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QCD Studies at LEP

Siegfried Bethke

TL;DR

The paper comprehensively reviews LEP-era tests of QCD using hadronic $e^+e^-$ final states, highlighting perturbative calculations, jet and event-shape analyses, and hadronisation models. It synthesizes determinations of $\alpha_s$ from EW precision data, tau decays, and event shapes, with a global LEP value around $\alpha_s(M_Z)\approx0.12$ and substantial cross-checks across methods. The review also reports on color-factor measurements, quark vs gluon jet differences, heavy-quark dynamics (gluon splitting and running $m_b$), and two-photon hadronic processes, collectively validating QCD's non-Abelian structure and its predictions for running couplings and masses. It concludes with prospects for NNLO calculations to further sharpen LEP’s legacy as a precision testbed of strong interaction physics.

Abstract

Studies of hadronic final states of $e^+e^-$ annihilations at LEP are reviewed. The topics included cover hadronic event shapes, measurements of $α_s$, determinations of QCD colour factors and tests of the non-Abelian gauge structure of QCD, differences between quark and gluon jets, QCD with heavy quarks and selected results of two-photon scattering processes.

QCD Studies at LEP

TL;DR

The paper comprehensively reviews LEP-era tests of QCD using hadronic final states, highlighting perturbative calculations, jet and event-shape analyses, and hadronisation models. It synthesizes determinations of from EW precision data, tau decays, and event shapes, with a global LEP value around and substantial cross-checks across methods. The review also reports on color-factor measurements, quark vs gluon jet differences, heavy-quark dynamics (gluon splitting and running ), and two-photon hadronic processes, collectively validating QCD's non-Abelian structure and its predictions for running couplings and masses. It concludes with prospects for NNLO calculations to further sharpen LEP’s legacy as a precision testbed of strong interaction physics.

Abstract

Studies of hadronic final states of annihilations at LEP are reviewed. The topics included cover hadronic event shapes, measurements of , determinations of QCD colour factors and tests of the non-Abelian gauge structure of QCD, differences between quark and gluon jets, QCD with heavy quarks and selected results of two-photon scattering processes.

Paper Structure

This paper contains 16 sections, 14 equations, 14 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Hadronic Events at LEP
  3. Hadronic Event Shapes and Jet Production
  4. Determinations of $\alpha_{\rm s}$
  5. $\alpha_{\rm s}$ from Electroweak Precision Measurements
  6. $\alpha_{\rm s}$ from $\tau$ lepton decays
  7. $\alpha_{\rm s}$ from event shape observables
  8. Other $\alpha_{\rm s}$ results from LEP
  9. LEP summary of $\alpha_{\rm s}$
  10. Colour Factors and nonabelian gauge structure of QCD
  11. Differences between q- and g-jets
  12. QCD with Heavy Quarks
  13. Gluon splitting into $c\bar{c}$ and $b\bar{b}$ quark pairs
  14. Flavour independence of $\alpha_{\rm s}$ and Measurements of the running b-quark mass
  15. Two photon physics
  16. ...and 1 more sections

Figures (14)

  • Figure 1: Hadronic event of the type ${\rm e^+\rm e^-} \rightarrow {\rm 4\ jets}$ recorded with the ALEPH detector at LEP-I.
  • Figure 2: Relative production rates of n-jet events (n = 2 to 5) for different values of the jet resolution parameter $y_{\rm cut}$, measured at the $\rm Z^0$ resonance at LEP O-global. The data are compared to predictions of the JETSET QCD shower and hadronisation model ( hadrons). The predictions for partons, before hadronisation, are also given in order to illustrate the size of the hadronisation effect.
  • Figure 3: Measured distributions of Thrust A-new-shapes, after corrections for backgrounds and detector effects, together with fitted QCD predictions.
  • Figure 4: The combined $\alpha_{\rm s}(M_{\rm Z^0})$ obtained from diffent observables at LEP lepqcdwg2. The shaded band represents the overall combined fit for all observables. The inner error bars and the dashed band represent the statistical uncertainties.
  • Figure 5: Mean values of Thrust $T$ as a function of the c.m. energy $\sqrt{s}$. The full line shows the QCD fit including power corrections, the perturbative part of which is indicated by the dashed line fernandez.
  • ...and 9 more figures