Logarithmic corrections to O($a^2$) effects in lattice QCD with unrooted Staggered quarks

Nikolai Husung

Logarithmic corrections to O($a^2$) effects in lattice QCD with unrooted Staggered quarks

High Energy Physics - Lattice 2025-09-01 v2

Authors: Nikolai Husung

Abstract

We derive the asymptotic lattice-spacing dependence $a^2[2b_0\bar{g}^2(1/a)]^{\hat{\gamma}_i}$ relevant for spectral quantities of lattice QCD, when using unrooted Staggered quarks. Without taking any effects from matching into account we find $\min_i\hat{\gamma}_i\approx -0.273, -0.301, -0.913, -2.614$ for $N_\mathrm{f}=0,4,8,12$ respectively. Common statements in the literature on the absence of mass-dimension~5 operators from the on-shell basis of the Symanzik Effective Field Theory action are being clarified for a description using strictly local tastes, here playing the role of continuum quark flavours. Potential impact of $\mathrm{O}(a)$ EOM-vanishing terms beyond spectral quantities is being discussed.

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@article{arxiv.2501.17036,
  title  = {Logarithmic corrections to O($a^2$) effects in lattice QCD with unrooted Staggered quarks},
  author = {Nikolai Husung},
  journal= {arXiv preprint arXiv:2501.17036},
  year   = {2025}
}

Comments

14 pages + 5 pages appendix, 1 table; supplemental material contains: Mathematica notebook relating 1CR symmetries to symmetries of local tastes (symm1CRtoTastes.nb), full mixing matrix (staggered.wl); Revised section on the lattice symmetries of local tastes. Added modified Euclidean reflection on the lattice as an explicit example involving a field-redefinition in the appendix

Logarithmic corrections to O($a^2$) effects in lattice QCD with unrooted Staggered quarks

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