Electron-Positron Annihilation into Four Jets at Next-to-Leading Order in $α_s$

Abstract

We calculate the rate for $e^+e^-$ annihilation into four jets at next-to-leading order in perturbative QCD, but omitting terms that are suppressed by one or more powers of $1/\Nc^2$, where $\Nc$ is the number of colors. The $\cO(α_s^3)$ corrections depend strongly on the jet resolution parameter $\ycut$ and on the clustering and recombination schemes, and they substantially improve the agreement between theory and data.

Figures (3)

• Figure 1: (a) Example of a leading-in-$N_c$ one-loop diagram for $e^+e^-\rightarrow q\bar{q} gg$. (b) A subleading one-loop diagram (omitted). (c) Sample tree diagram for $e^+e^-\rightarrow q\bar{q} ggg$. (d) Sample tree diagram for $e^+e^-\rightarrow q\bar{q} q'\bar{q}' g$.
• Figure 2: The four-jet fraction $R_4$ in $e^+e^-$ annihilation, as a function of $y_{\rm cut}$. Solid (dashed) lines represent the one-loop (tree-level) predictions in the (a) JADE, (b) E0, (c) Durham, and (d) Geneva algorithms, for $\mu=\sqrt{s}$ and $\alpha_s = 0.118$. The data points in (a) are from DELPHI LEPdata (uncorrected for hadronization), while (b), (c) and (d) contain preliminary SLD data SLDdata (corrected for hadronization).
• Figure 3: Solid (dashed) lines show the dependence of $R_4$ on the renormalization scale $\mu$ for the one-loop (tree-level) predictions in the (a) Durham, and (b) Geneva algorithms, for $\alpha_s = 0.118$ and $y_{\rm cut} = 0.03$.