The asymptotic approach to the continuum of lattice QCD spectral observables

We consider spectral quantities in lattice QCD and determine the asymptotic behaviour of their discretization errors. Wilson fermion with O(a)-improvement, (Möbius) Domain wall fermion (DWF), and overlap Dirac operators are considered in combination with the commonly used gauge actions. Wilson fermions and DWF with domain wall height M5=1+O(g02) have the same, approximate, form of the asymptotic cutoff effects: Ka2[g¯2(a−1)]0.760. A domain wall height M5=1.8, as often used, introduces large mass-dependent K′(m)a2[g¯2(a−1)]0.518 effects. Massless twisted mass fermions have the same form as Wilson fermions when the Sheikholeslami-Wohlert term [1] is included. For their mass-dependent cutoff effects we have information on the exponents Γˆi of g¯2(a−1) but not for the pre-factors. For staggered fermions there is only partial information on the exponents. We propose that tree-level O(a2) improvement, which is easy to do [2], should be used in the future – both for the fermion and the gauge action. It improves the asymptotic behaviour in all cases.