Measurement of event shapes in deep inelastic scattering at HERA

TL;DR

This work measures multiple event-shape observables in the current region of the Breit frame for DIS at HERA, using 45.0 pb^-1 of ZEUS data. It tests perturbative QCD with Dokshitzer-Webber power corrections by fitting NLO predictions to the Q-dependence of the means, extracting $ ext{α}_s(M_Z)$ and $ar{ ext{α}}_0$ under several model assumptions. While the power-correction framework describes several observables consistently, others show significant inconsistencies, and the extraction of a universal $ ext{α}_s$ is not achieved. The results emphasize the role of higher-order effects and model dependencies in DIS event shapes and highlight agreement with H1 and partial compatibility with $e^+e^-$ data, conditional on theoretical uncertainties. Overall, the study demonstrates both the utility and limitations of power corrections in DIS for QCD precision studies.

Abstract

Inclusive event-shape variables have been measured in the current region of the Breit frame for neutral current deep inelastic ep scattering using an integrated luminosity of 45.0 pb^-1 collected with the ZEUS detector at HERA. The variables studied included thrust, jet broadening and invariant jet mass. The kinematic range covered was 10 < Q^2 < 20,480 GeV^2 and 6.10^-4 < x < 0.6, where Q^2 is the virtuality of the exchanged boson and x is the Bjorken variable. The Q dependence of the shape variables has been used in conjunction with NLO perturbative calculations and the Dokshitzer-Webber non-perturbative corrections (`power corrections') to investigate the validity of this approach.

Figures (6)

• Figure 1: Comparison of the mean event-shape parameters (solid points) with ARIADNE and HERWIG predictions. The plots refer to a) thrust with respect to the thrust axis, b) jet broadening with respect to the thrust axis, c) invariant jet-mass squared, d) $C$-parameter, e) thrust with respect to the virtual photon axis, f) broadening with respect to the virtual photon axis. The data were corrected using ARIADNE. The inner error bars are statistical; the outer are statistical plus systematic added in quadrature. The open squares are H1 data, with statistical uncertainties which are in most cases covered by the symbol. In e) and f), where the $x$ variation is biggest, smoothed curves are drawn through the MC points for all $x$$(Q^2 > 320 {\,\text{Ge}\text{V}}^2)$ and low $x$$(Q^2 < 320 {\,\text{Ge}\text{V}}^2)$, and separately through the high-$x$ MC points $(Q^2 < 320 {\,\text{Ge}\text{V}}^2)$. A value of $\mathcal{E}_{lim}=0.1 Q$ was used.
• Figure 2: Fits to mean values of the shape variables versus $Q$, with $\mathcal{E}_{lim} = 0.25Q$. Plots a) - f) are defined in the caption to Fig. \ref{['fig:1']}. The lines join the fit values at the $Q$ values of the data: the solid line is the fitted NLO prediction from DISASTER++ plus the power correction, while the dashed line is the fitted DISASTER++ contribution alone. 'High $x$' and 'low $x$' refer to the subdivisions as defined in Table 1; 'all $x$' refers to the points with $Q > 20 {\,\text{Ge}\text{V}},$ which are not subdivided in $x$.
• Figure 3: Contour plots for the parameters $\alpha_{s}(M_Z)$ and $\overline{\alpha_{0}}$ fitted to the mean values of thrust and broadening measured with respect to the photon axis, jet-mass squared, $C$-parameter, and thrust and broadening measured with respect to the thrust axis. Results are shown for fits, using all data points for $Q^2> 80{\,\text{Ge}\text{V}}^2$, based on DISASTER++ and DISENT with $\mathcal{E}_{lim}=0.25 Q$. The contours show the one-standard-deviation limits determined using statistical uncertainties only.
• Figure 4: Contour plots for $\alpha_{s}(M_Z)$ and $\overline{\alpha_{0}}$ fitted to the mean values of the event-shape variables. The fits are based on DISASTER++, with $\mathcal{E}_{lim}=0.25 Q$. The contours show the one-standard-deviation limits determined using statistical uncertainties only. The high-$x$ and low-$x$ selections are as defined in Table 1, while 'all data' uses all measured bins for $Q^2 > 80{\,\text{Ge}\text{V}}^2$.
• Figure 5: Contour plots for $\alpha_{s}(M_Z)$ and $\overline{\alpha_{0}}$ fitted to the mean values of the event-shape variables. The fits are based on DISENT, using all data for $Q^2> 80{\,\text{Ge}\text{V}}^2$, with energy cuts $\mathcal{E}_{lim}=0.1 Q$ (open squares) and $0.25 Q$ (filled circles). The contours show the one-standard-deviation limits determined using statistical uncertainties only. The rectangles enclose the associated pairs of points to guide the eye.