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

• الحاوية / القاعدة: European Physical Journal C: Particles and Fields
• المؤلف الرئيسي: Nikolai Husung
• التنسيق: مقال
• اللغة: الإنجليزية
• منشور في: SpringerOpen 2023-02-01
• الوصول للمادة أونلاين: https://doi.org/10.1140/epjc/s10052-023-11258-8

Abstract We derive the asymptotic lattice spacing dependence $$a^n[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma }_i}$$ a n [ 2 b 0 g ¯ 2 ( 1 / a ) ] Γ ^ i relevant for spectral quantities of lattice QCD, when using Wilson, $$\textrm{O}(a)$$ O ( a ) improved Wilson or Ginsparg–Wilson quarks. We give some examples for the spectra encountered for $$\hat{\Gamma }_i$$ Γ ^ 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 $$\textrm{O}(a)$$ O ( a ) improvement. At $$\textrm{O}(a^2)$$ O ( a 2 ) , all cases considered have $$\min _i\hat{\Gamma }_i\gtrsim -0.3$$ min i Γ ^ i ≳ - 0.3 if $$N_{\textrm{f}}\le 4$$ N f ≤ 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).