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)[2b0g(2)(1/a)]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 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(a2), all cases considered have mini i -0.3 if Nf = 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 676:188192, 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).

Automated summary

We derive the asymptotic lattice spacing dependence relevant for spectral quantities of lattice QCD, when using different types of quarks. Examples are given for various scenarios, including partially quenched case, mixed actions, and different discretizations for dynamical quarks. The results show that the leading order lattice artifacts are not severely enhanced but a dense spectrum of leading powers may lead to pile-ups and cancellations. The computational strategy used to calculate the 1-loop anomalous dimensions is presented in detail.