Logarithmic corrections to O(a) and O($$a^2$$) effects in lattice QCD with Wilson or Ginsparg–Wilson quarks

Abstract We derive the asymptotic lattice spacing dependence $$a^n[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma }_i}$$ a n [ 2 b 0 g ¯ ( 1 / ) ] Γ ^ i relevant for spectral quantities of QCD, when using Wilson, $$\textrm{O}(a)$$ O improved Wilson or Ginsparg–Wilson quarks. give some examples spectra encountered $$\hat{\Gamma }_i$$ including partially quenched case, mixed actions and two different discretisations dynamical This also includes maximally twisted mass QCD relying on automatic improvement. At $$\textrm{O}(a^2)$$ , all cases considered have $$\min _i\hat{\Gamma }_i\gtrsim -0.3$$ min ≳ - 0.3 if $$N_{\textrm{f}}\le 4$$ N f ≤ 4 which ensures that leading order artifacts are not severely logarithmically enhanced in contrast to O(3) non-linear sigma model (Balog et al. Nucl Phys B 824:563–615, 2010; Balog Lett 676:188–192, 2009). However, we find a very dense spectrum these powers, may result major pile-ups cancellations. present detail computational strategy employed obtain 1-loop anomalous dimensions already used Husung (Phys 829:137069, 2022).