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World Summary of $α_s$ (2012)

Siegfried Bethke

TL;DR

The paper presents a consolidated, high-precision world average for $α_s$ at the $M_Z$ scale by forming per-field pre-averages of NNLO+ QCD determinations and then combining them with a correlated error framework. It confirms the running of $α_s$ consistent with QCD and asymptotic freedom, yielding $α_s(M_Z) = 0.1184 ± 0.0007$, unchanged from the 2009 value, and provides associated $Λ_{ extoverline{MS}}$ values. The analysis highlights tensions among some DIS and $e^+e^-$ extractions but shows overall stability of the global average, with lattice calculations driving the total precision. These results supply a standardized input for high-precision QCD phenomenology and tests of the Standard Model.

Abstract

Determinations of the strong coupling strength, $α_s$, are summarised and a new world average value of $α_s (M_Z)$ is determined, using a new method of pre-averaging results within classes of measurements like hadronic $τ$ decays, deep inelastic scattering processes, lattice calculations, electron-positron annihilation processes and electro-weak precision fits. The overall result is $$α_s (M_Z) = 0.1184 \pm 0.0007,$$ unchanged from the value obtained in 2009. This presentation is an excerpt from the QCD review section of the 2012 Review of Particle Physics (RPP) of the Particle Data Group.

World Summary of $α_s$ (2012)

TL;DR

The paper presents a consolidated, high-precision world average for at the scale by forming per-field pre-averages of NNLO+ QCD determinations and then combining them with a correlated error framework. It confirms the running of consistent with QCD and asymptotic freedom, yielding , unchanged from the 2009 value, and provides associated values. The analysis highlights tensions among some DIS and extractions but shows overall stability of the global average, with lattice calculations driving the total precision. These results supply a standardized input for high-precision QCD phenomenology and tests of the Standard Model.

Abstract

Determinations of the strong coupling strength, , are summarised and a new world average value of is determined, using a new method of pre-averaging results within classes of measurements like hadronic decays, deep inelastic scattering processes, lattice calculations, electron-positron annihilation processes and electro-weak precision fits. The overall result is unchanged from the value obtained in 2009. This presentation is an excerpt from the QCD review section of the 2012 Review of Particle Physics (RPP) of the Particle Data Group.

Paper Structure

This paper contains 10 sections, 7 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Selected results
  3. Hadronic $\tau$ decays
  4. Lattice QCD
  5. Deep inelastic lepton-nucleon scattering (DIS)
  6. Heavy quarkonia decays
  7. Hadronic final states of $e^+e^-$ annihilations
  8. Hadron collider jets
  9. Electroweak precision fits
  10. Determination of the world average value of $\alpha_{\rm s}(M_{\rm Z})$

Figures (3)

  • Figure 1: Summary of determinations of $\alpha_s$ from hadronic $\tau$-decays (a), from lattice calculations (b), from DIS structure functions (c) and from event shapes and jet production in $e^+e^-$-annihilation (d). The shaded bands indicate the average values chosen to be included in the determination of the new world average of $\alpha_s$. Figure taken from pdg2012.
  • Figure 2: Summary of values of $\alpha_{\rm s}(M_{\rm Z}))$ obtained for various sub-classes of measurements (see Fig. \ref{['fig:pre-averages']} (a) to (d)). The new central and world average value of $\alpha_{\rm s}(M_{\rm Z}) = 0.1184 \pm 0.0007$ is indicated by the dashed line and the shaded band. Figure taken from pdg2012.
  • Figure 3: Summary of measurements of $\alpha_s$ as a function of the respective energy scale $Q$. The respective degree of QCD perturbation theory used in the extraction of $\alpha_s$ is indicated in brackets (NLO: next-to-leading order; NNLO: next-to-next-to leading order; res. NNLO: NNLO matched with resummed next-to-leading logs; N$^3$LO: next-to-NNLO). Figure taken from pdg2012.