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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | https://arxiv.org/abs/2111.02347 |
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| _version_ | 1866909352089092096 |
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| author | Husung, Nikolai Marquard, Peter Sommer, Rainer |
| author_facet | Husung, Nikolai Marquard, Peter Sommer, Rainer |
| contents | 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 $M_5=1+{\rm O}(g_0^2)$ 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 $K'(m)\,a^2\left[\bar g^2(a^{-1})\right]^{0.518}$ 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 $\hatΓ_i$ 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 ${\rm O}(a^2)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_02347 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The asymptotic approach to the continuum of lattice QCD spectral observables Husung, Nikolai Marquard, Peter Sommer, Rainer High Energy Physics - Lattice 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 $M_5=1+{\rm O}(g_0^2)$ 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 $K'(m)\,a^2\left[\bar g^2(a^{-1})\right]^{0.518}$ 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 $\hatΓ_i$ 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 ${\rm O}(a^2)$ 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. |
| title | The asymptotic approach to the continuum of lattice QCD spectral observables |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2111.02347 |