The asymptotic approach to the continuum of lattice QCD spectral observables

Abstract

We consider spectral quantities in lattice QCD and determine the asymptotic behavior 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 $M_5=1+\mathrm{O}(g_0^2)$ have the same, approximate, form of the asymptotic cutoff effects: $K{a}^2{\left[{\bar{g}}^2(a^{-1})\right]}^{0.760}$. A domain wall height $M_5=1.8$, as often used, introduces large mass-dependent $K^{\prime }(m)a^2{\left[{\bar{g}}^2(a^{-1})\right]}^{0.518}$ 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 ${\hat{\Gamma }}_i$ of ${\bar{g}}^2(a^{-1})$ but not for the pre-factors. For staggered fermions there is only partial information on the exponents. We propose that tree-level $\mathrm{O}(a^2)$ 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 behavior in all cases.

corrected the normalisation of some of the operators in the massive basis (sect. 6.2 and Table 3)

References in corpus (5)

• The anomalous magnetic moment of the muon in the Standard Model
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• Scaling studies of QCD with the dynamical HISQ action
• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• Logarithmic corrections to O(a^2) lattice artifacts

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• Determination of ${\alpha }_s(m_Z)$ by the non-perturbative decoupling method
• Logarithmic corrections to O($a$) and O($a^2$) effects in lattice QCD with Wilson or Ginsparg-Wilson quarks
• Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings
• The determination of potential scales in 2+1 flavor QCD