  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].

High Energy Physics - Lattice