A study of the energy evolution of event shape distributions and their means with the DELPHI detector at LEP

TL;DR

The paper investigates how infrared- and collinear-safe event shape distributions and their means evolve with energy in e+e- annihilation across 45–202 GeV. It simultaneously tests two frameworks: (i) analytic power corrections, including hadron-mass effects, to extract alpha_s and nonperturbative parameters, and (ii) renormalisation group invariant (RGI) perturbation theory to describe mean values without sizeable power terms and to measure the QCD beta-function. The authors extract beta_0 ≈ 7.86 ± 0.32 (n_f ≈ 4.75 ± 0.44) and show that the full logarithmic energy slope excludes light gluinos below 5 GeV, while RGI fits yield a precise, scheme-independent alpha_s around 0.118–0.120 with good cross-observable consistency. Overall, the study demonstrates that RGI perturbation theory provides a compelling description of event-shape means and enables a robust determination of the QCD beta function, with implications for beyond-Standard-Model particles such as light gluinos.

Abstract

Infrared and collinear safe event shape distributions and their mean values are determined in e+e- collisions at centre-of-mass energies between 45 and 202 GeV. A phenomenological analysis based on power correction models including hadron mass effects for both differential distributions and mean values is presented. Using power corrections, alpha_s is extracted from the mean values and shapes. In an alternative approach, renormalisation group invariance (RGI) is used as an explicit constraint, leading to a consistent description of mean values without the need for sizeable power corrections. The QCD beta-function is precisely measured using this approach. From the DELPHI data on Thrust, including data from low energy experiments, one finds beta_0 = 7.86 +/- 0.32 for the one loop coefficient of the beta-function or, assuming QCD, n_f = 4.75 +/- 0.44 for the number of active flavours. These values agree well with the QCD expectation of beta_0=7.67 and n_f=5. A direct measurement of the full logarithmic energy slope excludes light gluinos with a mass below 5 GeV.

Figures (17)

• Figure 1: Left: Reconstructed centre-of-mass energy for accepted data before $\sqrt{s^{\prime}}$ cut compared to QCD and four-fermion simulation. Right: Simulation of four-fermion background and QCD events in the $N_{\mathrm{ch}}$--$B_{\mathrm{min}}$ plane. The upper two plots show the distributions for semi--leptonic and fully hadronic WW events, respectively. The lines indicate the cut values chosen.
• Figure 2: The energy distribution of the photon in the selected isolated photon events. The three classes (0,1,2) correspond to a mean centre-of-mass energy of 76, 66 and 45GeexV, respectively. The steps between the classes result from different $\pi^0$ rejection cuts.
• Figure 3: Corrections due to mass effects: The full line shows the relative change of the distribution of the observable due to a change into the E-scheme as a function of the energy. The dashed line shows the b--mass correction applied to the data.
• Figure 4: Distributions of the observable Major for centre-of-mass energies of 45, 66, 76 and 91.2GeexV compared to predictions of Jetset and Ariadne. In each plot the upper chart shows the size of the detector correction, defined as $\frac{MC_{\mathrm{gen}}}{MC_{\mathrm{acc}}}$. The grey area indicates the distribution of non-radiative background events which has been subtracted.
• Figure 5: Distributions of the observable Major for centre-of-mass energies of 189, 192, 200 and 202GeexV compared to predictions of Jetset and Ariadne. In each plot the upper chart shows the size of the detector correction, defined as $\frac{MC_{\mathrm{gen}}}{MC_{\mathrm{acc}}}$. The grey area indicates the distribution of WW and ZZ background events which has been subtracted.