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arXiv · 2206.03536

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

Nikolai Husung
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Abstract

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].

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Nikolai Husung. 2022-06-07. Logarithmic corrections to O($a$) and O($a^2$) effects in lattice QCD with Wilson or Ginsparg-Wilson quarks. https://doi.org/10.1140/epjc/s10052-023-11258-8

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