Logarithmic corrections to O(a) and O(a2) effects in lattice QCD with Wilson or Ginsparg–Wilson quarks

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