Abstract
AbstractWe 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).
Publisher
Springer Science and Business Media LLC
Subject
Physics and Astronomy (miscellaneous),Engineering (miscellaneous)
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