The asymptotic approach to the continuum of lattice QCD spectral observables

• Published in: Physics letters. B 2022-06, Vol.829, p.137069, Article 137069
• Main Authors: Husung, Nikolai, Marquard, Peter, Sommer, Rainer
• Format: Article
• Language: English
• Subjects: Discretisation effects; Effective field theory; Lattice QCD; Perturbation theory
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2022.137069

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.