Unbinned measurement of thrust in $e^+e^-$ collisions at $\sqrt{s}$ = 91.2 GeV with ALEPH archived data
The strong coupling constant ($\alpha_{S}$) is a fundamental parameter of quantum chromodynamics (QCD), the theory of the strong force. Some of the earliest precise constraints on $\alpha_{S}$ 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 $\alpha_{S}$ 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 $\tau=1-T$, and the potential implications of this shift for $\alpha_{S}$ extractions are illustrated by comparing to state-of-the-art theoretical calculations. In addition, the region of $-6<\log\tau<-2$, where poorly-understood non-perturbative effects are large, is compared to modern parton shower Monte Carlo simulations. This measurement provides unique new inputs for $\alpha_{S}$ extractions and also improves constraints on phenomenological models of QCD dynamics such as parton fragmentation and hadronization.