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The Realistic Lattice Determination of alpha_s(M_Z) Revisited

K. Maltman, D. Leinweber, P. Moran, A. Sternbeck

TL;DR

The paper revisits the lattice determination of $\alpha_s(M_Z)$ by perturbative analysis of short-distance-sensitive Wilson-loop observables, incorporating new high-scale lattice data and adopting a modified implementation using $\alpha_T$ to reduce perturbative uncertainties. It demonstrates improved consistency across high- and low-scale observables with final $\alpha_s(M_Z) = 0.1192(11)$, in good agreement with recent non-lattice determinations and HPQCD re-analyses. The study discusses the relationship between the HPQCD-style re-analyses and its own approach, highlighting how truncation and nonperturbative corrections are managed. The results bolster confidence in lattice-based extractions of $\alpha_s(M_Z)$ and help reconcile discrepancies among determinations from different methods.

Abstract

We revisit the earlier determination of alpha_s(M_Z) via perturbative analyses of short-distance-sensitive lattice observables, incorporating new lattice data and performing a modified version of the original analysis. We focus on two high-intrinsic-scale observables, log(W_11) and log(W_12), and one lower-intrinsic scale observable, log(W_{12}/u_0^6), finding improved consistency among the values extracted using the different observables and a final result, alpha_s(M_Z)=0.1192(11), 2 sigma higher than the earlier result, in excellent agreement with recent non-lattice determinations and, in addition, in good agreement with the results of a similar, but not identical, re-analysis by the HPQCD Collaboration. A discussion of the relation between the two re-analyses is given, focussing on the complementary aspects of the two approaches.

The Realistic Lattice Determination of alpha_s(M_Z) Revisited

TL;DR

The paper revisits the lattice determination of by perturbative analysis of short-distance-sensitive Wilson-loop observables, incorporating new high-scale lattice data and adopting a modified implementation using to reduce perturbative uncertainties. It demonstrates improved consistency across high- and low-scale observables with final , in good agreement with recent non-lattice determinations and HPQCD re-analyses. The study discusses the relationship between the HPQCD-style re-analyses and its own approach, highlighting how truncation and nonperturbative corrections are managed. The results bolster confidence in lattice-based extractions of and help reconcile discrepancies among determinations from different methods.

Abstract

We revisit the earlier determination of alpha_s(M_Z) via perturbative analyses of short-distance-sensitive lattice observables, incorporating new lattice data and performing a modified version of the original analysis. We focus on two high-intrinsic-scale observables, log(W_11) and log(W_12), and one lower-intrinsic scale observable, log(W_{12}/u_0^6), finding improved consistency among the values extracted using the different observables and a final result, alpha_s(M_Z)=0.1192(11), 2 sigma higher than the earlier result, in excellent agreement with recent non-lattice determinations and, in addition, in good agreement with the results of a similar, but not identical, re-analysis by the HPQCD Collaboration. A discussion of the relation between the two re-analyses is given, focussing on the complementary aspects of the two approaches.

Paper Structure

This paper contains 8 sections, 6 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The lattice determination of $\alpha_s(M_Z)$
  3. The original HPQCD/UKQCD analysis
  4. An alternate implementation of the HPQCD/UKQCD approach
  5. More on the relation between the two implementations
  6. Details of our re-analysis
  7. Results
  8. More on the relation to the HPQCD re-analysis

Figures (2)

  • Figure 1: Contributions to the errors on $\alpha_s(M_Z)$. Shown are the $\alpha_s(M_Z)$ obtained using (i) the 3-fold fit strategy, with all central input, (ii) the alternate 5-fold fit strategy, with all central input, and (iii) the 3-fold fit strategy, with, one at a time, each input shifted from its central value by $1\sigma$, retaining central values for the remaining input parameters. The error bars shown are those associated with the uncertainties in $r_1/a$.
  • Figure 2: Comparison of the results for $\alpha_s(M_Z)$ from our fits, the fits of Ref. latticealphas and the updated fits of Ref. hpqcd08 with the average of recent non-lattice determinations.