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

We derive the asymptotic lattice spacing dependence \(a^n[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma}_i}\) 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 \(\hat{\Gamma}_i\) 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 \(\min_i\hat{\Gamma}_i\gtrsim -0.3\) if \(N_\mathrm{f}\leq 4\), which ensures that the leading order lattice artifacts are not severely logarithmically enhanced in contrast to the O\((3)\) non-linear sigma model [1,2]. 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 [3].