The asymptotic approach to the continuum of lattice QCD spectral observables

We consider spectral quantities in lattice QCD and determine the asymptotic behavior of their discretization errors. Wilson fermion with O$(a)$-improvement, (M\"obius) Domain wall (DWF), overlap Dirac operators are considered combination commonly used gauge actions. fermions DWF domain height $M_5=1+{\rm O}(g_0^2)$ have same, approximate, form cutoff effects: $ K\,a^2\left[\bar g^2(a^{-1})\right]^{0.760}$. A $M_5=1.8$, as often used, introduces large mass-dependent $K'(m)\,a^2\left[\bar g^2(a^{-1})\right]^{0.518}$ effects. Massless twisted mass same when Sheikholeslami-Wohlert term [1] is included. For effects we information on exponents $\hat\Gamma_i$ $\bar g^2(a^{-1})$ but not for pre-factors. staggered there only partial exponents. propose that tree-level ${\rm O}(a^2)$ improvement, which easy to do [2], should be future -- both action. It improves all cases.