Jet algorithms in electron-positron annihilation: Perturbative higher order predictions

TL;DR

This work comprehensively compares eight jet algorithms in electron-positron annihilation within perturbative QCD, delivering high-order predictions (NNNLO for 2-jet, NNLO for 3-jet, NLO for 4-jet, LO for 5-jet) and examining both exclusive and inclusive schemes. By employing Mercutio2, it provides detailed coefficients and fine-bin results for the jet rates as functions of the jet-resolution parameter y_cut, and discusses the interplay between fixed-order calculations and resummation necessities at small y_cut. The study highlights the distinct behavior of inclusive algorithms due to soft cuts like E_min, and includes an erratum noting corrections to the four-jet rates after identifying a bug in the numerical implementation. Overall, the results serve as a precise baseline for alpha_s extractions from multi-jet events and offer valuable insights into the performance of infrared-safe jet algorithms, with implications for LHC analyses using inclusive jet definitions.

Abstract

This article gives results on several jet algorithms in electron-positron annihilation: Considered are the exclusive sequential recombination algorithms Durham, Geneva, Jade-E0 and Cambridge, which are typically used in electron-positron annihilation. In addition also inclusive jet algorithms are studied. Results are provided for the inclusive sequential recombination algorithms Durham, Aachen and anti-kt, as well as the infrared-safe cone algorithm SISCone. The results are obtained in perturbative QCD and are NNNLO for the two-jet rates, NNLO for the three-jet rates, NLO for the four-jet rates and LO for the five-jet rates.

Figures (8)

• Figure 1: The upper plot shows the jet rates for the Durham algorithm at order $\alpha_s^3$. The lower plot shows the three-jet rate for the Durham algorithm at LO, NLO and NNLO. All plots are done with $\sqrt{Q^2}=m_Z$ and $\alpha_s(m_Z)=0.118$. The bands give the range for the theoretical prediction obtained from varying the renormalisation scale from $\mu=m_Z/2$ to $\mu=2 m_Z$.
• Figure 2: The upper plot shows the jet rates for the Geneva algorithm at order $\alpha_s^3$. The lower plot shows the three-jet rate for the Geneva algorithm at LO, NLO and NNLO. All plots are done with $\sqrt{Q^2}=m_Z$ and $\alpha_s(m_Z)=0.118$. The bands give the range for the theoretical prediction obtained from varying the renormalisation scale from $\mu=m_Z/2$ to $\mu=2 m_Z$.
• Figure 3: The upper plot shows the jet rates for the Jade-E0 algorithm at order $\alpha_s^3$. The lower plot shows the three-jet rate for the Jade-E0 algorithm at LO, NLO and NNLO. All plots are done with $\sqrt{Q^2}=m_Z$ and $\alpha_s(m_Z)=0.118$. The bands give the range for the theoretical prediction obtained from varying the renormalisation scale from $\mu=m_Z/2$ to $\mu=2 m_Z$.
• Figure 4: The upper plot shows the jet rates for the Cambridge algorithm at order $\alpha_s^3$. The lower plot shows the three-jet rate for the Cambridge algorithm at LO, NLO and NNLO. All plots are done with $\sqrt{Q^2}=m_Z$ and $\alpha_s(m_Z)=0.118$. The bands give the range for the theoretical prediction obtained from varying the renormalisation scale from $\mu=m_Z/2$ to $\mu=2 m_Z$.
• Figure 5: The upper plot shows the jet rates for the inclusive Durham algorithm at order $\alpha_s^3$. The lower plot shows the three-jet rate for the inclusive Durham algorithm at LO, NLO and NNLO. All plots are done with $\sqrt{Q^2}=m_Z$ and $\alpha_s(m_Z)=0.118$. The bands give the range for the theoretical prediction obtained from varying the renormalisation scale from $\mu=m_Z/2$ to $\mu=2 m_Z$.