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_0bar{g}^2(1/a)]^{hat{Gamma }_i} relevant for spectral quantities of lattice QCD, when using Wilson, textrm{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 textrm{O}(a) improvement. At textrm{O}(a^2), all cases considered have min _ihat{Gamma }_igtrsim -0.3 if N_{textrm{f}}le 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).