Abstract Recently the asymptotic lattice spacing dependence of spectral quantities in lattice QCD has been computed to $$\textrm{O}(a^2)$$ O ( a 2 ) 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 $$\textrm{SU}(N_{\textrm{f}})_\textrm{V}\times \textrm{SU}(N_{\textrm{b}}|N_{\textrm{b}})_\textrm{V}$$ SU ( N f ) V × SU ( N b | N b ) V flavour symmetries for $$N_{\textrm{f}}$$ N f sea-quarks and $$N_{\textrm{b}}$$ N b quenched valence-quarks respectively in the massless limit. Overall we find only few cases $${\hat{\Gamma }}$$ Γ ^ , which worsen the asymptotic lattice spacing dependence $$a^n[2b_0{\bar{g}}^2(1/a)]^{{\hat{\Gamma }}}$$ a n [ 2 b 0 g ¯ 2 ( 1 / a ) ] Γ ^ compared to the classically expected $$a^n$$ a n -scaling. Other than for trivial flavour quantum numbers, only the axial-vector and much milder the tensor may cause some problems at $$\textrm{O}(a)$$ O ( a ) , strongly suggesting to use at least tree-level Symanzik improvement of those local fields.
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