Strong coupling constant from vacuum polarization functions in three-flavor lattice QCD with dynamical overlap fermions

TL;DR

This work determines the strong coupling constant by computing vacuum polarization functions in 2+1-flavor lattice QCD with dynamical overlap fermions and fitting to the continuum perturbative expansion augmented by the operator product expansion. The methodology leverages a conserved lattice current to satisfy Ward-Takahashi identities, enabling a clean extraction of VPFs and a controlled comparison to four-loop perturbative QCD, yielding a precise value $α_s^{(5)}(M_Z)=0.1181(3)(^{+14}_{-12})$. The primary contributions are (i) demonstration of a reliable lattice-based route to $α_s$ using VPFs, (ii) quantification of systematic errors from discretization, scale setting, and perturbative truncation, and (iii) a result consistent with other lattice determinations and the world average, validating QCD across energy scales. The approach advances nonperturbative determinations of $α_s$ and highlights the importance of accurate scale setting and lattice spacing control for precision lattice QCD phenomenology.

Abstract

We determine the strong coupling constant $α_s$ from a lattice calculation of vacuum polarization functions (VPF) in three-flavor QCD with dynamical overlap fermions. Fitting lattice data of VPF to the continuum perturbative formula including the operator product expansion, we extract the QCD scale parameter $Λ_{\overline{MS}}^{(3)}$. At the $Z$ boson mass scale, we obtain $α_s^{(5)}(M_Z)=0.1181(3)(^{+14}_{-12})$, where the first error is statistical and the second is our estimate of various systematic uncertainties.

Figures (7)

• Figure 1: $(aQ)^2$ dependence of VPF, $\Pi_{V+A}(Q)$, at all valence quark masses: $m_q=0.015$ (circle), $0.025$ (square), $0.035$ (diamond), and $0.050$ (triangle). Top half is a result at $m_s=0.08$ while the bottom is at $m_s=0.10$. Solid curves show a fit function at each quark masses. Filled symbols are the points for which each momentum component is equal to or smaller than $2\pi/16$ in the lattice unit.
• Figure 2: Comparison of $\Pi_{V+A}(Q)$ with different momentum definitions. Lattice data at $m_q=0.015$.
• Figure 3: Dependence of the fit parameters on the lower limit of the fit range. The maximum value is fixed at $(aQ)^2\simeq 0.994$. Open and filled symbols show the results with and without the $1/Q^4$ terms in (\ref{['eq:pi_J_OPE']}). (Thus, there is no filled symbol in the middle plot.)
• Figure 4: Difference between the lattice data and the fit function (\ref{['eq:pi_J_OPE']}). Dashed line shows a guiding line representing the $1/Q^6$ behavior.
• Figure 5: $(aQ)^2$ dependence of one-loop VPF $\Pi_{J=V,A}(Q^2)$ in lattice perturbation theory. Dashed line shows the leading logarithm term plus a constant, which corresponds to the continuum perturbation theory. Solid lines show the function including lattice artifact of $O((aQ^2))$. The shaded band represents an uncertainty due to the higher order effects. The red diamond denotes the value at the upper limit of our fit of VPF.