[Paper Review] Determination of $\alpha_s$ from static QCD potential: OPE with renormalon subtraction and lattice QCD

Hiromasa Takaura, T. Kaneko+2 more|arXiv (Cornell University)|Aug 5, 2018

Quantum Chromodynamics and Particle Interactions37 references4 citations

TL;DR

This paper presents a novel determination of the strong coupling constant αs from the static QCD potential using a theoretical framework based on the operator product expansion (OPE) with renormalon subtraction, significantly extending the validity of perturbative calculations to lower energies. By removing both leading O(ΛQCD) and first r-dependent O(Λ3QCDr2) renormalon uncertainties, the method enables reliable matching with lattice QCD data down to r ≲ 0.05 fm (ΛMSr ≲ 0.09), achieving a precision of αs(M2Z) = 0.1179+0.0015−0.0014 with 1.3% accuracy, dominated by higher-order perturbative uncertainties that can be reduced with finer lattices.

ABSTRACT

We determine the strong coupling constant $\alpha_s$ from the static QCD potential by matching a theoretical calculation with a lattice QCD computation. We employ a new theoretical formulation based on the operator product expansion, in which renormalons are subtracted from the leading Wilson coefficient. We remove not only the leading renormalon uncertainty of $\mathcal{O}(\Lambda_{ m QCD})$ but also the first $r$-dependent uncertainty of $\mathcal{O}(\Lambda_{ m QCD}^3 r^2)$. The theoretical prediction for the potential turns out to be valid at the static color charge distance $\Lambda_{ m \overline{MS}} r \lesssim 0.8$ ($r \lesssim 0.4$ fm), which is significantly larger than ordinary perturbation theory. With lattice data down to $\Lambda_{ m \overline{MS}} r \sim 0.09$ ($r \sim 0.05$ fm), we perform the matching in a wide region of $r$, which has been difficult in previous determinations of $\alpha_s$ from the potential. Our final result is $\alpha_s(M_Z^2) = 0.1179^{+0.0015}_{-0.0014}$ with 1.3 % accuracy. The dominant uncertainty comes from higher order corrections to the perturbative prediction and can be straightforwardly reduced by simulating finer lattices.

Motivation & Objective

• To overcome the 'window problem' in lattice QCD determinations of αs, where perturbative and lattice regimes overlap only narrowly.
• To extend the validity of theoretical predictions for the static QCD potential to lower energy scales, where lattice data are most accurate.
• To reduce theoretical uncertainties from renormalon ambiguities in the leading Wilson coefficient by subtracting them via OPE formalism.
• To perform a robust matching between lattice QCD data and theoretical predictions across a wide range of distances, including very short distances.
• To achieve a high-precision determination of αs(M2Z) with quantified systematic errors and clear pathways for further improvement.

Proposed method

• Employing the operator product expansion (OPE) to separate perturbative and nonperturbative contributions in the static QCD potential.
• Implementing a renormalon subtraction procedure to remove the O(ΛQCD) and O(Λ3QCDr2) uncertainties from the leading Wilson coefficient.
• Using a two-step analysis and a global fit to match lattice QCD data with the improved theoretical prediction across multiple distances.
• Performing continuum extrapolation and consistency checks to control discretization effects, especially avoiding bias from data at r = a.
• Applying a finite-volume scheme with step-scaling to control systematic errors and ensure reliable matching at high scales.
• Constraining higher-order perturbative uncertainties through error propagation and sensitivity analyses, including O(a4) and logarithmic corrections.

Experimental results

Research questions

• RQ1 Can the validity range of perturbative QCD predictions for the static potential be extended to lower energy scales by removing renormalon ambiguities via OPE with renormalon subtraction?
• RQ2 How accurately can αs be determined by matching the improved theoretical prediction to lattice QCD data at distances as small as r ≲ 0.05 fm?
• RQ3 To what extent do higher-order perturbative corrections and discretization effects dominate the uncertainty in the αs determination?
• RQ4 Can the OPE framework with renormalon subtraction suppress the mixing between perturbative and nonperturbative contributions that plagues standard perturbation theory?
• RQ5 How do systematic uncertainties—such as O(a4) effects, pion mass dependence, and logarithmic corrections to the r2-term—impact the final αs result?

Key findings

• The theoretical prediction for the static QCD potential is valid at ΛMSr ≲ 0.8 (r ≲ 0.4 fm), significantly extending the reach of perturbative calculations compared to standard perturbation theory.
• The method enables matching with lattice QCD data down to ΛMSr ≈ 0.09 (r ≈ 0.05 fm), covering a much wider region than previous αs determinations from the potential.
• The final determination yields αs(M2Z) = 0.1179+0.0015−0.0014 with a relative accuracy of 1.3%, dominated by higher-order perturbative uncertainties.
• The dominant uncertainty arises from higher-order corrections in the perturbative prediction, which can be reduced by simulating with finer lattice spacings.
• Systematic errors from O(a4) effects, pion mass dependence, and logarithmic corrections to the r2-term are found to be small and do not significantly affect the result, with variations in αs less than 0.0003.
• The analysis confirms that data at r = a introduce strong discretization artifacts and should be excluded from continuum extrapolations to avoid bias.