Unbinned measurement of thrust in $e^+e^-$ collisions at $\sqrt{s}$ = 91.2 GeV with ALEPH archived data

TL;DR

The paper addresses tensions in extractions of the strong coupling constant $\alpha_S$ from event-shape observables in $e^+e^-$ collisions by reanalyzing archived ALEPH data at $\sqrt{s}=91.2$ GeV with an unbinned unfolding of the thrust proxy $\tau=1-T$ using OmniFold. The approach applies neural-likelihood estimation and sequential reweighting to correct detector effects, enabling high-resolution comparisons to state-of-the-art perturbative plus non-perturbative QCD calculations and to modern parton shower models. A small systematic shift toward larger $\tau$ values is observed, which could imply a larger $\alpha_S(m_Z)$ when fitted to theory; the fine $\log\tau$ binning reveals enhanced sensitivity to non-perturbative effects in the dijet core and discriminates among hadronization/showering models. The results provide new inputs for $\alpha_S$ extractions, tighter constraints on non-perturbative shape functions, and demonstrate a successful ML-based unbinned unfolding framework for legacy $e^+e^-$ data, with data and analysis code publicly released.

Abstract

The strong coupling constant ($α_{S}$) is a fundamental parameter of quantum chromodynamics (QCD), the theory of the strong force. Some of the earliest precise constraints on $α_{S}$ came from measurements of event shape observables, such as thrust ($T$), using hadronic $Z$ boson decays produced in $e^+e^-$ collisions. However, recent work has revealed discrepancies between event-shape-based extractions of $α_{S}$ and values determined using other experimental methods. This work reexamines archived $e^+e^-$ data collected at a collision energy of $\sqrt{s}=91.2$ GeV by the ALEPH detector at the Large Electron-Positron Collider. Modern machine learning techniques are used to correct for detector effects in an unbinned manner, allowing the $T$ distribution to be measured with higher granularity than previous ALEPH measurements. The new measurement reveals a small but systematic shift towards larger values of $τ=1-T$, and the potential implications of this shift for $α_{S}$ extractions are illustrated by comparing to state-of-the-art theoretical calculations. In addition, the region of $-6<\logτ<-2$, where poorly-understood non-perturbative effects are large, is compared to modern parton shower Monte Carlo simulations. This measurement provides unique new inputs for $α_{S}$ extractions and also improves constraints on phenomenological models of QCD dynamics such as parton fragmentation and hadronization.

Figures (7)

• Figure 1: Unfolded thrust distribution with OmniFold (black) and Iterative Bayesian Unfolding (blue) using a binning consistent with the previous ALEPH publication (orange). The lower panels show the ratio to the OmniFold measurement and comparisons of the total, statistical, experimental, and theoretical uncertainties.
• Figure 2: Unfolded thrust distribution (black) in the tail region, compared with theoretical predictions varying $\alpha_{S}(m_{Z})$ and $\Omega_{1}^{R}$. The unbinned measurement is re-binned to the bin centers provided of the theoretical predictions. The global fit (red) shown reflects the best theory description of existing thrust data, excluding the measurement presented here.
• Figure 3: Unfolded thrust distribution (black) in the dijet peak region in fine $\log\tau$ bins to highlight the sensitivity to non-perturbative effects in comparison to the logarithm of the previous ALEPH thrust publication (orange). Shown are comparisons to Pythia 8.230 with the Lund string hadronization model and $p_{\mathrm{T}}$ ordered dipole shower (gray), identical Pythia 8.230 except with hadronization disabled (red), Herwig 7.1.5 with the cluster hadronization model and angular-ordered shower (purple), and Sherpa 2.2.6 with the Lund string hadronization model (via Pythia) and the dipole shower (green).
• Figure 4: Uncertainty breakdown for the fully corrected $\tau$ distribution, unfolded with Iterative Bayesian Unfolding in the previous ALEPH publication binning: (top) statistical, (middle) experimental, and (bottom) MC prior theoretical uncertainties.
• Figure 5: Uncertainty breakdown for the fully corrected $\tau$ distribution, unfolded with OmniFold and partitioned in the previous ALEPH publication binning: (top) statistical, (middle) experimental, and (bottom) MC prior theoretical uncertainties.