Measurement of Event Shape Variables in Deep-Inelastic Scattering at HERA

TL;DR

This study analyzes hadronic final states in deep-inelastic $ep$ scattering at HERA using event shape observables to probe perturbative and non-perturbative QCD. By combining resummed NLL pQCD with analytic power corrections parameterised by a universal $\alpha_0$, the authors extract $\alpha_s(m_Z)$ and test hadronisation universality across multiple observables. The data show clear evidence of the running of $\alpha_s(Q)$ and yield a universal $\alpha_0$ around 0.5, consistent with the power correction framework. The combined analysis gives $\alpha_s(m_Z)=0.1198^{+0.0013}_{-0.0043}$ (exp) $^{+0.0056}_{-0.0043}$ (theo) and $\alpha_0=0.476^{+0.018}_{-0.059}$ (theo), with running confirmed over $Q=15$–116 GeV. Mean-value fits are less precise, indicating areas for theoretical improvement or resummation in the mean-value approach.

Abstract

Deep-inelastic ep scattering data taken with the H1 detector at HERA and corresponding to an integrated luminosity of 106 pb^{-1} are used to study the differential distributions of event shape variables. These include thrust, jet broadening, jet mass and the C-parameter. The four-momentum transfer Q is taken to be the relevant energy scale and ranges between 14 GeV and 200 GeV. The event shape distributions are compared with perturbative QCD predictions, which include resummed contributions and analytical power law corrections, the latter accounting for non-perturbative hadronisation effects. The data clearly exhibit the running of the strong coupling alpha_s(Q) and are consistent with a universal power correction parameter alpha_0 for all event shape variables. A combined QCD fit using all event shape variables yields alpha_s(mZ) = 0.1198 \pm 0.0013 ^{+0.0056}_{-0.0043} and alpha_0 = 0.476 \pm 0.008 ^{+0.018} _{-0.059}.

Figures (7)

• Figure 1: Normalised event shape distributions corrected to the hadron level for $\tau_C$, $\tau$ and $B$. The data are presented with statistical errors (inner bars) and total errors (outer bars). The measurements are compared with fits based on a NLO QCD calculation including resummation (NLL) and supplemented by power corrections (PC). The fit results are shown as solid lines and are extended as dashed lines to those data points which are not included in the QCD fit (see Section \ref{['fitstospectra']}).
• Figure 2: Normalised event shape distributions corrected to the hadron level for $\rho_0$ and the $C$-parameter. The data are presented with statistical errors (inner bars) and total errors (outer bars). The measurements are compared with fits based on a NLO QCD calculation including resummation (NLL) and supplemented by power corrections (PC). The fit results are shown as solid lines and are extended as dashed lines to those data points which are not included in the QCD fit (see Section \ref{['fitstospectra']}). The symbols and scale factors are defined in Fig. \ref{['figureshapesdistributions1']}.
• Figure 3: Mean values of event shape variables corrected to the hadron level as a function of the scale $Q$. The data, presented with statistical errors (inner bars) and total errors (outer bars), are compared with the results of NLO QCD fits including power corrections (PC). The dashed curves show the NLO QCD contribution to the fits.
• Figure 4: Fit results to the differential distributions of $\tau$, $B$, $\rho_0$, $\tau_C$ and the $C$-parameter in the $(\alpha_s,\alpha_0)$ plane. The $1\sigma$ contours correspond to $\chi^2 = \chi^2_{\rm min}+1$, including statistical and experimental systematic uncertainties. The value of $\alpha_s$ (vertical line) and its uncertainty (shaded band) are taken from Bethke:2004uy.
• Figure 5: The strong coupling $\alpha_s$ as a function of the scale $Q$. The individual fit results, shown as points with error bars, are obtained from fits to the differential distributions in $\tau_C$, $\tau$, $B$, $\rho_0$ and $C$ within each $Q$ bin. The errors represent the total experimental uncertainties. For each event shape observable a value of $\alpha_s(m_Z)$ is indicated in the plot, determined from a fit to the $\alpha_s(Q)$ results using the QCD renormalisation group equation. The corresponding fit curves are shown as full lines. The shaded bands represent the uncertainties on $\alpha_s(Q)$ from renormalisation scale variations.