Analysis note: measurement of thrust and track energy-energy correlator in $e^+e^-$ collisions at 91.2 GeV with DELPHI open data

TL;DR

This paper demonstrates a precision QCD study using DELPHI open data at $\sqrt{s}=91.2~\mathrm{GeV}$ by measuring thrust and track-based EEC with unprecedented angular resolution. The analysis employs a rigorous two-dimensional unfolding in angle and energy weight, full covariance propagation, and extensive systematic studies to produce fully corrected distributions that can be compared to modern MC generators and analytic predictions. The results show good agreement with contemporary MC models in many regions, extend the angular reach relative to previous measurements, and provide a robust benchmark for future LEP data analyses, including cross-checks with an ALEPH re-analysis. By making the data and software openly accessible, this work paves the way for re-interpretations, precision extractions of $\alpha_s$, and enhanced tests of hadronization in both collinear and back-to-back QCD regimes, with implications for future $e^{+}e^{-}$ colliders.

Abstract

Recent theoretical developments, as well as experimental measurements at hadron collisions, have renewed interest in studying event shape variables in $e^+e^-$ collisions. We present a measurement of thrust and track-based energy-energy correlator in $e^+e^-$ collisions at center-of-mass energy of 91.2 GeV, using newly released open data from the DELPHI experiment. The event shapes, measured with unprecedented resolution and precision, are compared to various Monte Carlo and analytic predictions. Leveraging DELPHI's unique detector geometry and reconstruction capabilities, the track energy-energy correlator measurement provides data with the highest angular resolution, offering critical inputs for precision tests of QCD in both collinear and back-to-back limits. This note presents the first physics analysis using DELPHI open data and establishes benchmarks necessary for future studies exploiting this legacy dataset.

Figures (85)

• Figure 1: Example distributions of the EEC as a function of $\theta_{\rm L}$ (top) and $z$ (bottom) using a "flipped double-log style" as described in the main text. The various regions of the distribution are marked for illustration purposes, where the green represents the free hadron (or soft emission) region, the blue represents the quark/gluon region, and the gray represents the transition between these two regions. The collinear region (where $\theta_{\rm L}\sim 0$ and $z \sim 0$) and the back-to-back or Sudakov region (where $\theta_{\rm L}\sim\pi$ and $z \sim 1$) is also marked.
• Figure 2: Example distribution of thrust (left) and $\log \tau$ (right). The thrust distribution clearly separates two distinct QCD regimes: the perturbative multi-jet region at lower thrust values (light blue), characterized by a broad distribution from isotropic particle production, and the non-perturbative dijet region (light green) at high thrust values near unity. The sharp dijet peak located just below the thrust maximum results from Sudakov form factor suppression, which represents the probability of no additional parton emission. This suppression makes perfect two-jet configurations less probable, creating the characteristic peaked structure. The $\log \tau$ parameterization provides an enhanced view of the non-perturbative region by expanding the logarithmic scale, offering detailed resolution of the peak structure that complements the linear thrust binning.
• Figure 3: Schematic of the DELPHI detector.
• Figure 4: Comparisons of track $p_{\rm T}$, $\theta$, and $\phi$ in 1994 data (black), reconstructed PYTHIA 5.7/JETSET 7.4 (red), ARIADNE (green), PYTHIA 8.3 (orange), and PYTHIA 8.3 Dire (brown) samples. Note that the corresponding number of selected events of each sample normalizes the distributions.
• Figure 5: Comparisons of track $p_{\rm T}$, $\theta$, and $\phi$ in 1995 data (black), reconstructed PYTHIA 5.7/JETSET 7.4 (red), ARIADNE (green), PYTHIA 8.3 (orange), and PYTHIA 8.3 Dire (brown) samples. Note that the corresponding number of selected events of each sample normalizes the distributions.