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Accurate Determinations of $α_s$ from Realistic Lattice QCD

Q. Mason, H. D. Trottier, C. T. H. Davies, K. Foley, A. Gray, G. P. Lepage, M. Nobes, J. Shigemitsu

Abstract

We obtain a new value for the QCD coupling constant by combining lattice QCD simulations with experimental data for hadron masses. Our lattice analysis is the first to: 1) include vacuum polarization effects from all three light-quark flavors (using MILC configurations); 2) include third-order terms in perturbation theory; 3) systematically estimate fourth and higher-order terms; 4) use an unambiguous lattice spacing; and 5) use an $\order(a^2)$-accurate QCD action. We use 28~different (but related) short-distance quantities to obtain $α_{\bar{\mathrm{MS}}}^{(5)}(M_Z) = 0.1170(12)$.

Accurate Determinations of $α_s$ from Realistic Lattice QCD

Abstract

We obtain a new value for the QCD coupling constant by combining lattice QCD simulations with experimental data for hadron masses. Our lattice analysis is the first to: 1) include vacuum polarization effects from all three light-quark flavors (using MILC configurations); 2) include third-order terms in perturbation theory; 3) systematically estimate fourth and higher-order terms; 4) use an unambiguous lattice spacing; and 5) use an -accurate QCD action. We use 28~different (but related) short-distance quantities to obtain .

Paper Structure

This paper contains 10 equations, 2 figures, 1 table.

Figures (2)

  • Figure 1: Values for the 5-flavor $\alpha_{\overline{\mathrm{MS}}}$ at the $Z$ mass from each short-distance quantity. The dashed lines indicate our final result, 0.1170(12) ($\chi^2$ per data point is 0.77).
  • Figure 2: Values for $\alpha_V$ versus $d/a$ (Eq. (\ref{['pert-exp']})) from each short-distance quantity at each lattice spacing, with (top) and without (bottom) light-quark vacuum polarization. The dashed lines show predictions from Eq. (\ref{['evol-eq']}) assuming $\alpha_V(7.5\,\mathrm{GeV})$ is $0.2082(40)$ and $0.1645(14)$ for $n_f=3$ and 0, respectively.